ORIGINAL_ARTICLE
Cover for Volume.13, No.2
http://ijfs.usb.ac.ir/article_2629_01f14615681aca7b51d39c6611ee7c7b.pdf
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10.22111/ijfs.2016.2629
ORIGINAL_ARTICLE
Fuzzy multi-criteria decision making method based on fuzzy structured element with incomplete weight information
The fuzzy structured element (FSE) theory is a very useful toolfor dealing with fuzzy multi-criteria decision making (MCDM)problems by transforming the criterion value vectors of eachalternative into the corresponding criterion function vectors. Inthis paper, some concepts related to function vectors are firstdefined, such as the inner product of two function vectors, thecosine of the included angle between two function vectors and theprojection of a function vector on another. Then a method based onFSE is developed to solve fuzzy MCDM problems in which thecriterion values take the form of general bounded closed fuzzynumbers and the criterion weight information is incompletecertain. In this method, the projections of criterion functionvectors on the fuzzy ideal function point (FIFP) are used to rankall the alternatives and then select the most desirable one, andan optimization model is constructed to determine the weights ofcriteria according to the incomplete weight information. Finally,an example is given to illustrate the feasibility andeffectiveness of the developed method.
http://ijfs.usb.ac.ir/article_2356_5a40d370d70c87597df91b924bd8af47.pdf
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17
10.22111/ijfs.2016.2356
Multi-criteria decision making (MCDM)
Fuzzy structured element (FSE)
Inner product
Projection
Entropy
Xinfan
Wang
true
1
School of Science, Hunan University of Technology, Zhuzhou, Hunan,
412007, China
School of Science, Hunan University of Technology, Zhuzhou, Hunan,
412007, China
School of Science, Hunan University of Technology, Zhuzhou, Hunan,
412007, China
AUTHOR
Jianqiang
Wang
true
2
School of Business, Central South University, Changsha, Hunan,
410083, China
School of Business, Central South University, Changsha, Hunan,
410083, China
School of Business, Central South University, Changsha, Hunan,
410083, China
LEAD_AUTHOR
Xiaohong
Chen
cxh@csu.edu.cn
true
3
School of Business, Central South University, Changsha, Hunan,
410083, China
School of Business, Central South University, Changsha, Hunan,
410083, China
School of Business, Central South University, Changsha, Hunan,
410083, China
AUTHOR
[1] T. M. Apostol, Mathematical analysis, Second Edition, China Machine Press, Beijing, 2004.
1
[2] E. Cables, M. S. Garca-Cascales and M. T. Lamata, The LTOPSIS: An alternative to TOP-
2
SIS decision-making approach for linguistic variables, Expert Systems with Applications,
3
39(2) (2012), 2119-2126.
4
[3] H. Y. Chen and L. G. Zhou, An approach to group decision making with interval fuzzy prefer-
5
ence relations based on induced generalized continuous ordered weighted averaging operator,
6
Expert Systems with Applications, 38(10) (2011), 13432-13440.
7
[4] S. J. Chen and C. L. Hwang, Fuzzy Multiple Attribute Decision Making: Methods and Ap-
8
plications, Springer-Verlag, Berlin, 1992.
9
[5] D. Dubois and H. Prade, Comment on tolerance analysis using fuzzy sets and a procedure
10
for multiple aspect decision making, International Journal of System Science, 9(3) (1978),
11
[6] D. Dubois and H. Prade, A review of fuzzy set aggregation connectives, Information Science,
12
36(1/2) (1985), 85-121.
13
[7] J. Figueira, S. Greco and M. Ehrgott, Multiple Criteria Decision Analysis: State of the Art
14
Surveys, Springer, Boston, 2005.
15
[8] J. C. Fodor and M. Roubens, Fuzzy Preference Modeling and Multicriteria Decision Support,
16
Kluwer, Dordrecht, 1994.
17
[9] S. Z. Guo, Method of structuring element in fuzzy analysis (I), Journal of Liaoning Technical
18
University, 21(5) (2002), 670-673.
19
[10] S. Z. Guo, Method of structuring element in fuzzy analysis (II), Journal of Liaoning Technical
20
University, 21(6) (2002), 808-810.
21
[11] S. Z. Guo, Principle of fuzzy mathematical analysis based on structured element, Northeastern
22
University Press, Shengyang, 2004.
23
[12] S. Z. Guo, Homeomorphic property between fuzzy number space and family of bounded mono-
24
tone function, Advances in Natural Science, 14(11) (2004), 1318-1321.
25
[13] S. Z. Guo, Transformation group of monotone functions with same monotonic formal on [-1,
26
1] and operations of fuzzy numbers, Fuzzy Systems and Mathematics, 19(3) (2005), 105-110.
27
[14] S. Z. Guo, Commonly express method of fuzzy-valued function based on structured element,
28
Fuzzy Systems and Mathematics, 19(1) (2005), 82-86.
29
[15] S. Z. Guo, Comparison and sequencing of fuzzy numbers based on the method of structured
30
element, Systems Engineering-Theory and Practice, 29(3) (2009), 106-111.
31
[16] G. Jahanshahloo, F. Lot and M. Izadikhah, Extension of the TOPSIS method for decision-
32
making problems with fuzzy data, Applied Mathematics and Computation, 181(2) (2006),
33
1544-1551.
34
[17] E. Jaynes, Information theory and statistical mechanics, Physical Reviews, 106(4) (1957),
35
[18] S. H. Kim, S. H. Choi and J. K. Kim, An interactive procedure for multiple attribute group
36
decision making with incomplete information: Range-based approach, European Journal of
37
Operational Research, 118(1) (1999), 139-152.
38
[19] S. H. Kim and B. S. Ahn, Interactive group decision making procedure under incomplete
39
information, European Journal of Operational Research, 116(3) (1999), 498-507.
40
[20] D. F. Li, Fuzzy multi-objective many-person decision makings and games, National Defense
41
Industry Press, Beijing, 2003.
42
[21] D. F. Li, Compromise ratio method for fuzzy multi-attribute group decision making, Applied
43
Soft Computing, 7(3) (2007), 807-817.
44
[22] R. J. Li, Theory and application of fuzzy multiple criteria decision making, Science Press,
45
Beijing, 2002.
46
[23] J. Lin, Fuzzy multi-attribute decision-making method based on Hausdau distance, Journal
47
of Systems Engineering, 22(4) (2007), 367 -372.
48
[24] T. S. Liou and M. J. Wang, Fuzzy weighted average: an improved algorithm, Fuzzy Sets and
49
Systems, 49(1) (1992), 307-315.
50
[25] H. T. Liu and S. Z. Guo, Fuzzy multi-attribute group decision making methods based on
51
structured element, Pattern Recognition and Articial Intelligence, 20(3) (2007), 343-348.
52
[26] H. T. Liu and S. Z. Guo, Fuzzy linear programming with fuzzy variables based on structured
53
element method, Systems Engineering-Theory and Practice, 28(6) (2008), 94-100.
54
[27] H. T. Liu and S. Z. Guo, The method of fuzzy multi-attribute decision making based on
55
structured element and information entropy, Mathematics in Practice and Theory, 39(17)
56
(2009), 1-5.
57
[28] P. D. Liu and F. Jin, A multi-attribute group decision-making method based on weighted
58
geometric aggregation operators of interval-valued trapezoidal fuzzy numbers, Applied Math-
59
ematical Modelling, 36(6) (2012), 2498-2509.
60
[29] P. D. Liu, X. Zhang and F. Jin, A multi-attribute group decision-making method based on
61
interval-valued trapezoidal fuzzy numbers hybrid harmonic averaging operators, Journal of
62
Intelligent and Fuzzy Systems, 23(5) (2012), 159-168.
63
[30] J. M. Merig, Fuzzy multi-person decision making with fuzzy probabilistic aggregation opera-
64
tors, International Journal of Fuzzy Systems, 13(3) (2011), 163-174.
65
[31] J. M. Merig and M. Casanovas, The fuzzy generalized OWA operator and its application in
66
strategic decision making, Cybernetics and Systems, 41(5) (2010), 359-370.
67
[32] J. M. Merig and A. M. Gil-Lafuente, Fuzzy induced generalized aggregation operators and
68
its application in multi-person decision making, Expert Systems with Applications, 38(8)
69
(2011), 9761-9772.
70
[33] C. Shannon, The mathematical theory of communication, The University of Illinois Press,
71
Urbana, 1949.
72
[34] L. Wang and S. Z. Guo, Linear formed fully fuzzy linear dierential systems, Systems
73
Engineering-Theory and Practice, 32(2) (2012), 341-348.
74
[35] T. C. Wang and H. D. Lee, Developing a fuzzy TOPSIS approach based on subjective weights
75
and objective weights, Expert Systems with Applications, 36(5) (2009), 8980-8985.
76
[36] G. W. Wei, GRA method for multiple attribute decision making with incomplete weight
77
information in intuitionistic fuzzy setting, Knowledge-Based Systems, 23(3) (2010), 243-
78
[37] G. W. Wei, FIOWHM operator and its application to multiple attribute group decision mak-
79
ing, Expert Systems with Applications, 38(4) (2011), 2984-2989.
80
[38] G. W. Wei, X. F. Zhao and R. Lin, Some induced aggregating operators with fuzzy number
81
intuitionistic fuzzy information and their applications to group decision making, International
82
Journal of Computational Intelligence Systems, 3(1) (2010), 84-95.
83
[39] Z. S. Xu, Method based on expected values for fuzzy multiple attribute decision making prob-
84
lems with preference informationon alternatives, Systems Engineering-Theory and Practice,
85
24(1) (2004), 109-113.
86
[40] Z. S. Xu, Fuzzy harmonic mean operators, International Journal of Intelligent Systems, 24(2)
87
(2009), 152-172.
88
[41] Z. S. Xu and Q. L. Da, Projection method for uncertain multi-attribute decision making with
89
preference information on alternatives, International Journal of Information Technology and
90
Decision Making, 3(3) (2004), 429-434.
91
[42] J. Yang and W. H. Qiu, Method for multi-attribute decision-making based on projection,
92
Control and Decision, 24(4) (2009), 637-640.
93
[43] L. Z. Yue, Y. Yan and W. Q. Zhong, Solution of matrix fuzzy game based on structuring
94
element theory, Systems Engineering-Theory and Practice, 30(2) (2010), 272-276.
95
[44] L. A. Zadeh, Fuzzy sets, Information and Control, 8(3) (1965), 338-356.
96
[45] E. K. Zavadskas and Z. Turskis, Multiple criteria decision making (MCDM) methods in eco-
97
nomics: an overview, Technological and Economic Development of Economy, 17(2) (2011),
98
[46] S. Z. Zeng, W. H. Su and A. Le, Fuzzy generalized ordered weighted averaging distance
99
operator and its application to decision making, International Journal of Fuzzy Systems,
100
14(3) (2012), 402-412.
101
[47] J. J. Zhang, D. S. Wu and D. L. Olson, The method of grey related analysis to multiple at-
102
tribute decision making problems with interval numbers, Mathematical and Computer Mod-
103
elling, 42(9) (2005), 991-998.
104
[48] Y. J. Zhang and J. X. Liu, Multi-server fuzzy queues based on fuzzy structured element,
105
Systems Engineering-Theory and Practice, 30(10) (2010), 1815-1821.
106
ORIGINAL_ARTICLE
A NEW APPROACH BASED ON OPTIMIZATION OF RATIO FOR SEASONAL FUZZY TIME SERIES
In recent years, many studies have been done on forecasting fuzzy time series. First-order fuzzy time series forecasting methods with first-order lagged variables and high-order fuzzy time series forecasting methods with consecutive lagged variables constitute the considerable part of these studies. However, these methods are not effective in forecasting fuzzy time series which contain seasonal structures. In this respect, it would be more appropriate to use methods that consider the seasonal relations in seasonal fuzzy time series forecasting. Although seasonal fuzzy time series forecasting methods exist in literature, these methods use equal interval lengths in partition of the universe of discourse. This situation incapacitates the performance of the method in forecasting time series including seasonality and trend. In this study, a new fuzzy time series forecasting method in which intervals constituting partition of the universe of discourse increase in time at a rate that obtained based on optimization was proposed. The proposed method was applied to two real time series and obtained results were compared with other methods and the superior performance of the proposed method was proved.
http://ijfs.usb.ac.ir/article_2357_6875b4f9aecc564feec951e7b3ddb660.pdf
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36
10.22111/ijfs.2016.2357
Seasonal fuzzy time series
Optimization
Forecasting
Feed forward neural networks
Ufuk
Yolcu
uyolcu@ankara.edu.tr
true
1
Department of Statistics, Faculty of Science, Ankara University, 06100
Ankara, Turkey
Department of Statistics, Faculty of Science, Ankara University, 06100
Ankara, Turkey
Department of Statistics, Faculty of Science, Ankara University, 06100
Ankara, Turkey
LEAD_AUTHOR
[1] C. H. Aladag, M. A. Basaran, E. Egrioglu, U. Yolcu and V. R. Uslu, Forecasting in high
1
order fuzzy time series by using neural networks to dene fuzzy relations, Expert Systems
2
with Applications, 36 (2009), 4228-4231.
3
[2] C. H. Aladag, U. Yolcu and E. Egrioglu, A high order fuzzy time series forecasting model
4
based on adaptive expectation and articial neural networks, Mathematics and Computers in
5
Simulation, 81 (2010), 875-882.
6
[3] C. H. Aladag, E. Egrioglu, U. Yolcu and V. R. Uslu, A high order seasonal fuzzy time series
7
model and application to international tourism demand of Turkey, Journal of Intelligent and
8
Fuzzy Systems, 26 (2014), 295-302.
9
[4] C. H. Aladag, U. Yolcu, E. Egrioglu and E. Bas, Fuzzy lagged variable selection in fuzzy time
10
series with genetic algorithms, Applied Soft Computing, 22 (2014), 465-473.
11
[5] F. Alpaslan, O. Cagcag, C. H. Aladag, U. Yolcu and E. Egrioglu, A novel seasonal fuzzy time
12
series method, Hacettepe Journal of Mathematics and Statistics, 41 (2012), 375-385.
13
[6] E. Bas, V. R. Uslu, U. Yolcu and E. Egrioglu, A modied genetic algorithm for forecasting
14
fuzzy time series, Applied Intelligence, 41 (2014), 453-463.
15
[7] G. E. P. Box and G. M. Jenkins, Time series analysis: Forecasting and control. CA: Holdan-
16
Day, San Francisco, 1976.
17
[8] O. Cagcag Yolcu, A Hybrid Fuzzy Time Series Approach Based on Fuzzy Clustering and
18
Articial Neural Network with Single Multiplicative Neuron Model, Mathematical Problems
19
in Engineering, Article ID 560472, 2013 (2013), 9 pages.
20
[9] S. M. Chen, Forecasting enrollments based on fuzzy time-series, Fuzzy Sets and Systems, 81
21
(1996), 311-31.
22
[10] S. M. Chen, Forecasting enrolments based on high order fuzzy time series, Cybernetics and
23
Systems, 33 (2002), 1-16.
24
[11] S. M. Chen and N. Y. Chung, Forecasting enrolments using high order fuzzy time series and
25
genetic algorithms, International Journal of Intelligent Systems, 21 (2006), 485-501.
26
[12] C. H. Cheng, T. L. Chen, H. J. Teoh and C. H. Chiang, Fuzzy time-series based on adaptive
27
expectation model for TAIEX forecasting, Expert Systems with Applications, 34 (2008),
28
1126-1132.
29
[13] C. H. Cheng, G. W. Cheng and J. W. Wang, Multi-attribute fuzzy time series method based
30
on fuzzy clustering, Expert Systems with Applications, 34 (2008), 1235-1242.
31
[14] S. Davari, M. H. F. Zarandi and I. B. Turksen, An Improved fuzzy time series forecasting
32
model based on particle swarm intervalization, The 28th North American Fuzzy Information
33
Processing Society Annual Conferences (NAFIPS 2009), Cincinnati, Ohio, USA, June 14-17,
34
[15] E. Egrioglu, PSO-based high order time invariant fuzzy time series method: Application to
35
stock exchange data, Economic Modelling, 38 (2014), 633-639.
36
[16] E. Egrioglu, C. H. Aladag, U. Yolcu, M. A. Basaran and V. R. Uslu, A new hybrid approach
37
based on SARIMA and partial high order bivariate fuzzy time series forecasting model, Expert
38
Systems with Applications, 36 (2009), 7424-7434.
39
[17] E. Egrioglu, C. H. Aladag, U. Yolcu, V. R. Uslu and M. A. Basaran, A new approach based
40
on articial neural networks for high order multivariate fuzzy time series, Expert Systems
41
with Applications, 36 (2009), 10589-10594.
42
[18] E. Egrioglu, C. H. Aladag, U. Yolcu, V. R. Uslu and M. A. Basaran, Finding an optimal
43
interval length in high order fuzzy time series, Expert Systems with Applications, 37 (2010),
44
5052-5055.
45
[19] E. Egrioglu, C. H. Aladag, M. A. Basaran, V. R. Uslu and U. Yolcu, A New Approach Based
46
on the Optimization of the Length of Intervals in Fuzzy Time Series, Journal of Intelligent
47
and Fuzzy Systems, 22 (2011), 15-19.
48
[20] E. Egrioglu, C. H. Aladag, U. Yolcu, V. R. Uslu and N. A. Erilli, Fuzzy Time Series Forecast-
49
ing Method Based on Gustafson-Kessel Fuzzy Clustering, Expert Systems with Applications,
50
38 (2011), 10355-10357.
51
[21] E. Egrioglu, U. Yolcu, C. H. Aladag and C. Kocak, An ARMA Type Fuzzy Time Series
52
Forecasting Method Based on Particle Swarm Optimization, Mathematical Problems in En-
53
gineering, Article ID 935815, 2013 (2013), 12 pages.
54
[22] S. Gunay, E. Egrioglu and C. H. Aladag, Introduction to univariate time series analysis.
55
Hacettepe University Press, Ankara Turkey, 2007.
56
[23] L. Y. Hsu, S. J. Horng, T. W. Kao, Y. H. Chen, R. S. Run, R. J. Chen, J. L. Lai and I.
57
H. Kuo, Temperature prediction and TAIFEX forecasting based on fuzzy relationships and
58
MTPSO techniques, Expert Systems with Application, 37 (2010), 2756-2770.
59
[24] K. Huarng, Eective length of intervals to improve forecasting in fuzzy time-series, Fuzzy
60
Sets and Systems, 123 (2001a), 387-394.
61
[25] K. Huarng and H. K. Yu, Ratio-based lengths of intervals to improve fuzzy time series fore-
62
casting, IEEE Trans. Syst. Man Cybern. B, Cybern., 36 (2006), 328-340.
63
[26] K. Huarng and H. K. Yu, The application of neural networks to forecast fuzzy time series,
64
Physica A, 363 (2006), 481-491.
65
[27] M. Khashei, S. R. Hejazi and M. Bijari, A new hybrid articial neural networks and fuzzy
66
regression model for time series forecasting, Fuzzy Sets and Systems, 159(7) (2008), 769-786.
67
[28] I. H. Kuo, S. J. Horng, T. W. Kao, T. L. Lin, C. L. Lee and Y. Pan, An improved method for
68
forecasting enrollments based on fuzzy time series and particle swarm optimization, Expert
69
Systems with Application, 36 (2009), 6108-6117.
70
[29] I. H. Kuo, S. J. Horng, Y. H. Chen, R. S. Run, T. W. Kao, R. J. Chen, J. L. Lai and T.
71
L. Lin, Forecasting TAIFEX based on fuzzy time series and particle swarm optimization,
72
Expert Systems with Application, 37 (2010), 1494-1502.
73
[30] L. W. Lee, L. H. Wang and S. M. Chen, Temperature prediction and TAIFEX forecasting
74
based on fuzzy logical relationships and genetic algorithms, Expert Systems with Applications,
75
33 (2007), 539-550.
76
[31] K. Levenberg, A Method for the Solution of Certain Non-Linear Problems in Least Squares,
77
The Quarterly of Applied Mathematics, 2 (1944), 164-168.
78
[32] D. W. Marquardt, An algorithm for least-squares estimation of nonlinear parameters, Journal
79
of the Society for Industrial and Applied Mathematics, 11 (1963), 431-441.
80
[33] J. I. Park, D. J. Lee, C. K. Song and M. G. Chun, TAIFEX and KOSPI 200 forecasting
81
based on two factors high order fuzzy time series and particle swarm optimization, Expert
82
Systems with Application, 37 (2010), 959-967.
83
[34] Q. Song, Seasonal forecasting in fuzzy time series, Fuzzy Sets and Systems, 107 (1999),
84
[35] Q. Song and B. S. Chissom, Fuzzy time series and its models, Fuzzy Sets and Systems, 54
85
(1993), 269-277.
86
[36] Q. Song and B. S. Chissom, Forecasting enrollments with fuzzy time series- Part I, Fuzzy
87
Sets and Systems, 54 (1993), 1-10.
88
[37] Q. Song and B. S. Chissom, Forecasting enrollments with fuzzy time series- Part II, Fuzzy
89
Sets and Systems, 62 (1994), 1-8.
90
[38] U. Yolcu, E. Egrioglu, V. R. Uslu, M. A. Basaran and C. H. Aladag, A new approach for
91
determining the length of intervals for fuzzy time series, Applied Soft Computing, 9(2)
92
(2009), 647-651.
93
[39] U. Yolcu, C. H. Aladag, E. Egrioglu and V. R. Uslu, Time series forecasting with a novel
94
fuzzy time series approach: an example for Istanbul stock market, Journal of Statistical
95
Computation and Simulation, 83(4) (2013), 597-610.
96
[40] H. K. Yu, Weighted fuzzy time series models for TAIEX forecasting, Physica A, 349 (2005),
97
[41] H. K. Yu and K. Huarng, A bivariate fuzzy time series model to forecast TAIEX, Expert
98
Systems with Applications, 34 (2008), 2945-2952.
99
[42] H. K. Yu and K. Huarng, A neural network- based fuzzy time series model to improve fore-
100
casting, Expert Systems with Application, 37 (2010), 3366-3372.
101
[43] L. A. Zadeh, Fuzzy Sets, Inform and Control, 8 (1965), 338-353.
102
[44] G. P., Zhang, B. E., Patuwo and Y. M. Hu, Forecasting with articial neural networks: The
103
state of the art, International Journal of Forecasting, 14 (1998), 35{62.
104
[45] J. M. Zurada, Introduction of articial neural systems. St. Paul: West Publishing, (1992),
105
ORIGINAL_ARTICLE
A Hybrid Multi-attribute Group Decision Making Method Based on Grey Linguistic 2-tuple
Because of the complexity of decision-making environment, the uncertainty of fuzziness and the uncertainty of grey maybe coexist in the problems of multi-attribute group decision making. In this paper, we study the problems of multi-attribute group decision making with hybrid grey attribute data (the precise values, interval numbers and linguistic fuzzy variables coexist, and each attribute value has a certain grey degree), and present a new grey hybrid multi-attribute group decision making method based on grey linguistic 2-tuple. Concretely, the concept of grey linguistic 2-tuple is defined based on the traditional linguistic 2-tuple, and the transformation methods of transforming the precise values, interval numbers and linguistic fuzzy variables into the grey linguistic 2-tuples are presented respectively. Further, a new grey linguistic 2-tuple weighted averaging (emph{GLTWA}) operator is presented to aggregate multiple decision makers' individual decision information into comprehensive decision information, and then a ranking method based on grey 2-tuple correlation degree is presented to rank all alternatives and to select the winners. An application decision making example of supplier selection is also given to validate the method developed and to highlight the implementation, practicality and effectiveness of the presented method.
http://ijfs.usb.ac.ir/article_2358_921ff0008ea7f62892c5003e6baad75f.pdf
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59
10.22111/ijfs.2016.2358
Hybrid multi-attribute group decision making
Grey linguistic 2-tuple
GLTWA operator
Grey 2-tuple correlation degree
Congjun
Rao
cjrao@foxmail.com
true
1
School of Science, Wuhan University of Technology, Wuhan 430070,
P. R. China
School of Science, Wuhan University of Technology, Wuhan 430070,
P. R. China
School of Science, Wuhan University of Technology, Wuhan 430070,
P. R. China
AUTHOR
Junjun
Zheng
jjzhengwhu@foxmail.com
true
2
School of Economics and Management, Wuhan University, Wuhan
430072, P. R. China
School of Economics and Management, Wuhan University, Wuhan
430072, P. R. China
School of Economics and Management, Wuhan University, Wuhan
430072, P. R. China
LEAD_AUTHOR
Cheng
Wang
wangc80@163.com
true
3
School of Mathematics and Economics, Hubei University of Education,
Wuhan 430072, P. R. China
School of Mathematics and Economics, Hubei University of Education,
Wuhan 430072, P. R. China
School of Mathematics and Economics, Hubei University of Education,
Wuhan 430072, P. R. China
AUTHOR
Xinping
Xiao
true
4
School of Science, Wuhan University of Technology, Wuhan 430070,
P. R. China
School of Science, Wuhan University of Technology, Wuhan 430070,
P. R. China
School of Science, Wuhan University of Technology, Wuhan 430070,
P. R. China
AUTHOR
[1] G. Bordogna, M. Fedrizzi and G. Pasi, A linguistic modeling of consensus in group decision
1
making based on OWA operators, IEEE Transactions on Systems, Man and Cybernetics, Part
2
A: Systems and Humans, 27 (1997), 126-132.
3
[2] R. Degani and G. Bortolan, The problem of linguistic approximation in clinical decision
4
making, International Journal of Approximate Reasoning, 2 (1988), 143-162.
5
[3] M. Delgado, J. L. Verdegay and M. A. Vila, On aggregation operators of linguistic labels,
6
International Journal of Intelligent Systems, 8 (1993), 351-370.
7
[4] J. L. Deng, Grey system theory, Huazhong University of Science & Technology Press, Wuhan,
8
[5] Y. C. Dong, Y. F. Xu, H. Y. Li and B. Feng, The OWA-based consensus operator under
9
linguistic representation models using position indexes, European Journal of Operational
10
Research, 203 (2010), 455-463.
11
[6] H. Doukas, A. Tsiousi, V. Marinakis and J. Psarras, Linguistic multi-criteria decision making
12
for energy and environmental corporate policy, Information Sciences, 258 (2014), 328-338.
13
[7] F. J. Estrella, M. Espinilla, F. Herrera and L. Martnez, FLINTSTONES: A fuzzy linguis-
14
tic decision tools enhancement suite based on the 2-tuple linguistic model and extensions,
15
Information Sciences, 280 (2014), 152-170.
16
[8] Y. B. Gong, N. Hu, J. G. Zhang, G. F. Liu and J. G. Deng, Multi-attribute group decision
17
making method based on geometric Bonferroni mean operator of trapezoidal interval type-2
18
fuzzy numbers, Computers & Industrial Engineering, 81 (2015), 167-176.
19
[9] Y. D. He, H. Y. Chen, Z. He and L. G. Zhou, Multi-attribute decision making based on neutral
20
averaging operators for intuitionistic fuzzy information, Applied Soft Computing, 27 (2015),
21
[10] F. Herrera and E. Herrera-Viedma, Aggregation operators for linguistic weighted information,
22
IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans, 27
23
(1997), 646-656.
24
[11] F. Herrera and L. Martnez, A 2-tuple fuzzy linguistic representation model for computing
25
with words, IEEE Transactions on Fuzzy Systems, 8(6) (2000), 746-752.
26
[12] F. Herrera and L. Martnez, A model based on linguistic 2-Tuples for dealing with multigran-
27
ular hierarchical linguistic contexts in multi-expert decision-making, IEEE Transactions on
28
Systems, Man, and Cybernetics-Part B: Cybernetics, 31(2) (2001), 227-234.
29
[13] F. Herrera, L. Martnez and P. J. Sanchez, Managing non-homogeneous information in group
30
decision-making, European Journal of Operational Research, 166(1) (2005), 115-132.
31
[14] C. W. Hsu, T. C. Kuo, S. H. Chen and A. H. Hu, Using DEMATEL to develop a carbon man-
32
agement model of supplier selection in green supply chain management, Journal of Cleaner
33
Production, 56 (2013), 164-172.
34
[15] Y. B. Ju and A. H. Wang, Extension of VIKOR method for multi-criteria group decision
35
making problem with linguistic information, Applied Mathematical Modelling, 37 (2013),
36
3112-3125.
37
[16] Y. B. Ju, A. H. Wang and X. Y. Liu, Evaluating emergency response capacity by fuzzy
38
AHP and 2-tuple fuzzy linguistic approach, Expert Systems with Applications, 39 (2012),
39
6972-6981.
40
[17] A. Kumar, V. Jain and S. Kumar, A comprehensive environment friendly approach for sup-
41
plier selection, Omega, 42 (2014), 109-123.
42
[18] J. B. Lan, Q. Sun, Q. M. Chen and Z. X. Wang, Group decision making based on induced
43
uncertain linguistic OWA operators, Decision Support Systems, 55 (2013), 296-303.
44
[19] J. Lin, Q. Zhang and F. Y. Meng, An approach for facility location selection based on optimal
45
aggregation operator, Knowledge-Based Systems, 85 (2015), 143-158.
46
[20] B. S. Liu, Y. H. Shen, X. H. Chen, Y. Chen and X. Q. Wang, A partial binary tree DEA-
47
DA cyclic classication model for decision makers in complex multi-attribute large-group
48
interval-valued intuitionistic fuzzy decision-making problems, Information Fusion, 18 (2014),
49
[21] H. C. Liu, J. X. You, C. Lu and M. M. Shan, Application of interval 2-tuple linguistic
50
MULTIMOORA method for health-care waste treatment technology evaluation and selection,
51
Waste Management, 34 (2014), 2355-2364.
52
[22] S. Liu, F. T. S. Chan and W. X. Ran, Multi-attribute group decision-making with multi-
53
granularity linguistic assessment information: An improved approach based on deviation
54
and TOPSIS, Applied Mathematical Modelling, 37 (2013), 10129-10140.
55
[23] P. D. Liu and F. Jin, A multi-attribute group decision-making method based on weighted
56
geometric aggregation operators of interval-valued trapezoidal fuzzy numbers, Applied Mathematical
57
Modelling, 36 (2012), 2498-2509.
58
[24] P. D. Liu and Y. M. Wang, Multiple attribute group decision making methods based on
59
intuitionistic linguistic power generalized aggregation operators, Applied Soft Computing,
60
17 (2014), 90-104.
61
[25] L. Martnez and F. Herrera, An overview on the 2-tuple linguistic model for computing with
62
words in decision making: Extensions, applications and challenges, Information Sciences,
63
207 (2012), 1-18.
64
[26] F. Y. Meng, X. H. Chen and Q. Zhang, Some interval-valued intuitionistic uncertain linguistic
65
Choquet operators and their application to multi-attribute group decision making, Applied
66
Mathematical Modelling, 38 (2014), 2543-2557.
67
[27] J. M. Merigo, M. Casanovas and L. Martnez, Linguistic aggregation operators for linguistic
68
decision making based on the Dempster-Shafer theory of evidence, International Journal of
69
Uncertainty, Fuzziness and Knowledge-Based Systems, 18(3) (2010), 287-304.
70
[28] J. M. Merigo and A. M. Gil-Lafuente, Induced 2-tuple linguistic generalized aggregation op-
71
erators and their application in decision-making, Information Sciences, 236 (2013), 1-16.
72
[29] J. H. Park, J. M. Park and Y. C. Kwun, 2-Tuple linguistic harmonic operators and their
73
applications in group decision making, Knowledge-Based Systems, 44 (2013), 10-19.
74
[30] J. I. Pelaez and J. M. Do~na, LAMA: a linguistic aggregation of majority additive operator,
75
International Journal of Intelligent Systems, 18 (2003), 809-820.
76
[31] B. Peng, C. M. Ye and S. Z. Zeng, Uncertain pure linguistic hybrid harmonic averaging oper-
77
ator and generalized interval aggregation operator based approach to group decision making,
78
Knowledge-Based Systems, 36 (2012), 175-181.
79
[32] C. J. Rao, M. Goh, Y. Zhao, J. J. Zheng, Location selection of city logistics centers under
80
sustainability, Transportation Research Part D: Transport and Environment,36(2015),29-44.
81
[33] C. J. Rao and J. Peng, Fuzzy group decision making model based on credibility theory and
82
gray relative degree, International Journal of Information Technology & Decision Making,
83
8(3) (2009), 515-527.
84
[34] C. J. Rao and J. Peng, Group decision making model based on grey relational analysis, The
85
Journal of Grey System, 21(1) (2009), 15-24.
86
[35] C. J. Rao and Y. Zhao, Multi-attribute auction method based on grey relational degree of
87
hybrid sequences, The Journal of Grey System, 21(2) (2009), 175-184.
88
[36] C. J. Rao and Y. Zhao, Multi-attribute decision making model based on optimal membership
89
and relative entropy, Journal of Systems Engineering and Electronics, 20(3) (2009), 537-542.
90
[37] Z. F. Tao, H. Y. Chen, X. Song, L. G. Zhou and J. P. Liu, Uncertain linguistic fuzzy soft
91
sets and their applications in group decision making, Applied Soft Computing, 34 (2015),
92
[38] I. Truck, Comparison and links between two 2-tuple linguistic models for decision making,
93
Knowledge-Based Systems, (2015), In Press.
94
[39] S. P. Wan, Power average operators of trapezoidal intuitionistic fuzzy numbers and applica-
95
tion to multi-attribute group decision making, Applied Mathematical Modelling, 37 (2013),
96
4112-4126.
97
[40] S. P. Wan, 2-Tuple linguistic hybrid arithmetic aggregation operators and application to
98
multi-attribute group decision making, Knowledge-Based Systems, 45 (2013), 31-40.
99
[41] S. P. Wan, Q. Y. Wang and J. Y. Dong, The extended VIKOR method for multi-attribute
100
group decision making with triangular intuitionistic fuzzy numbers, Knowledge-Based Systems,
101
52 (2013), 65-77.
102
[42] S. P. Wan and J. Y. Dong, Interval-valued intuitionistic fuzzy mathematical programming
103
method for hybrid multi-criteria group decision making with interval-valued intuitionistic
104
fuzzy truth degrees, Information Fusion, 26 (2015), 49-65.
105
[43] S. P. Wan and J. Y. Dong, Power geometric operators of trapezoidal intuitionistic fuzzy
106
numbers and application to multi-attribute group decision making, Applied Soft Computing,
107
29 (2015), 153-168.
108
[44] S. Y. Wang, Applying 2-tuple multigranularity linguistic variables to determine the supply
109
performance in dynamic environment based on product-oriented strategy, IEEE Transactions
110
on Fuzzy Systems, 16 (2008), 29-39.
111
[45] J. H.Wang and J. Y. Hao, An approach to aggregation of ordinal information in multi-criteria
112
multi-person decision making using Choquet integral of Fubini type, Fuzzy Optimization and
113
Decision Making, 8 (2009), 365-380.
114
[46] J. Q. Wang, J. Wang, Q. H. Chen, H. Y. Zhang and X. H. Chen, An outranking approach for
115
multi-criteria decision-making with hesitant fuzzy linguistic term sets, Information Sciences,
116
280 (2014), 338-351.
117
[47] J. Q. Wang, P. Lu, H. Y. Zhang and X. H. Chen, Method of multi-criteria group decision-
118
making based on cloud aggregation operators with linguistic information, Information Sciences,
119
274 (2014), 177-191.
120
[48] W. Z. Wang and X. W. Liu, The multi-attribute decision making method based on interval-
121
valued intuitionistic fuzzy Einstein hybrid weighted geometric operator, Computers and Mathematics
122
with Applications, 66 (2013), 1845-1856.
123
[49] G. W. Wei, Uncertain linguistic hybrid geometric mean operator and its application to group
124
decision making under uncertain linguistic environment, International Journal of Uncertainty,
125
Fuzziness and Knowledge-Based Systems, 17 (2009), 251-267.
126
[50] G. W. Wei, A method for multiple attribute group decision making based on the ET-WG and
127
ET-OWG operators with 2-tuple linguistic information, Expert Systems with Applications,
128
37 (2010), 7895-7900.
129
[51] G. W. Wei, Grey relational analysis model for dynamic hybrid multiple attribute decision
130
making, Knowledge-Based Systems, 24 (2011), 672-679.
131
[52] G. W. Wei, Grey relational analysis method for 2-tuple linguistic multiple attribute group
132
decision making with incomplete weight information, Expert Systems with Applications, 38
133
(2011), 4824-4828.
134
[53] G. W. Wei, Hesitant fuzzy prioritized operators and their application to multiple attribute
135
decision making, Knowledge-Based Systems, 31 (2012), 176-182.
136
[54] G. W. Wei and X. F. Zhao, Some dependent aggregation operators with 2-tuple linguistic in-
137
formation and their application to multiple attribute group decision making, Expert Systems
138
with Applications, 39 (2012), 5881-5886.
139
[55] J. Wu and Y. J. Liu, An approach for multiple attribute group decision making problems with
140
interval-valued intuitionistic trapezoidal fuzzy numbers, Computers & Industrial Engineering,
141
66 (2013), 311-324.
142
[56] X. P. Xiao and S. H. Mao, Grey forecast and decision method, Science Press, Beijing, 2013.
143
[57] Z. S. Xu, EOWA and EOWG operators for aggregating linguistic labels based on linguistic
144
preference relations, International Journal of Uncertainty, Fuzziness and Knowledge-Based
145
Systems, 12 (2004), 791-810.
146
[58] Z. S. Xu, Induced uncertain linguistic OWA operators applied to group decision making,
147
Information Fusion, 7 (2006), 231-238.
148
[59] Z. S. Xu, An approach based on the uncertain LOWG and the induced uncertain LOWG op-
149
erators to group decision making with uncertain multiplicative linguistic preference relations,
150
Decision Support Systems, 41 (2006), 488-499.
151
[60] Z. S. Xu and R. R. Yager, Power-geometric operators and their use in group decision making,
152
IEEE Transactions on Fuzzy Systems, 18(1) (2010), 94-105.
153
[61] Z. S. Xu and X. L. Zhang, Hesitant fuzzy multi-attribute decision making based on TOPSIS
154
with incomplete weight information, Knowledge-Based Systems, 52 (2013), 53-64.
155
[62] Y. J. Xu, F. Ma, F. F. Tao and H. M. Wang, Some methods to deal with unacceptable
156
incomplete 2-tuple fuzzy linguistic preference relations in group decision making, Knowledge-
157
Based Systems, 56 (2014), 179-190.
158
[63] Y. J. Xu, J. M. Merigo and H. M. Wang, Linguistic power aggregation operators and their
159
application to multiple attribute group decision making, Applied Mathematical Modelling,
160
36(11) (2012), 5427-5444.
161
[64] Y. J. Xu, P. Shi, J. M. Merig0 and H. M. Wang, Some proportional 2-tuple geometric ag-
162
gregation operators for linguistic decision making, Journal of Intelligent & Fuzzy Systems,
163
25(3) (2013), 833-843.
164
[65] W. Yang and Z. P. Chen, New aggregation operators based on the Choquet integral and 2-tuple
165
linguistic information, Expert Systems with Applications, 39 (2012), 2662-2668.
166
[66] F. Ye and Y. Li, An extended TOPSIS model based on the Possibility theory under fuzzy
167
environment, Knowledge-Based Systems, 67 (2014), 263-269.
168
[67] X. Y. You, J. X. You, H. C. Liu and L. Zhen, Group multi-criteria supplier selection using an
169
extended VIKOR method with interval 2-tuple linguistic information, Expert Systems with
170
Applications, 42 (2015), 1906-1916.
171
[68] H. M. Zhang, Some interval-valued 2-tuple linguistic aggregation operators and application
172
in multi-attribute group decision making, Applied Mathematical Modelling, 37 (2013), 4269-
173
[69] L. G. Zhou and H. Y. Chen, The induced linguistic continuous ordered weighted geometric
174
operator and its application to group decision making, Computers & Industrial Engineering,
175
66 (2013), 222-232.
176
ORIGINAL_ARTICLE
A FUZZY-BASED SPEED CONTROLLER FOR IMPROVEMENT OF INDUCTION MOTOR'S DRIVE PERFORMANCE
Induction motors (IMs) are widely used in many industrial applications due to their robustness, low cost, simplicity and relative good efficiency. One of the major considerations for IMs is their speed control. PI (proportional-integrator) controllers are usually used as speed controller. Adjusting the gain of PI controller is time-consuming which needs thorough considerations. Hence, fuzzy controllers are proposed to overcome such problems. In this paper, firstly drive of a three-phase induction motor is designed based on PI controller and then fuzzy logic controller is implemented. This paper presents a novel speed control technique based on fuzzy logic with two inputs and one output for drive of an IM. The inputs are speed error and derivation of speed error and the output is speed. Finally comparison is done between the PI and fuzzy controllers which shows superiority of the fuzzy controller over PI controller.
http://ijfs.usb.ac.ir/article_2359_d0c6ddbaed27b7b597713095ad41c16e.pdf
2016-04-30T11:23:20
2018-09-19T11:23:20
61
70
10.22111/ijfs.2016.2359
Induction Motor
Speed Control
PI controller
Fuzzy Logic Controller
H.
Asgharpour-Alamdari
true
1
Department of Electrical Engineering, Semnan University, Semnan, Iran
Department of Electrical Engineering, Semnan University, Semnan, Iran
Department of Electrical Engineering, Semnan University, Semnan, Iran
LEAD_AUTHOR
Y.
Alinejad-Beromi
true
2
Department of Electrical Engineering, Semnan University, Semnan, Iran
Department of Electrical Engineering, Semnan University, Semnan, Iran
Department of Electrical Engineering, Semnan University, Semnan, Iran
AUTHOR
H.
Yaghobi
true
3
Department of Electrical Engineering, Semnan University, Semnan, Iran
Department of Electrical Engineering, Semnan University, Semnan, Iran
Department of Electrical Engineering, Semnan University, Semnan, Iran
AUTHOR
[1] M. N. Afrozi, M. Hassanpour, A. Naebi and S. Hassanpour, Simulation and Optimization of
1
asynchronous AC motor control by Particle Swarm Optimization (PSO) and Emperor Algo-
2
rithm, In Computer Modeling and Simulation (EMS), 2011 Fifth UKSim European Sympo-
3
sium , IEEE, (2011), 251-256.
4
[2] A. Al-Odienat and A. Al-Lawama, The advantages of PID fuzzy controllers over the conven-
5
tional types, American Journal of Applied Sciences 5(6) (2008), 653-658.
6
[3] D. Asija, Speed control of induction motor using fuzzy-PI controller, 2nd International Con-
7
ference In Mechanical and Electronics Engineering (ICMEE), 2(460) (2010).
8
[4] F. Barrero, et al, Speed control of induction motors using a novel fuzzy sliding-mode structure,
9
Fuzzy Systems, IEEE Transactions on, 10(3) (2002), 375-383.
10
[5] E. Bim, Fuzzy optimization for rotor constant identication of an indirect FOC induction
11
motor drive, Industrial Electronics, IEEE Transactions, 48(6) (2001), 1293-1295.
12
[6] V. Chitra and R. S. Prabhakar, Induction motor speed control using fuzzy logic controller,
13
World Academy of Science, Engineering and Technology, (23) (2006),17-22.
14
[7] R. Dhobale and D. M. Chandwadkar, FPGA Implementation of Three-Phase Induction Mo-
15
tor Speed Control Using Fuzzy Logic and Logic Based PWM, International Conference on
16
Recent Trends in Engineering & Technology, (2012), 185-189.
17
[8] A. Goedtel, I. N. Silva and P. J. A. Serni, Load torque identication in induction motor using
18
neural networks technique, Electric Power Systems Research, 77(1) (2007), 35-45.
19
[9] H. E. Kalhoodashti and M. Hahbazian, Hybrid Speed Control of Induction Motor using PI
20
and Fuzzy Controller, International Journal of Computer Applications, 30(11) (2011), 44-50.
21
[10] P. Kumar, V. Agarwal and A. K. Singh, Design of fuzzy PI controller for CSI Fed induction
22
motor drive, International Journal of Electrical and Electronic System Research, 1(4)(2011),
23
[11] F. Lima, et al,, Peed neuro-fuzzy estimator applied to sensorless induction motor contro,
24
Latin America Transactions, IEEE (Revista IEEE America Latina), 10(5) (2012), 2065-2073.
25
[12] A. Lokriti, et al, Induction motor speed drive improvement using fuzzy IP-self-tuning con-
26
troller. A real time implementation, ISA transactions, 52(3) (2013), 406-417.
27
[13] M. A. Mannan, et al, Fuzzy-logic based speed control of induction motor considering core loss
28
into account, Intelligent Control and Automation, (2012), 229-235.
29
[14] D. Rai, S. Sharma and V. Bhuria, Fuzzy speed controller design of three phase induction mo-
30
tor, International Journal of Emerging Technology and Advanced Engineering, 5(2)( 2012),
31
[15] C. Raj, S. Thanga, P. Srivastava and P. Agarwal, Energy ecient control of three-phase
32
induction motor-a review, International Journal of Computer and Electrical Engineering,
33
1(1) (2009), 1793-1808.
34
[16] L. Ramesh, S. P. Chowdhury, S. Chowdhury, A. K. Saha and Y. H. Song, Eciency op-
35
timization of induction motor using a fuzzy logic based optimum
36
ux search controller, In
37
Power Electronics, Drives and Energy Systems, 2006. PEDES'06. International Conference,
38
(2006), 1-6.
39
[17] A. Sudhakar and M. V. Kumar, , A comparative analysis of PI and neuro fuzzy controllers
40
in direct torque control of induction motor drives, Int. J. Eng. Res, 2(4) (2012), 672-680.
41
[18] P. Tripura and Y. S. K. Babu, Fuzzy logic speed control of three phase induction motor drive,
42
World Academy of Science, Engineering and Technology, 60(3) (2011), 1371-1375.
43
[19] M. N. Uddin, and H. Wen, Development of a self-tuned neuro-fuzzy controller for induction
44
motor drives, Industry Applications, IEEE Transactions , 43(4) (2007), 1108-1116.
45
[20] F. Zidani, et al, A fuzzy-based approach for the diagnosis of fault modes in a voltage-fed PWM
46
inverter induction motor drive, Industrial Electronics, IEEE Transactions, 55(2) (2008), 586-
47
[21] F. Zidani, et al, A fuzzy technique for loss minimization in scalar-controlled induction motor,
48
Electric Power Components and Systems, 30(6) (2002), 625-635.
49
ORIGINAL_ARTICLE
Alternating Regular Tree Grammars in the Framework of Lattice-Valued Logic
In this paper, two different ways of introducing alternation for lattice-valued (referred to as {L}valued) regular tree grammars and {L}valued top-down tree automata are compared. One is the way which defines the alternating regular tree grammar, i.e., alternation is governed by the non-terminals of the grammar and the other is the way which combines state with alternation. The first way is taken over to prove a main theorem: the class of languages generated by an {L}valued alternating regular tree grammar {LAG}) is equal to the class of languages accepted by an {L}valued alternating top-down tree automaton {LAA}). The second way is taken over to define a new type of automaton by combining the {L}valued alternating top-down tree automaton with stack, called {L}-valued alternating stack tree automaton {LASA} and the generative power of it is compared to some well-known language classes, especially to {LAA} and to {LAG}Also, we have derived a characterization of the state alternating regular tree grammar {LSAG}) in terms of {LASA}.
http://ijfs.usb.ac.ir/article_2360_9a374f39abaa600423ce805945586dd1.pdf
2016-04-30T11:23:20
2018-09-19T11:23:20
71
94
10.22111/ijfs.2016.2360
Lattice-valued logic
Alternating top-down tree automaton
State alternating regular tree grammar
Alternating stack tree automaton
Maryam
Ghorani
maryamghorani@gmail.com
true
1
Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran
Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran
Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran
LEAD_AUTHOR
Mohammad Mehdi
Zahedi
zahedi_mm@kgut.ac.ir
true
2
Department of Mathematics, Graduate University of Advanced Technology, Kerman, Iran
Department of Mathematics, Graduate University of Advanced Technology, Kerman, Iran
Department of Mathematics, Graduate University of Advanced Technology, Kerman, Iran
AUTHOR
[1] A. Bouhoula, J. P. Jouannaud and J. Meseguer, Specication and proof in membeship equa-
1
tional logic, Theoretical Computer Science, 236 (2000), 35-132.
2
[2] G. Birkho, Lattice theory, American Mathematical Society Colloquium Publications, New
3
York, 1984.
4
[3] S. Bozapalidis and O. L. Bozapalidoy, Fuzzy tree language recognizability, Fuzzy Sets and
5
Systems, 161(5) (2010), 716-734.
6
[4] J. R. Buchi, Weak second-order arithmetic and nite automata, Zeitschrift fur Mathematische
7
Logik und Grundlagen der Mathematik, 6 (1960), 66-92.
8
[5] Y. Cao, L. Xia and M. Ying, Probabilistic automata for computing with words, Journal of
9
Computer and System Sciences, 79(1) (2013), 152-172.
10
[6] A. K. Chandra, D. C. Kozen and L. J. Stockmeyer, Alternation, Journal of the ACM, 28(1)
11
(1981), 114-133.
12
[7] S. R. Chaudhari and M. N. Joshi, A note on fuzzy tree automata, International Journal of
13
Computer Applications, 56(17) (2012), 1-5.
14
[8] H. Comon, M. Dauchet, R. Gilleron, F. Jacquemard, D. Lugiez, C. Loding, S. Ti-
15
son and M. Tommasi, Tree automata: technigues and applications, 2007. Available:
16
http://tata.gforge.inria.fr.
17
[9] Z. Esik and G. Liu, Fuzzy tree automata, Fuzzy Sets and Systems, 158 (2007), 1450-1460.
18
[10] B. Finkbeiner and H. Sipma, Checking nite traces using alternating automata, Formal Meth-
19
ods in System Design, 24(2) (2004), 101-127.
20
[11] F. Gecseg and M. Steinby, Tree automata, Akademiai Kiado, Budapest, 1984.
21
[12] M. Ghorani and M. M. Zahedi, Characterization of complete residuated lattice-valued nite
22
tree automata, Fuzzy Sets and Systems, 199 (2012), 28-46.
23
[13] M. Ghorani, M. M. Zahedi and R. Ameri, Algebraic properties of complete residuated lattice-
24
valued tree automata, Soft Computing, 16 (2012), 1723-1732.
25
[14] J. E. Hopcroft, R. Motwani and J. D. Ullman, Introduction to automata theory, languages
26
and computation, 3rd edition, Addison-Wesley, 2006.
27
[15] H. Hosoya, J. Vouillon and B. C. Pierce, Regular expression types for XML, ACM Transac-
28
tions on Programming Languages and Systems, 27(1) (2005), 46-90.
29
[16] J. Ignjatovic, M. Ciric and S. Bogdanovic, Determinization of fuzzy automata with member-
30
ship values in complete residuated lattices, Information Sciences, 178 (2008), 164-180.
31
[17] J. Jin, Q. Li and Y. Li, Algebraic properties of L-fuzzy nite automata, Information Science,
32
234 (2013), 182-202.
33
[18] D. Kirsten, Alternating tree automata and parity games, In: E. Gradel (Ed.), Automata,
34
Logics, and Innite Games, Springer-Verlag, Berlin, 2002.
35
[19] R. E. Ladner, R. J. Lipton and L. J. Stockmeyer, Alternating pushdown automata, Proceeding
36
of 19th FOCS, IEEE Computer Society Press, Silver Spring, (1978), 92-106.
37
[20] R. E. Ladner, R. J. Lipton and L. J. Stockmeyer, Alternating pushdown and stack automata,
38
SIAM Journal on Computing, 13 (1984), 135-155.
39
[21] E. T. Lee and L. A. Zadeh, Note on fuzzy languages, Information Sciences, 1 (1969), 421-434.
40
[22] H. X. Lei and Y. Li, Minimization of states in automata theory based on nite lattice-ordered
41
monoids, Information Sciences, 177 (2007), 1413-1421.
42
[23] Y. M. Li and W. Pedrycz, Minimization of lattice nite automata and its application to the
43
decomposition of lattice languages, Fuzzy Sets and Systems, 158(13) (2007), 1423-1436.
44
[24] L. Li and D. Qiu, On the state minimization of fuzzy automata, IEEE Transaction on Fuzzy
45
Systems, 23(3) (2015), 434 - 443.
46
[25] Y. Li and Q. Wang, The universal fuzzy automata, Fuzzy Sets and Systems, 249 (2014),
47
[26] F. Lin and H. Ying, Modeling and control of fuzzy discrete event systems, IEEE Trans. Syst.,
48
Man, Cybern. B, Cybern., 32 (2002), 408- 415.
49
[27] J. N. Mordeson and D. S. Malik, Fuzzy automata and languages: theory and applications,
50
Chapman & Hall CRC, London, Boca Raton, 2002.
51
[28] E. Moriya, A grammatical characterization of alternating pushdown automata, Theoretical
52
Computer Science, 67 (1989), 75-85.
53
[29] E. Moriya, D. Hofbauer, M. Huber and F. Otto, On state-alternating context-free grammars,
54
Theoretical Computer Science, 337 (2005), 183-216.
55
[30] E. Moriya and F. Otto, Two ways of introducing alternation into context-free grammars and
56
pushdown automata, IEICE Transactions on Information and Systems, E90D(6) (2007),
57
[31] E. Moriya and F. Otto, On alternating phrase-structure grammars, In: C. Martin-Vide, F.
58
Otto and H. Fernau (Eds.), Language and Automata Theory and Applications, Springer-
59
Verlag Berlin, Heidelberg, 2008.
60
[32] C. W. Omlin, K. K. Thornber and C. L. Giles, Fuzzy nite-state automata can be determin-
61
istically encoded in recurrent neural networks, IEEE Trans. Fuzzy Syst., 5 (1998), 76-89.
62
[33] W. Pedrycz and A. Gacek, Learning of fuzzy automata, International Journal of Computa-
63
tional Intelligence and Applications, 1 (2001), 19-33.
64
[34] D. W. Qiu, Automata theory based on completed residuated lattice-valued logic (I), Science
65
in China (Series F), 44 (2001), 419{429.
66
[35] D. W. Qiu, Automata theory based on completed residuated lattice-valued logic (II), Science
67
in China (Series F), 45 (2002), 442{452.
68
[36] D. W. Qiu, Characterizations of fuzzy nite automata, Fuzzy Sets and Systems, 141 (2004),
69
[37] D. W. Qiu, Supervisory control of fuzzy discrete event systems: a formal approach, IEEE
70
Transactions on Systems, Man and Cybernetics-Part B, 35(1) (2005), 72-88.
71
[38] D. W. Qiu, Pumping lemma in automata theory based on complete residuated lattice-valued
72
logic: a note, Fuzzy Sets and Systems, 157 (2006), 2128-2138.
73
[39] E. S. Santos, Maximin automata, Inform. and Control, 12 (1968), 367-377.
74
[40] G. Slutzki, Alternating tree automata, In: G. Goos and J. Hartmanis (Eds.), 8th colloquium
75
Laquila Proceeding on Trees in Algebra and Programming, Springer-Verlag, Berlin, 1983.
76
[41] G. Slutzki, Alternating tree automata, Theorical Computer Science, 41 (1985), 305-318.
77
[42] J. Tang, Y. Fang and J. G. Tang, The lattice-valued Turing machines and the lattice-valued
78
type 0 grammars, Mathematical Problems in Engineering, 2014 (2014), 1-6.
79
[43] M. G. Thomason and P. N. Marinos, Deterministic acceptors of regular fuzzy languages,
80
IEEE Trans. Syst., Man, Cybern., 4 (1974), 228-230.
81
[44] M. Y. Vardi, Alternating automata and program verication, In: J. Van Leeuwen (Ed.),
82
Computer Science Today, Recent Trends and Developments, Springer-Verlag, Berlin, 1995.
83
[45] M. Y. Vardi, An automata-theoretic approach to linear temporal logic, In: F. Moller and
84
G. Birtwistle (Eds.): Logics for Concurrency: Structure versus Automata, Springer-Verlag,
85
Berlin, 1996.
86
[46] M. Y. Vardi, Alternating automata: checking truth and validity for temporal logics, Proceding
87
of the 14th Int. Conference on Automated Deduction, Springer-Verlag, Berlin, 1997.
88
[47] K. N. Verma and J. Goubault-Larrecq, Alternating two-way AC-tree automata, Information
89
and Computation, 205 (2007), 817-869.
90
[48] W. G. Wee and K. S. Fu, A formulation of fuzzy automata and its application as a model of
91
learning systems, IEEE Trans. Systems Man Cybern., 5 (1969), 215-223.
92
[49] T. Wilke, Alternating tree automata, parity games, and modal -calculus, Bulletin of the
93
Belgian Mathematical Society-Simon Stevin, 8(2) (2001), 359-391.
94
[50] L. Wu and D. W. Qiu, Automata theory based on completed residuated lattice-valued logic:
95
reduction and minimization, Fuzzy Sets and Systems, 161 (2010), 1635-1656.
96
[51] H. Y. Xing and D. W. Qiu, Pumping lemma in context-free grammar theory based on complete
97
residuated lattice-valued logic, Fuzzy Sets and Systems, 160 (2009), 1141-1151.
98
[52] H. Y. Xing, D. W. Qiu and F. C. Liu, Automata theory based on complete residuated lattice-
99
valued logic: pushdown automata, Fuzzy Sets and Systems, 160 (2009), 1125-1140.
100
[53] H. Y. Xing, D. W. Qiu, F. C. Liu and Z. J. Fan, Equivalence in automata theory based on
101
complete residuated lattice-valued logic, Fuzzy Sets and Systems, 158 (2007), 1407-1422.
102
ORIGINAL_ARTICLE
Algebraic Properties of Intuitionistic Fuzzy Residuated Lattices
In this paper, we investigate more relations between the symmetric residuated lattices $L$ with their corresponding intuitionistic fuzzy residuated lattice $tilde{L}$. It is shown that some algebraic structures of $L$ such as Heyting algebra, Glivenko residuated lattice and strict residuated lattice are preserved for $tilde{L}$. Examples are given for those structures that do not remain the same. Also some special subsets of $tilde{L}$ such as regular elements $Rg(tilde{L})$, dense elements $D(tilde{L})$, infinitesimal elements $Inf(tilde{L})$, boolean elements $B(tilde{L})$ and $Rad_{BL}(tilde{L})$ are characterized. The relations between these and corresponding sets in $L$ will be investigated.
http://ijfs.usb.ac.ir/article_2361_a03406f1388de5728fafa2ef1c358332.pdf
2016-04-30T11:23:20
2018-09-19T11:23:20
95
109
10.22111/ijfs.2016.2361
Intuitionstic fuzzy residuated lattice
Heyting algebra
Relative Stone lattice
Glivenko residuated lattice
MV (MTL
SRL)-algebra
Farnaz
Ghanavizi Maroof
farnaz.ghanavizi@yahoo.com
true
1
Department of Mathematics, Faculty of Mathematics and
Compute, Shahid Bahonar University of Kerman, 76169-14111, Kerman, Iran
Department of Mathematics, Faculty of Mathematics and
Compute, Shahid Bahonar University of Kerman, 76169-14111, Kerman, Iran
Department of Mathematics, Faculty of Mathematics and
Compute, Shahid Bahonar University of Kerman, 76169-14111, Kerman, Iran
AUTHOR
Esfandiar
Eslami
esfandiar.eslami@uk.ac.ir
true
2
Department of Mathematics, Faculty of Mathematics and Com-
pute, Shahid Bahonar University of Kerman, 76169-14111, Kerman, Iran
Department of Mathematics, Faculty of Mathematics and Com-
pute, Shahid Bahonar University of Kerman, 76169-14111, Kerman, Iran
Department of Mathematics, Faculty of Mathematics and Com-
pute, Shahid Bahonar University of Kerman, 76169-14111, Kerman, Iran
LEAD_AUTHOR
[1] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87{96.
1
[2] K. T. Atanassov and S. Stoeva, Intuitionistic L-fuzzy sets, in:R.Trapple (ed.), Elsevier
2
Science Publishers B.V., North Holland, 1984.
3
[3] K. T. Atanassov and G. Gargov, Elements of intuitionistic fuzzy logic. part I, Fuzzy Sets and
4
Systems, 145 (1998), 267{277.
5
[4] P. Burillo and H. Bustince, Intuitionistic fuzzy relations. eects of Atanassov's operators
6
on the properties of Intuitionistic Fuzzy relations, Mathware and Soft Computing, 2 (1995),
7
[5] G. Cattaneo and D. Ciucci, Basic intuitionistic principles in fuzzy set theories and its
8
extensions (A terminological debate on Atanassov IFS), Fuzzy Sets and Systems, 24 (2006),
9
3198{3219.
10
[6] R. Cignoli and F. Esteva, Commutative integral bounded residuated lattices with an added
11
involution, Annals of Pure and Applied Logic, 171 (2009), 150{170.
12
[7] C. Cornelis and G. Deschrijver and E. E. Kerre, Classication on intuitionistic fuzzy impli-
13
cators: an algebraic approach, In Proceedings of the FT & T' 02, Durham, North Carolina,
14
[8] D. Dubois and S. Gottwald and P. Hajek and J. Kacprzyk and H. Prade, Terminological dif-
15
culties in fuzzy set theory- The case of "Intuitionistic Fuzzy Sets", Fuzzy Sets and Systems,
16
156 (2005), 485{491.
17
[9] G. Deschrijver and C. Cornelis and E. E. Kerre, Intuitionistic fuzzy connectives revisited, In
18
proceedings of IPMU'02, 2002.
19
[10] E. Eslami, An algebraic structure for Intuitionistic Fuzzy Logic, Iranian Journal of Fuzzy
20
Systems, 9(6) (2012), 31{41.
21
[11] E. Eslami and W. Peng-Yung, More on intutionistic fuzzy residuated lattices, Journal of
22
Multiple-Valued Logic and Soft Computing, 20(3) (2013), 335{352.
23
[12] E. Eslami and F. Ghanavizi Maroof, A Proposed axiomatic system for atanassov intuition-
24
istic fuzzy logic (A-IFL), Notes on Intuitionistic Fuzzy Sets, 19(3) (2013), 1{14.
25
[13] P. Hajek, Metamathematics of fuzzy logic, Trends in Logic, Kluwer Academic Publishers,
26
Drdrecht, 1998.
27
[14] Y. Hong and X. Ruiping and F. Xianwen, Characterizing ordered semigroups by means of
28
Intuitionistic Fuzzy Bi- ideals, Mathware and Soft Computing, 14 (2007), 57{66.
29
[15] M. Kondo, Note on strict residuated lattices with an involutive negation, AAA80 Workshop
30
on General Algebra& Workshop on Non- classical algebraic Structures, Bedlewo, Poland, 1-6
31
june, 2010.
32
[16] C. Muresan, Dense elements and classes of a residuated lattices, Bull. Math. Soc. Sci. Math.
33
Roumanie Tome, 53(1) (2010), 11{24.
34
[17] H. Ono, Substructural logics and residuated lattices - an introduction, Trends in Logic,
35
(2003), 177{212.
36
[18] D. Piciu, Algebras of fuzzy logic, Craiova: Ed universtaria, 2007.
37
[19] E. Szmidt and K. Marta, Atanassov's intuitionistic fuzzy sets in classication of imbalanced
38
and overlapping classes. intelligent techniques and tools for novel system architectures, Studies
39
in Computational Intelligence (SCI), 109 (2008), 455{471.
40
[20] A. Tepavcevic and M. G. Ranitovic, General form of lattice valued intuitionistic fuzzy sets,
41
Computational Intelligence, Theory and Applications, Springer Berlin Heidelberg, Germany,
42
(2006), 375{381.
43
[21] A. Tepavcevic and T. Gerstenkorn, Lattice valued intuitionistic fuzzy sets, Central European
44
Journal of Mathematics, 2(3) (2004), 388{398.
45
[22] G. Takeuti and S. Titani, Intuitionistic fuzzy logic and intuitionistic fuzzy set theory, Journal
46
of Symbolic Logic, 49(3) (1984), 851{866.
47
ORIGINAL_ARTICLE
Width invariant approximation of fuzzy numbers
In this paper, we consider the width invariant trapezoidal and triangularapproximations of fuzzy numbers. The presented methods avoid the effortful computation of Karush-Kuhn-Tucker Theorem. Some properties of the new approximation methods are presented and the applicability of the methods is illustrated by examples. In addition, we show that the proposed approximations of fuzzy numbers preserve the expected value too.
http://ijfs.usb.ac.ir/article_2362_b6a4f056d6dc711eada410b16ef83211.pdf
2016-04-30T11:23:20
2018-09-19T11:23:20
111
130
10.22111/ijfs.2016.2362
Extended trapezoidal fuzzy numbers
Trapezoidal approximations
Triangular approximations
Width
Expected value
Alireza
Khastan
khastan@iasbs.ac.ir
true
1
Department of Mathematics, Institute for Advanced Studies in
Basic Sciences, Zanjan, Iran
Department of Mathematics, Institute for Advanced Studies in
Basic Sciences, Zanjan, Iran
Department of Mathematics, Institute for Advanced Studies in
Basic Sciences, Zanjan, Iran
LEAD_AUTHOR
Zahra
Moradi
zahramoradi@iasbs.ac.ir
true
2
Department of Mathematics, Institute for Advanced Studies in Basic
Sciences, Zanjan, Iran
Department of Mathematics, Institute for Advanced Studies in Basic
Sciences, Zanjan, Iran
Department of Mathematics, Institute for Advanced Studies in Basic
Sciences, Zanjan, Iran
AUTHOR
[1] S. Abbasbandy and M. Amirfakhrian, The nearest approximation of a fuzzy quantity in
1
parametric form, Applied Mathematics and Computation, 172 (2006), 624–632.
2
[2] S. Abbasbandy and M. Amirfakhrian, The nearest trapezoidal form of a generalized left right
3
fuzzy number, International Journal of Approximate Reasoning, 43 (2006), 166–178.
4
[3] S. Abbasbandy and B. Asady, The nearest trapezoidal fuzzy number to a fuzzy quantity,
5
Applied Mathematics and Computation, 156 (2004), 381–386.
6
[4] S. Abbasbandy and T. Hajjari, Weighted trapezoidal approximation-preserving core of a fuzzy
7
number, Computers and Mathematics with Applications, 59 (2010),3066–3077.
8
[5] T. Allahviranloo and M. Adabitabar Firozja, Note on "Trapezoidal approximation of fuzzy
9
numbers", Fuzzy Sets and Systems, 158 (2007), 755–756.
10
[6] A. I. Ban, Approximation of fuzzy numbers by trapezoidal fuzzy numbers preserving the
11
expected interval, Fuzzy Sets and Systems, 159 (2008), 1327-1344.
12
[7] A. I. Ban, Trapezoidal and triangular approximations of fuzzy numbers-inadvertences and
13
corrections, Fuzzy Sets and Systems, 160 (2009), 3048-3058.
14
[8] A. I. Ban, A. Brandas, L. Coroianu, C. Negrutiu and O. Nica, Approximations of fuzzy
15
numbers by trapezoidal fuzzy numbers preserving the ambiguity and value, Computers and
16
Mathematics with Applications, 61 (2011), 1379-1401.
17
[9] A. I. Ban and L. Coroianu, Translation invariance and scale invariance of approximations of
18
fuzzy numbers, in: 7th Conference of the European Society for Fuzzy Logic and Technology,
19
Aix-Les-Bains, 18-22 July 2011.
20
[10] A. I. Ban and L. Coroianu, Nearest interval, triangular and trapezoidal approximation of
21
a fuzzy number preserving ambiguity, International Journal of Approximate Reasoning, 53
22
(2012), 805–836.
23
[11] A.I. Ban, L. Coroianu, Existence, uniqueness and continuity of trapezoidal approximations
24
of fuzzy numbers under a general condition, Fuzzy Sets and Systems, 257(2014), 3-22.
25
[12] A. Brandas, Approximation of fuzzy numbers by trapezoidal fuzzy numbers preserving the
26
core, the ambiguity and the value, Advanced Studies in Contemporary Mathematics, 21
27
(2011), 247259.
28
[13] S. Bodjanova, Median value and median interval of a fuzzy number, Information Sciences,
29
172 (2005), 73-89.
30
[14] S. Chanas, On the interval approximation of a fuzzy number, Fuzzy Sets and Systems, 122
31
(2001), 353-356.
32
[15] L. Coroianu, M. Gagolewski and P. Grzegorzewski, Nearset piecewise linear approximation
33
of fuzzy numbers, Fuzzy Sets and Systems, 233 (2013), 26-51.
34
[16] P. Diamond and P. Kloeden, Metric spaces of fuzzy sets, theory and applications, World
35
Scientific, Singapore, 1994.
36
[17] D. Dubois and H. Prade, Operations on fuzzy numbers, Int. J. Syst. Sci., 30 (1978), 613-626.
37
[18] D. Dubois, H. Prade, The mean value of a fuzzy number, Fuzzy Sets and Systems, 24 (1987),
38
[19] P. Grzegorzewski, Metrics and orders in space of fuzzy numbers, Fuzzy Sets and Systems, 97
39
(1998), 83-94.
40
[20] P. Grzegorzewski, Nearest interval approximation of a fuzzy number, Fuzzy Sets and Systems,
41
130 (2002), 321-330.
42
[21] P. Grzegorzewski, E. Mr´owka, Trapezoidal approximations of fuzzy numbers, Fuzzy Sets and
43
Systems, 153 (2005), 115-135.
44
[22] P. Grzegorzewski, E. Mr´owka, Trapezoidal approximations of fuzzy numbers-revisited, Fuzzy
45
Sets and Systems, 158 (2007), 757-768.
46
[23] S. Heilpern, The expected value of a fuzzy number, Fuzzy Sets and Systems, 47 (1992) 81-86.
47
[24] W. Rudin, Real and Complex Analysis, McGraw-Hill, New York, 1986.
48
[25] C. T. Yeh, A note on trapezoidal approximation of fuzzy numbers, Fuzzy Sets and Systems,
49
158 (2007), 747-754.
50
[26] C. T. Yeh, On improving trapezoidal and triangular approximations of fuzzy numbers, International
51
Journal of Approximate Reasoning, 48 (2008), 297-313.
52
[27] C. T. Yeh, Trapezoidal and triangular approximations preserving the expected interval, Fuzzy
53
Sets and Systems, 159 (2008), 1345–1353.
54
[28] C. T. Yeh, Weighted trapezoidal and triangular approximations of fuzzy numbers, Fuzzy Sets
55
and Systems, 160 (2009), 3059–3079.
56
[29] C. T. Yeh, Weighted semi-trapezoidal approximations of fuzzy numbers, Fuzzy Sets and Systems,
57
165 (2011), 61-80.
58
[30] C. T. Yeh, H. M. Chu, Approximations by LR-type fuzzy numbers, Fuzzy Sets and Systems,
59
257 (2014) 23-40.
60
[31] W. Zeng, H. Li, Weighted triangular approximation of fuzzy numbers, International Journal
61
of Approximate Reasoning, 46 (2007), 137–150.
62
ORIGINAL_ARTICLE
Irreducibility on General Fuzzy Automata
The aim of this paper is the study of a covering of a max-mingeneral fuzzy automaton by another, admissible relations, admissiblepartitions of a max-min general fuzzy automaton,$tilde{delta}$-orthogonality of admissible partitions, irreduciblemax-min general fuzzy automata. Then we obtain the relationshipsbetween them.
http://ijfs.usb.ac.ir/article_2363_d9fe18c52e5072bf681626d5f67c6ab5.pdf
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131
144
10.22111/ijfs.2016.2363
(General) Fuzzy automata
Equivalence relation
Admissible relation
Admissible partition
Irreducibility
Mohammad
Horry
true
1
Shahid Chamran University of Kerman, Kerman, Iran
Shahid Chamran University of Kerman, Kerman, Iran
Shahid Chamran University of Kerman, Kerman, Iran
LEAD_AUTHOR
[1] M. Doostfatemeh and S. C. Kremer, New directions in fuzzy automata, International Journal
1
of Approximate Reasoning, 38 (2005), 175{214.
2
[2] M. Horry and M. M. Zahedi, Fuzzy subautomata of an invertible general fuzzy automaton,
3
Annals of fuzzy sets, fuzzy logic and fuzzy systems, 2(2) (2013), 29{47.
4
[3] J. Jin, Q. Li and Y. Li, Algebric properties of L-fuzzy nite automata, Information Sciences,
5
234 (2013), 182-202.
6
[4] Y. Li and W. Pedrycz, Fuzzy nite automata and fuzzy regular expressions with membership
7
values in lattice-ordered monoids, Fuzzy Sets and Systems, 156 (2005), 68{92.
8
[5] J. N. Mordeson and D. S. Malik, Fuzzy automata and languages, theory and applications,
9
Chapman and Hall/CRC, London/Boca Raton, FL, 2002.
10
[6] D. S. Malik, J. N. Mordeson and M. K. Sen, On subsystems of fuzzy nite state machines,
11
Fuzzy Sets and Systems, 68 (1994), 83{92.
12
[7] M. Mizumoto, J. Tanaka and K. Tanaka, Some consideration on fuzzy automata, J. Compute.
13
Systems Sci., 3 (1969), 409{422.
14
[8] W. Omlin, K. K. Giles and K. K. Thornber, Equivalence in knowledge representation: au-
15
tomata, rnns, and dynamic fuzzy systems, Proc. IEEE, 87(9) (1999), 1623{1640.
16
[9] W. Omlin, K. K. Thornber and K. K. Giles, Fuzzy nite-state automata can be deterministi-
17
cally encoded into recurrent neural networks, IEEE Trans. Fuzzy Syst., 5(1) (1998), 76{89.
18
[10] E. S. Santos, Realization of fuzzy languages by probabilistic, max-prod and maximin au-
19
tomata, Inform. Sci., 8 (1975), 39{53.
20
[11] S. P. Tiwari, A. K. Singh, S. Sharan and V. K. Yadav Bifuzzy core of fuzzy automata, Iranian
21
Journal of Fuzzy Systems, 12(2) (2015), 63{73.
22
[12] W. G. Wee, On generalization of adaptive algorithm and application of the fuzzy sets concept
23
to pattern classif ication, Ph.D. dissertation Purdue University, IN, 1967.
24
[13] M. M. Zahedi, M. Horry and Kh. Abolpor, Bifuzzy (General) topology on max-min general
25
fuzzy automata, Advanced in Fuzzy Mathematics, 3(1) (2008), 51{68.
26
ORIGINAL_ARTICLE
On metric spaces induced by fuzzy metric spaces
For a class of fuzzy metric spaces (in the sense of George and Veeramani) with an H-type t-norm, we present a method to construct a metric on a fuzzy metric space. The induced metric space shares many important properties with the given fuzzy metric space. Specifically, they generate the same topology, and have the same completeness. Our results can give the constructive proofs to some problems for fuzzy metric spaces in the literature, which are shown by examples in this paper.
http://ijfs.usb.ac.ir/article_2364_95750b4afd0e7c65b341f7f2c7bce7d7.pdf
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145
160
10.22111/ijfs.2016.2364
Fuzzy analysis
Complete metric spaces
Fuzzy metric
H-type t-norms
D.
Qiu
true
1
College of Mathematics and Physics,, Chongqing University of Posts and
Telecommunications,, Nanan, Chongqing, 400065, P. R. China
College of Mathematics and Physics,, Chongqing University of Posts and
Telecommunications,, Nanan, Chongqing, 400065, P. R. China
College of Mathematics and Physics,, Chongqing University of Posts and
Telecommunications,, Nanan, Chongqing, 400065, P. R. China
LEAD_AUTHOR
R.
Dong
true
2
College of Mathematics and Physics,, Chongqing University of Posts and
Telecommunications,, Nanan, Chongqing, 400065, P. R. China
College of Mathematics and Physics,, Chongqing University of Posts and
Telecommunications,, Nanan, Chongqing, 400065, P. R. China
College of Mathematics and Physics,, Chongqing University of Posts and
Telecommunications,, Nanan, Chongqing, 400065, P. R. China
AUTHOR
H.
Li
true
3
College of Mathematics and Physics,, Chongqing University of Posts and
Telecommunications,, Nanan, Chongqing, 400065, P. R. China
College of Mathematics and Physics,, Chongqing University of Posts and
Telecommunications,, Nanan, Chongqing, 400065, P. R. China
College of Mathematics and Physics,, Chongqing University of Posts and
Telecommunications,, Nanan, Chongqing, 400065, P. R. China
AUTHOR
[1] T. Altun and D. Mihet, Ordered non-archimedean fuzzy metric spaces and some xed point
1
results, Fixed Point Theory Appl., Article ID 782680, 2010, 11 pages.
2
[2] D. Burago, Y. Burago and S. Ivanov, A course in metric geometry, American Mathematical
3
Society, Ann Arbor, 2001.
4
[3] A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Set Syst., 64(2)
5
(1994), 395{399.
6
[4] A. George and P. Veeramani, On some results of analysis for fuzzy metric spaces, Fuzzy Set
7
Syst., 90(2) (1997), 365{368.
8
[5] M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Set Syst., 27(2) (1989), 385{389.
9
[6] V. Gregori, A. Lopez-Crevillen, S. Morillas and A. Sapena, On convergence in fuzzy metric
10
spaces, Topol. Appl., 156 (18) (2009), 3002{3006.
11
[7] V. Gregori, J. Mi~nana and S. Morillas, Some questions in fuzzy metric spaces, Fuzzy Set
12
Syst., 204(1) (2012), 71{85.
13
[8] V. Gregori, J. Mi~nana and S. Morillas, A note on local bases and convergence in fuzzy metric
14
spaces, Topol. Appl., 163 (15) (2014), 142{148.
15
[9] V. Gregori, S. Morillas and A. Sapena, On a class of completable fuzzy metric spaces, Fuzzy
16
Set Syst., 161(5) (2010), 2193{2205.
17
[10] V. Gregori, S. Morillas and A. Sapena, Examples of fuzzy metrics and applications, Fuzzy
18
Set Syst., 107(1) (2011), 95{111.
19
[11] V. Gregori and S. Romaguera, Some properties of fuzzy metric spaces, Fuzzy Set Syst.,
20
115(3) (2000), 485{489.
21
[12] V. Gregori and S. Romaguera, On completion of fuzzy metric spaces, Fuzzy Set Syst., 130
22
(3) (2002), 399{404.
23
[13] V. Gregori and S. Romaguera, Characterizing completable fuzzy metric spaces, Fuzzy Set
24
Syst., 144 (3) (2004), 411{420.
25
[14] V. Gregori and A. Sapena, On xed point theorems in fuzzy metric spaces, Fuzzy Set Syst.,
26
125 (2) (2002), 245{252.
27
[15] O. Hadzic and E. Pap, Fixed point theory in probabilistic metric spaces, Kluwer Academic
28
Publishers, Dordrecht, 2001.
29
[16] O. Kaleva and S. Seikkala, On fuzzy metric spaces, Fuzzy Set Syst., 12(1) (1984), 215{229.
30
[17] E. Klement, R. Mesiar and E. Pap, Triangular norms, Kluwer, Dordrecht (2000).
31
[18] I. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetika, 11(2)
32
(1975), 326{334.
33
[19] C. Li, On some results of metrics induced by a fuzzy ultrametric, Filomat, 27(6) (2013),
34
1133{1140.
35
[20] K. Menger, Statistical metrics, Proc. Natl. Acad. Sci. USA, 28(1) (1942), 535{537.
36
[21] D. Mihet, Fuzzy -contractive mappings in non-Archimedean fuzzy metric spaces, Fuzzy Set
37
Syst., 159(4) (2008), 739{744.
38
[22] E. Pap, O. Hadzio and R. Mesiar, A xed point theorem in probabilistic metric spaces and
39
applications in fuzzy set theory, J. Math. Anal. Appl., 202 (2) (1996), 433{449.
40
[23] D. Qiu and W. Zhang, The strongest t-norm for fuzzy metric spaces, Kybernetika,49 (1)
41
(2013), 141{148.
42
[24] D. Qiu, W. Zhang and C. Li, Extension of a class of decomposable measures using fuzzy
43
pseudometrics, Fuzzy Set Syst., 222(1) (2013), 33{44.
44
[25] V. Radu, Some suitable metrics on fuzzy metric spaces, Fixed Point Theory, 5 (2) (2004),
45
[26] A. Razani, A contraction theorem in fuzzy metric spaces, Fixed Point Theory Appl., 3(1)
46
(2005), 257{265.
47
[27] W. Rudin, Functional analysis, McGraw-Hill, New York, 1973.
48
[28] A. Sapena, A contribution to the study of fuzzy metric spaces, Appl. Gen. Topol., 2(1) (2001),
49
[29] P. Veeramani, Best approximation in fuzzy metric spaces, J. Fuzz. Math., 9(1) (2001), 75{80.
50
[30] L. A. Zadeh, Fuzzy sets,Inform Control., 8(2) (1965), 338{353.
51
ORIGINAL_ARTICLE
Persian-translation vol.13, no.2
http://ijfs.usb.ac.ir/article_2630_64fcd74af2b71ca479d7c69999b15d9a.pdf
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162
171
10.22111/ijfs.2016.2630