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Cover for Volume.13, No.2
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Fuzzy multicriteria decision making method based on fuzzy structured element with incomplete weight information
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The fuzzy structured element (FSE) theory is a very useful toolfor dealing with fuzzy multicriteria 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.
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17


Xinfan
Wang
School of Science, Hunan University of Technology, Zhuzhou, Hunan,
412007, China
School of Science, Hunan University of Technology,
China


Jianqiang
Wang
School of Business, Central South University, Changsha, Hunan,
410083, China
School of Business, Central South University,
China


Xiaohong
Chen
School of Business, Central South University, Changsha, Hunan,
410083, China
School of Business, Central South University,
China
cxh@csu.edu.cn
Multicriteria decision making (MCDM)
Fuzzy structured element (FSE)
Inner product
Projection
Entropy
[[1] T. M. Apostol, Mathematical analysis, Second Edition, China Machine Press, Beijing, 2004.##[2] E. Cables, M. S. GarcaCascales and M. T. Lamata, The LTOPSIS: An alternative to TOP##SIS decisionmaking approach for linguistic variables, Expert Systems with Applications,##39(2) (2012), 21192126.##[3] H. Y. Chen and L. G. Zhou, An approach to group decision making with interval fuzzy prefer##ence relations based on induced generalized continuous ordered weighted averaging operator,##Expert Systems with Applications, 38(10) (2011), 1343213440.##[4] S. J. Chen and C. L. Hwang, Fuzzy Multiple Attribute Decision Making: Methods and Ap##plications, SpringerVerlag, Berlin, 1992.##[5] D. Dubois and H. Prade, Comment on tolerance analysis using fuzzy sets and a procedure##for multiple aspect decision making, International Journal of System Science, 9(3) (1978),##[6] D. Dubois and H. Prade, A review of fuzzy set aggregation connectives, Information Science,##36(1/2) (1985), 85121.##[7] J. Figueira, S. Greco and M. Ehrgott, Multiple Criteria Decision Analysis: State of the Art##Surveys, Springer, Boston, 2005.##[8] J. C. Fodor and M. Roubens, Fuzzy Preference Modeling and Multicriteria Decision Support,##Kluwer, Dordrecht, 1994. ##[9] S. Z. Guo, Method of structuring element in fuzzy analysis (I), Journal of Liaoning Technical##University, 21(5) (2002), 670673.##[10] S. Z. Guo, Method of structuring element in fuzzy analysis (II), Journal of Liaoning Technical##University, 21(6) (2002), 808810.##[11] S. Z. Guo, Principle of fuzzy mathematical analysis based on structured element, Northeastern##University Press, Shengyang, 2004.##[12] S. Z. Guo, Homeomorphic property between fuzzy number space and family of bounded mono##tone function, Advances in Natural Science, 14(11) (2004), 13181321.##[13] S. Z. Guo, Transformation group of monotone functions with same monotonic formal on [1,##1] and operations of fuzzy numbers, Fuzzy Systems and Mathematics, 19(3) (2005), 105110.##[14] S. Z. Guo, Commonly express method of fuzzyvalued function based on structured element,##Fuzzy Systems and Mathematics, 19(1) (2005), 8286.##[15] S. Z. Guo, Comparison and sequencing of fuzzy numbers based on the method of structured##element, Systems EngineeringTheory and Practice, 29(3) (2009), 106111.##[16] G. Jahanshahloo, F. Lot and M. Izadikhah, Extension of the TOPSIS method for decision##making problems with fuzzy data, Applied Mathematics and Computation, 181(2) (2006),##15441551.##[17] E. Jaynes, Information theory and statistical mechanics, Physical Reviews, 106(4) (1957),##[18] S. H. Kim, S. H. Choi and J. K. Kim, An interactive procedure for multiple attribute group##decision making with incomplete information: Rangebased approach, European Journal of##Operational Research, 118(1) (1999), 139152.##[19] S. H. Kim and B. S. Ahn, Interactive group decision making procedure under incomplete##information, European Journal of Operational Research, 116(3) (1999), 498507.##[20] D. F. Li, Fuzzy multiobjective manyperson decision makings and games, National Defense##Industry Press, Beijing, 2003.##[21] D. F. Li, Compromise ratio method for fuzzy multiattribute group decision making, Applied##Soft Computing, 7(3) (2007), 807817.##[22] R. J. Li, Theory and application of fuzzy multiple criteria decision making, Science Press,##Beijing, 2002.##[23] J. Lin, Fuzzy multiattribute decisionmaking method based on Hausdau distance, Journal##of Systems Engineering, 22(4) (2007), 367 372.##[24] T. S. Liou and M. J. Wang, Fuzzy weighted average: an improved algorithm, Fuzzy Sets and##Systems, 49(1) (1992), 307315.##[25] H. T. Liu and S. Z. Guo, Fuzzy multiattribute group decision making methods based on##structured element, Pattern Recognition and Articial Intelligence, 20(3) (2007), 343348.##[26] H. T. Liu and S. Z. Guo, Fuzzy linear programming with fuzzy variables based on structured##element method, Systems EngineeringTheory and Practice, 28(6) (2008), 94100.##[27] H. T. Liu and S. Z. Guo, The method of fuzzy multiattribute decision making based on##structured element and information entropy, Mathematics in Practice and Theory, 39(17)##(2009), 15.##[28] P. D. Liu and F. Jin, A multiattribute group decisionmaking method based on weighted##geometric aggregation operators of intervalvalued trapezoidal fuzzy numbers, Applied Math##ematical Modelling, 36(6) (2012), 24982509.##[29] P. D. Liu, X. Zhang and F. Jin, A multiattribute group decisionmaking method based on##intervalvalued trapezoidal fuzzy numbers hybrid harmonic averaging operators, Journal of##Intelligent and Fuzzy Systems, 23(5) (2012), 159168.##[30] J. M. Merig, Fuzzy multiperson decision making with fuzzy probabilistic aggregation opera##tors, International Journal of Fuzzy Systems, 13(3) (2011), 163174.##[31] J. M. Merig and M. Casanovas, The fuzzy generalized OWA operator and its application in##strategic decision making, Cybernetics and Systems, 41(5) (2010), 359370.##[32] J. M. Merig and A. M. GilLafuente, Fuzzy induced generalized aggregation operators and##its application in multiperson decision making, Expert Systems with Applications, 38(8)##(2011), 97619772. ##[33] C. Shannon, The mathematical theory of communication, The University of Illinois Press,##Urbana, 1949.##[34] L. Wang and S. Z. Guo, Linear formed fully fuzzy linear dierential systems, Systems##EngineeringTheory and Practice, 32(2) (2012), 341348.##[35] T. C. Wang and H. D. Lee, Developing a fuzzy TOPSIS approach based on subjective weights##and objective weights, Expert Systems with Applications, 36(5) (2009), 89808985.##[36] G. W. Wei, GRA method for multiple attribute decision making with incomplete weight##information in intuitionistic fuzzy setting, KnowledgeBased Systems, 23(3) (2010), 243##[37] G. W. Wei, FIOWHM operator and its application to multiple attribute group decision mak##ing, Expert Systems with Applications, 38(4) (2011), 29842989.##[38] G. W. Wei, X. F. Zhao and R. Lin, Some induced aggregating operators with fuzzy number##intuitionistic fuzzy information and their applications to group decision making, International##Journal of Computational Intelligence Systems, 3(1) (2010), 8495.##[39] Z. S. Xu, Method based on expected values for fuzzy multiple attribute decision making prob##lems with preference informationon alternatives, Systems EngineeringTheory and Practice,##24(1) (2004), 109113.##[40] Z. S. Xu, Fuzzy harmonic mean operators, International Journal of Intelligent Systems, 24(2)##(2009), 152172.##[41] Z. S. Xu and Q. L. Da, Projection method for uncertain multiattribute decision making with##preference information on alternatives, International Journal of Information Technology and##Decision Making, 3(3) (2004), 429434.##[42] J. Yang and W. H. Qiu, Method for multiattribute decisionmaking based on projection,##Control and Decision, 24(4) (2009), 637640.##[43] L. Z. Yue, Y. Yan and W. Q. Zhong, Solution of matrix fuzzy game based on structuring##element theory, Systems EngineeringTheory and Practice, 30(2) (2010), 272276.##[44] L. A. Zadeh, Fuzzy sets, Information and Control, 8(3) (1965), 338356.##[45] E. K. Zavadskas and Z. Turskis, Multiple criteria decision making (MCDM) methods in eco##nomics: an overview, Technological and Economic Development of Economy, 17(2) (2011),##[46] S. Z. Zeng, W. H. Su and A. Le, Fuzzy generalized ordered weighted averaging distance##operator and its application to decision making, International Journal of Fuzzy Systems,##14(3) (2012), 402412.##[47] J. J. Zhang, D. S. Wu and D. L. Olson, The method of grey related analysis to multiple at##tribute decision making problems with interval numbers, Mathematical and Computer Mod##elling, 42(9) (2005), 991998.##[48] Y. J. Zhang and J. X. Liu, Multiserver fuzzy queues based on fuzzy structured element,##Systems EngineeringTheory and Practice, 30(10) (2010), 18151821.##]
A NEW APPROACH BASED ON OPTIMIZATION OF RATIO FOR SEASONAL FUZZY TIME SERIES
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In recent years, many studies have been done on forecasting fuzzy time series. Firstorder fuzzy time series forecasting methods with firstorder lagged variables and highorder 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.
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Ufuk
Yolcu
Department of Statistics, Faculty of Science, Ankara University, 06100
Ankara, Turkey
Department of Statistics, Faculty of Science,
Turkey
uyolcu@ankara.edu.tr
Seasonal fuzzy time series
Optimization
Forecasting
Feed forward neural networks
[[1] C. H. Aladag, M. A. Basaran, E. Egrioglu, U. Yolcu and V. R. Uslu, Forecasting in high##order fuzzy time series by using neural networks to dene fuzzy relations, Expert Systems##with Applications, 36 (2009), 42284231.##[2] C. H. Aladag, U. Yolcu and E. Egrioglu, A high order fuzzy time series forecasting model##based on adaptive expectation and articial neural networks, Mathematics and Computers in##Simulation, 81 (2010), 875882.##[3] C. H. Aladag, E. Egrioglu, U. Yolcu and V. R. Uslu, A high order seasonal fuzzy time series##model and application to international tourism demand of Turkey, Journal of Intelligent and##Fuzzy Systems, 26 (2014), 295302.##[4] C. H. Aladag, U. Yolcu, E. Egrioglu and E. Bas, Fuzzy lagged variable selection in fuzzy time##series with genetic algorithms, Applied Soft Computing, 22 (2014), 465473.##[5] F. Alpaslan, O. Cagcag, C. H. Aladag, U. Yolcu and E. Egrioglu, A novel seasonal fuzzy time##series method, Hacettepe Journal of Mathematics and Statistics, 41 (2012), 375385.##[6] E. Bas, V. R. Uslu, U. Yolcu and E. Egrioglu, A modied genetic algorithm for forecasting##fuzzy time series, Applied Intelligence, 41 (2014), 453463.##[7] G. E. P. Box and G. M. Jenkins, Time series analysis: Forecasting and control. CA: Holdan##Day, San Francisco, 1976. ##[8] O. Cagcag Yolcu, A Hybrid Fuzzy Time Series Approach Based on Fuzzy Clustering and##Articial Neural Network with Single Multiplicative Neuron Model, Mathematical Problems##in Engineering, Article ID 560472, 2013 (2013), 9 pages.##[9] S. M. Chen, Forecasting enrollments based on fuzzy timeseries, Fuzzy Sets and Systems, 81##(1996), 31131.##[10] S. M. Chen, Forecasting enrolments based on high order fuzzy time series, Cybernetics and##Systems, 33 (2002), 116.##[11] S. M. Chen and N. Y. Chung, Forecasting enrolments using high order fuzzy time series and##genetic algorithms, International Journal of Intelligent Systems, 21 (2006), 485501.##[12] C. H. Cheng, T. L. Chen, H. J. Teoh and C. H. Chiang, Fuzzy timeseries based on adaptive##expectation model for TAIEX forecasting, Expert Systems with Applications, 34 (2008),##11261132.##[13] C. H. Cheng, G. W. Cheng and J. W. Wang, Multiattribute fuzzy time series method based##on fuzzy clustering, Expert Systems with Applications, 34 (2008), 12351242.##[14] S. Davari, M. H. F. Zarandi and I. B. Turksen, An Improved fuzzy time series forecasting##model based on particle swarm intervalization, The 28th North American Fuzzy Information##Processing Society Annual Conferences (NAFIPS 2009), Cincinnati, Ohio, USA, June 1417,##[15] E. Egrioglu, PSObased high order time invariant fuzzy time series method: Application to##stock exchange data, Economic Modelling, 38 (2014), 633639.##[16] E. Egrioglu, C. H. Aladag, U. Yolcu, M. A. Basaran and V. R. Uslu, A new hybrid approach##based on SARIMA and partial high order bivariate fuzzy time series forecasting model, Expert##Systems with Applications, 36 (2009), 74247434.##[17] E. Egrioglu, C. H. Aladag, U. Yolcu, V. R. Uslu and M. A. Basaran, A new approach based##on articial neural networks for high order multivariate fuzzy time series, Expert Systems##with Applications, 36 (2009), 1058910594.##[18] E. Egrioglu, C. H. Aladag, U. Yolcu, V. R. Uslu and M. A. Basaran, Finding an optimal##interval length in high order fuzzy time series, Expert Systems with Applications, 37 (2010),##50525055.##[19] E. Egrioglu, C. H. Aladag, M. A. Basaran, V. R. Uslu and U. Yolcu, A New Approach Based##on the Optimization of the Length of Intervals in Fuzzy Time Series, Journal of Intelligent##and Fuzzy Systems, 22 (2011), 1519.##[20] E. Egrioglu, C. H. Aladag, U. Yolcu, V. R. Uslu and N. A. Erilli, Fuzzy Time Series Forecast##ing Method Based on GustafsonKessel Fuzzy Clustering, Expert Systems with Applications,##38 (2011), 1035510357.##[21] E. Egrioglu, U. Yolcu, C. H. Aladag and C. Kocak, An ARMA Type Fuzzy Time Series##Forecasting Method Based on Particle Swarm Optimization, Mathematical Problems in En##gineering, Article ID 935815, 2013 (2013), 12 pages.##[22] S. Gunay, E. Egrioglu and C. H. Aladag, Introduction to univariate time series analysis.##Hacettepe University Press, Ankara Turkey, 2007.##[23] L. Y. Hsu, S. J. Horng, T. W. Kao, Y. H. Chen, R. S. Run, R. J. Chen, J. L. Lai and I.##H. Kuo, Temperature prediction and TAIFEX forecasting based on fuzzy relationships and##MTPSO techniques, Expert Systems with Application, 37 (2010), 27562770.##[24] K. Huarng, Eective length of intervals to improve forecasting in fuzzy timeseries, Fuzzy##Sets and Systems, 123 (2001a), 387394.##[25] K. Huarng and H. K. Yu, Ratiobased lengths of intervals to improve fuzzy time series fore##casting, IEEE Trans. Syst. Man Cybern. B, Cybern., 36 (2006), 328340.##[26] K. Huarng and H. K. Yu, The application of neural networks to forecast fuzzy time series,##Physica A, 363 (2006), 481491.##[27] M. Khashei, S. R. Hejazi and M. Bijari, A new hybrid articial neural networks and fuzzy##regression model for time series forecasting, Fuzzy Sets and Systems, 159(7) (2008), 769786.##[28] I. H. Kuo, S. J. Horng, T. W. Kao, T. L. Lin, C. L. Lee and Y. Pan, An improved method for##forecasting enrollments based on fuzzy time series and particle swarm optimization, Expert##Systems with Application, 36 (2009), 61086117. ##[29] I. H. Kuo, S. J. Horng, Y. H. Chen, R. S. Run, T. W. Kao, R. J. Chen, J. L. Lai and T.##L. Lin, Forecasting TAIFEX based on fuzzy time series and particle swarm optimization,##Expert Systems with Application, 37 (2010), 14941502.##[30] L. W. Lee, L. H. Wang and S. M. Chen, Temperature prediction and TAIFEX forecasting##based on fuzzy logical relationships and genetic algorithms, Expert Systems with Applications,##33 (2007), 539550.##[31] K. Levenberg, A Method for the Solution of Certain NonLinear Problems in Least Squares,##The Quarterly of Applied Mathematics, 2 (1944), 164168.##[32] D. W. Marquardt, An algorithm for leastsquares estimation of nonlinear parameters, Journal##of the Society for Industrial and Applied Mathematics, 11 (1963), 431441.##[33] J. I. Park, D. J. Lee, C. K. Song and M. G. Chun, TAIFEX and KOSPI 200 forecasting##based on two factors high order fuzzy time series and particle swarm optimization, Expert##Systems with Application, 37 (2010), 959967.##[34] Q. Song, Seasonal forecasting in fuzzy time series, Fuzzy Sets and Systems, 107 (1999),##[35] Q. Song and B. S. Chissom, Fuzzy time series and its models, Fuzzy Sets and Systems, 54##(1993), 269277.##[36] Q. Song and B. S. Chissom, Forecasting enrollments with fuzzy time series Part I, Fuzzy##Sets and Systems, 54 (1993), 110.##[37] Q. Song and B. S. Chissom, Forecasting enrollments with fuzzy time series Part II, Fuzzy##Sets and Systems, 62 (1994), 18.##[38] U. Yolcu, E. Egrioglu, V. R. Uslu, M. A. Basaran and C. H. Aladag, A new approach for##determining the length of intervals for fuzzy time series, Applied Soft Computing, 9(2)##(2009), 647651.##[39] U. Yolcu, C. H. Aladag, E. Egrioglu and V. R. Uslu, Time series forecasting with a novel##fuzzy time series approach: an example for Istanbul stock market, Journal of Statistical##Computation and Simulation, 83(4) (2013), 597610.##[40] H. K. Yu, Weighted fuzzy time series models for TAIEX forecasting, Physica A, 349 (2005),##[41] H. K. Yu and K. Huarng, A bivariate fuzzy time series model to forecast TAIEX, Expert##Systems with Applications, 34 (2008), 29452952.##[42] H. K. Yu and K. Huarng, A neural network based fuzzy time series model to improve fore##casting, Expert Systems with Application, 37 (2010), 33663372.##[43] L. A. Zadeh, Fuzzy Sets, Inform and Control, 8 (1965), 338353.##[44] G. P., Zhang, B. E., Patuwo and Y. M. Hu, Forecasting with articial neural networks: The##state of the art, International Journal of Forecasting, 14 (1998), 35{62.##[45] J. M. Zurada, Introduction of articial neural systems. St. Paul: West Publishing, (1992),##]
A Hybrid Multiattribute Group Decision Making Method Based on Grey Linguistic 2tuple
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Because of the complexity of decisionmaking environment, the uncertainty of fuzziness and the uncertainty of grey maybe coexist in the problems of multiattribute group decision making. In this paper, we study the problems of multiattribute 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 multiattribute group decision making method based on grey linguistic 2tuple. Concretely, the concept of grey linguistic 2tuple is defined based on the traditional linguistic 2tuple, and the transformation methods of transforming the precise values, interval numbers and linguistic fuzzy variables into the grey linguistic 2tuples are presented respectively. Further, a new grey linguistic 2tuple 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 2tuple 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.
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Congjun
Rao
School of Science, Wuhan University of Technology, Wuhan 430070,
P. R. China
School of Science, Wuhan University of Technology,
China
cjrao@foxmail.com


Junjun
Zheng
School of Economics and Management, Wuhan University, Wuhan
430072, P. R. China
School of Economics and Management, Wuhan
China
jjzhengwhu@foxmail.com


Cheng
Wang
School of Mathematics and Economics, Hubei University of Education,
Wuhan 430072, P. R. China
School of Mathematics and Economics, Hubei
China
wangc80@163.com


Xinping
Xiao
School of Science, Wuhan University of Technology, Wuhan 430070,
P. R. China
School of Science, Wuhan University of Technology,
China
Hybrid multiattribute group decision making
Grey linguistic 2tuple
GLTWA operator
Grey 2tuple correlation degree
[[1] G. Bordogna, M. Fedrizzi and G. Pasi, A linguistic modeling of consensus in group decision##making based on OWA operators, IEEE Transactions on Systems, Man and Cybernetics, Part##A: Systems and Humans, 27 (1997), 126132.##[2] R. Degani and G. Bortolan, The problem of linguistic approximation in clinical decision##making, International Journal of Approximate Reasoning, 2 (1988), 143162.##[3] M. Delgado, J. L. Verdegay and M. A. Vila, On aggregation operators of linguistic labels,##International Journal of Intelligent Systems, 8 (1993), 351370.##[4] J. L. Deng, Grey system theory, Huazhong University of Science & Technology Press, Wuhan,##[5] Y. C. Dong, Y. F. Xu, H. Y. Li and B. Feng, The OWAbased consensus operator under##linguistic representation models using position indexes, European Journal of Operational##Research, 203 (2010), 455463.##[6] H. Doukas, A. Tsiousi, V. Marinakis and J. Psarras, Linguistic multicriteria decision making##for energy and environmental corporate policy, Information Sciences, 258 (2014), 328338.##[7] F. J. Estrella, M. Espinilla, F. Herrera and L. Martnez, FLINTSTONES: A fuzzy linguis##tic decision tools enhancement suite based on the 2tuple linguistic model and extensions,##Information Sciences, 280 (2014), 152170.##[8] Y. B. Gong, N. Hu, J. G. Zhang, G. F. Liu and J. G. Deng, Multiattribute group decision##making method based on geometric Bonferroni mean operator of trapezoidal interval type2##fuzzy numbers, Computers & Industrial Engineering, 81 (2015), 167176.##[9] Y. D. He, H. Y. Chen, Z. He and L. G. Zhou, Multiattribute decision making based on neutral##averaging operators for intuitionistic fuzzy information, Applied Soft Computing, 27 (2015),##[10] F. Herrera and E. HerreraViedma, Aggregation operators for linguistic weighted information,##IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans, 27##(1997), 646656.##[11] F. Herrera and L. Martnez, A 2tuple fuzzy linguistic representation model for computing##with words, IEEE Transactions on Fuzzy Systems, 8(6) (2000), 746752.##[12] F. Herrera and L. Martnez, A model based on linguistic 2Tuples for dealing with multigran##ular hierarchical linguistic contexts in multiexpert decisionmaking, IEEE Transactions on##Systems, Man, and CyberneticsPart B: Cybernetics, 31(2) (2001), 227234.##[13] F. Herrera, L. Martnez and P. J. Sanchez, Managing nonhomogeneous information in group##decisionmaking, European Journal of Operational Research, 166(1) (2005), 115132.##[14] C. W. Hsu, T. C. Kuo, S. H. Chen and A. H. Hu, Using DEMATEL to develop a carbon man##agement model of supplier selection in green supply chain management, Journal of Cleaner##Production, 56 (2013), 164172.##[15] Y. B. Ju and A. H. Wang, Extension of VIKOR method for multicriteria group decision##making problem with linguistic information, Applied Mathematical Modelling, 37 (2013),##31123125. ##[16] Y. B. Ju, A. H. Wang and X. Y. Liu, Evaluating emergency response capacity by fuzzy##AHP and 2tuple fuzzy linguistic approach, Expert Systems with Applications, 39 (2012),##69726981.##[17] A. Kumar, V. Jain and S. Kumar, A comprehensive environment friendly approach for sup##plier selection, Omega, 42 (2014), 109123.##[18] J. B. Lan, Q. Sun, Q. M. Chen and Z. X. Wang, Group decision making based on induced##uncertain linguistic OWA operators, Decision Support Systems, 55 (2013), 296303.##[19] J. Lin, Q. Zhang and F. Y. Meng, An approach for facility location selection based on optimal##aggregation operator, KnowledgeBased Systems, 85 (2015), 143158.##[20] B. S. Liu, Y. H. Shen, X. H. Chen, Y. Chen and X. Q. Wang, A partial binary tree DEA##DA cyclic classication model for decision makers in complex multiattribute largegroup##intervalvalued intuitionistic fuzzy decisionmaking problems, Information Fusion, 18 (2014),##[21] H. C. Liu, J. X. You, C. Lu and M. M. Shan, Application of interval 2tuple linguistic##MULTIMOORA method for healthcare waste treatment technology evaluation and selection,##Waste Management, 34 (2014), 23552364.##[22] S. Liu, F. T. S. Chan and W. X. Ran, Multiattribute group decisionmaking with multi##granularity linguistic assessment information: An improved approach based on deviation##and TOPSIS, Applied Mathematical Modelling, 37 (2013), 1012910140.##[23] P. D. Liu and F. Jin, A multiattribute group decisionmaking method based on weighted##geometric aggregation operators of intervalvalued trapezoidal fuzzy numbers, Applied Mathematical##Modelling, 36 (2012), 24982509.##[24] P. D. Liu and Y. M. Wang, Multiple attribute group decision making methods based on##intuitionistic linguistic power generalized aggregation operators, Applied Soft Computing,##17 (2014), 90104.##[25] L. Martnez and F. Herrera, An overview on the 2tuple linguistic model for computing with##words in decision making: Extensions, applications and challenges, Information Sciences,##207 (2012), 118.##[26] F. Y. Meng, X. H. Chen and Q. Zhang, Some intervalvalued intuitionistic uncertain linguistic##Choquet operators and their application to multiattribute group decision making, Applied##Mathematical Modelling, 38 (2014), 25432557.##[27] J. M. Merigo, M. Casanovas and L. Martnez, Linguistic aggregation operators for linguistic##decision making based on the DempsterShafer theory of evidence, International Journal of##Uncertainty, Fuzziness and KnowledgeBased Systems, 18(3) (2010), 287304.##[28] J. M. Merigo and A. M. GilLafuente, Induced 2tuple linguistic generalized aggregation op##erators and their application in decisionmaking, Information Sciences, 236 (2013), 116.##[29] J. H. Park, J. M. Park and Y. C. Kwun, 2Tuple linguistic harmonic operators and their##applications in group decision making, KnowledgeBased Systems, 44 (2013), 1019.##[30] J. I. Pelaez and J. M. Do~na, LAMA: a linguistic aggregation of majority additive operator,##International Journal of Intelligent Systems, 18 (2003), 809820.##[31] B. Peng, C. M. Ye and S. Z. Zeng, Uncertain pure linguistic hybrid harmonic averaging oper##ator and generalized interval aggregation operator based approach to group decision making,##KnowledgeBased Systems, 36 (2012), 175181.##[32] C. J. Rao, M. Goh, Y. Zhao, J. J. Zheng, Location selection of city logistics centers under##sustainability, Transportation Research Part D: Transport and Environment,36(2015),2944.##[33] C. J. Rao and J. Peng, Fuzzy group decision making model based on credibility theory and##gray relative degree, International Journal of Information Technology & Decision Making,##8(3) (2009), 515527.##[34] C. J. Rao and J. Peng, Group decision making model based on grey relational analysis, The##Journal of Grey System, 21(1) (2009), 1524.##[35] C. J. Rao and Y. Zhao, Multiattribute auction method based on grey relational degree of##hybrid sequences, The Journal of Grey System, 21(2) (2009), 175184.##[36] C. J. Rao and Y. Zhao, Multiattribute decision making model based on optimal membership##and relative entropy, Journal of Systems Engineering and Electronics, 20(3) (2009), 537542. ##[37] Z. F. Tao, H. Y. Chen, X. Song, L. G. Zhou and J. P. Liu, Uncertain linguistic fuzzy soft##sets and their applications in group decision making, Applied Soft Computing, 34 (2015),##[38] I. Truck, Comparison and links between two 2tuple linguistic models for decision making,##KnowledgeBased Systems, (2015), In Press.##[39] S. P. Wan, Power average operators of trapezoidal intuitionistic fuzzy numbers and applica##tion to multiattribute group decision making, Applied Mathematical Modelling, 37 (2013),##41124126.##[40] S. P. Wan, 2Tuple linguistic hybrid arithmetic aggregation operators and application to##multiattribute group decision making, KnowledgeBased Systems, 45 (2013), 3140.##[41] S. P. Wan, Q. Y. Wang and J. Y. Dong, The extended VIKOR method for multiattribute##group decision making with triangular intuitionistic fuzzy numbers, KnowledgeBased Systems,##52 (2013), 6577.##[42] S. P. Wan and J. Y. Dong, Intervalvalued intuitionistic fuzzy mathematical programming##method for hybrid multicriteria group decision making with intervalvalued intuitionistic##fuzzy truth degrees, Information Fusion, 26 (2015), 4965.##[43] S. P. Wan and J. Y. Dong, Power geometric operators of trapezoidal intuitionistic fuzzy##numbers and application to multiattribute group decision making, Applied Soft Computing,##29 (2015), 153168.##[44] S. Y. Wang, Applying 2tuple multigranularity linguistic variables to determine the supply##performance in dynamic environment based on productoriented strategy, IEEE Transactions##on Fuzzy Systems, 16 (2008), 2939.##[45] J. H.Wang and J. Y. Hao, An approach to aggregation of ordinal information in multicriteria##multiperson decision making using Choquet integral of Fubini type, Fuzzy Optimization and##Decision Making, 8 (2009), 365380.##[46] J. Q. Wang, J. Wang, Q. H. Chen, H. Y. Zhang and X. H. Chen, An outranking approach for##multicriteria decisionmaking with hesitant fuzzy linguistic term sets, Information Sciences,##280 (2014), 338351.##[47] J. Q. Wang, P. Lu, H. Y. Zhang and X. H. Chen, Method of multicriteria group decision##making based on cloud aggregation operators with linguistic information, Information Sciences,##274 (2014), 177191.##[48] W. Z. Wang and X. W. Liu, The multiattribute decision making method based on interval##valued intuitionistic fuzzy Einstein hybrid weighted geometric operator, Computers and Mathematics##with Applications, 66 (2013), 18451856.##[49] G. W. Wei, Uncertain linguistic hybrid geometric mean operator and its application to group##decision making under uncertain linguistic environment, International Journal of Uncertainty,##Fuzziness and KnowledgeBased Systems, 17 (2009), 251267.##[50] G. W. Wei, A method for multiple attribute group decision making based on the ETWG and##ETOWG operators with 2tuple linguistic information, Expert Systems with Applications,##37 (2010), 78957900.##[51] G. W. Wei, Grey relational analysis model for dynamic hybrid multiple attribute decision##making, KnowledgeBased Systems, 24 (2011), 672679.##[52] G. W. Wei, Grey relational analysis method for 2tuple linguistic multiple attribute group##decision making with incomplete weight information, Expert Systems with Applications, 38##(2011), 48244828.##[53] G. W. Wei, Hesitant fuzzy prioritized operators and their application to multiple attribute##decision making, KnowledgeBased Systems, 31 (2012), 176182.##[54] G. W. Wei and X. F. Zhao, Some dependent aggregation operators with 2tuple linguistic in##formation and their application to multiple attribute group decision making, Expert Systems##with Applications, 39 (2012), 58815886.##[55] J. Wu and Y. J. Liu, An approach for multiple attribute group decision making problems with##intervalvalued intuitionistic trapezoidal fuzzy numbers, Computers & Industrial Engineering,##66 (2013), 311324.##[56] X. P. Xiao and S. H. Mao, Grey forecast and decision method, Science Press, Beijing, 2013. ##[57] Z. S. Xu, EOWA and EOWG operators for aggregating linguistic labels based on linguistic##preference relations, International Journal of Uncertainty, Fuzziness and KnowledgeBased##Systems, 12 (2004), 791810.##[58] Z. S. Xu, Induced uncertain linguistic OWA operators applied to group decision making,##Information Fusion, 7 (2006), 231238.##[59] Z. S. Xu, An approach based on the uncertain LOWG and the induced uncertain LOWG op##erators to group decision making with uncertain multiplicative linguistic preference relations,##Decision Support Systems, 41 (2006), 488499.##[60] Z. S. Xu and R. R. Yager, Powergeometric operators and their use in group decision making,##IEEE Transactions on Fuzzy Systems, 18(1) (2010), 94105.##[61] Z. S. Xu and X. L. Zhang, Hesitant fuzzy multiattribute decision making based on TOPSIS##with incomplete weight information, KnowledgeBased Systems, 52 (2013), 5364.##[62] Y. J. Xu, F. Ma, F. F. Tao and H. M. Wang, Some methods to deal with unacceptable##incomplete 2tuple fuzzy linguistic preference relations in group decision making, Knowledge##Based Systems, 56 (2014), 179190.##[63] Y. J. Xu, J. M. Merigo and H. M. Wang, Linguistic power aggregation operators and their##application to multiple attribute group decision making, Applied Mathematical Modelling,##36(11) (2012), 54275444.##[64] Y. J. Xu, P. Shi, J. M. Merig0 and H. M. Wang, Some proportional 2tuple geometric ag##gregation operators for linguistic decision making, Journal of Intelligent & Fuzzy Systems,##25(3) (2013), 833843.##[65] W. Yang and Z. P. Chen, New aggregation operators based on the Choquet integral and 2tuple##linguistic information, Expert Systems with Applications, 39 (2012), 26622668.##[66] F. Ye and Y. Li, An extended TOPSIS model based on the Possibility theory under fuzzy##environment, KnowledgeBased Systems, 67 (2014), 263269.##[67] X. Y. You, J. X. You, H. C. Liu and L. Zhen, Group multicriteria supplier selection using an##extended VIKOR method with interval 2tuple linguistic information, Expert Systems with##Applications, 42 (2015), 19061916.##[68] H. M. Zhang, Some intervalvalued 2tuple linguistic aggregation operators and application##in multiattribute group decision making, Applied Mathematical Modelling, 37 (2013), 4269##[69] L. G. Zhou and H. Y. Chen, The induced linguistic continuous ordered weighted geometric##operator and its application to group decision making, Computers & Industrial Engineering,##66 (2013), 222232.##]
A FUZZYBASED SPEED CONTROLLER FOR IMPROVEMENT OF INDUCTION MOTOR'S DRIVE PERFORMANCE
2
2
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 (proportionalintegrator) controllers are usually used as speed controller. Adjusting the gain of PI controller is timeconsuming which needs thorough considerations. Hence, fuzzy controllers are proposed to overcome such problems. In this paper, firstly drive of a threephase 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.
1

61
70


H.
AsgharpourAlamdari
Department of Electrical Engineering, Semnan University, Semnan, Iran
Department of Electrical Engineering, Semnan
Iran


Y.
AlinejadBeromi
Department of Electrical Engineering, Semnan University, Semnan, Iran
Department of Electrical Engineering, Semnan
Iran


H.
Yaghobi
Department of Electrical Engineering, Semnan University, Semnan, Iran
Department of Electrical Engineering, Semnan
Iran
Induction Motor
Speed Control
PI controller
Fuzzy Logic Controller
[[1] M. N. Afrozi, M. Hassanpour, A. Naebi and S. Hassanpour, Simulation and Optimization of##asynchronous AC motor control by Particle Swarm Optimization (PSO) and Emperor Algo##rithm, In Computer Modeling and Simulation (EMS), 2011 Fifth UKSim European Sympo##sium , IEEE, (2011), 251256.##[2] A. AlOdienat and A. AlLawama, The advantages of PID fuzzy controllers over the conven##tional types, American Journal of Applied Sciences 5(6) (2008), 653658.##[3] D. Asija, Speed control of induction motor using fuzzyPI controller, 2nd International Con##ference In Mechanical and Electronics Engineering (ICMEE), 2(460) (2010).##[4] F. Barrero, et al, Speed control of induction motors using a novel fuzzy slidingmode structure,##Fuzzy Systems, IEEE Transactions on, 10(3) (2002), 375383.##[5] E. Bim, Fuzzy optimization for rotor constant identication of an indirect FOC induction##motor drive, Industrial Electronics, IEEE Transactions, 48(6) (2001), 12931295.##[6] V. Chitra and R. S. Prabhakar, Induction motor speed control using fuzzy logic controller,##World Academy of Science, Engineering and Technology, (23) (2006),1722.##[7] R. Dhobale and D. M. Chandwadkar, FPGA Implementation of ThreePhase Induction Mo##tor Speed Control Using Fuzzy Logic and Logic Based PWM, International Conference on##Recent Trends in Engineering & Technology, (2012), 185189.##[8] A. Goedtel, I. N. Silva and P. J. A. Serni, Load torque identication in induction motor using##neural networks technique, Electric Power Systems Research, 77(1) (2007), 3545.##[9] H. E. Kalhoodashti and M. Hahbazian, Hybrid Speed Control of Induction Motor using PI##and Fuzzy Controller, International Journal of Computer Applications, 30(11) (2011), 4450.##[10] P. Kumar, V. Agarwal and A. K. Singh, Design of fuzzy PI controller for CSI Fed induction##motor drive, International Journal of Electrical and Electronic System Research, 1(4)(2011),##[11] F. Lima, et al,, Peed neurofuzzy estimator applied to sensorless induction motor contro,##Latin America Transactions, IEEE (Revista IEEE America Latina), 10(5) (2012), 20652073.##[12] A. Lokriti, et al, Induction motor speed drive improvement using fuzzy IPselftuning con##troller. A real time implementation, ISA transactions, 52(3) (2013), 406417. ##[13] M. A. Mannan, et al, Fuzzylogic based speed control of induction motor considering core loss##into account, Intelligent Control and Automation, (2012), 229235.##[14] D. Rai, S. Sharma and V. Bhuria, Fuzzy speed controller design of three phase induction mo##tor, International Journal of Emerging Technology and Advanced Engineering, 5(2)( 2012),##[15] C. Raj, S. Thanga, P. Srivastava and P. Agarwal, Energy ecient control of threephase##induction motora review, International Journal of Computer and Electrical Engineering,##1(1) (2009), 17931808.##[16] L. Ramesh, S. P. Chowdhury, S. Chowdhury, A. K. Saha and Y. H. Song, Eciency op##timization of induction motor using a fuzzy logic based optimum ##ux search controller, In##Power Electronics, Drives and Energy Systems, 2006. PEDES'06. International Conference,##(2006), 16.##[17] A. Sudhakar and M. V. Kumar, , A comparative analysis of PI and neuro fuzzy controllers##in direct torque control of induction motor drives, Int. J. Eng. Res, 2(4) (2012), 672680.##[18] P. Tripura and Y. S. K. Babu, Fuzzy logic speed control of three phase induction motor drive,##World Academy of Science, Engineering and Technology, 60(3) (2011), 13711375.##[19] M. N. Uddin, and H. Wen, Development of a selftuned neurofuzzy controller for induction##motor drives, Industry Applications, IEEE Transactions , 43(4) (2007), 11081116.##[20] F. Zidani, et al, A fuzzybased approach for the diagnosis of fault modes in a voltagefed PWM##inverter induction motor drive, Industrial Electronics, IEEE Transactions, 55(2) (2008), 586##[21] F. Zidani, et al, A fuzzy technique for loss minimization in scalarcontrolled induction motor,##Electric Power Components and Systems, 30(6) (2002), 625635.##]
Alternating Regular Tree Grammars in the Framework of LatticeValued Logic
2
2
In this paper, two different ways of introducing alternation for latticevalued (referred to as {L}valued) regular tree grammars and {L}valued topdown tree automata are compared. One is the way which defines the alternating regular tree grammar, i.e., alternation is governed by the nonterminals 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 topdown tree automaton {LAA}). The second way is taken over to define a new type of automaton by combining the {L}valued alternating topdown tree automaton with stack, called {L}valued alternating stack tree automaton {LASA} and the generative power of it is compared to some wellknown 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}.
1

71
94


Maryam
Ghorani
Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran
Faculty of Mathematical Sciences, Shahrood
Iran
maryamghorani@gmail.com


Mohammad Mehdi
Zahedi
Department of Mathematics, Graduate University of Advanced Technology, Kerman, Iran
Department of Mathematics, Graduate University
Iran
zahedi_mm@kgut.ac.ir
Latticevalued logic
Alternating topdown tree automaton
State alternating regular tree grammar
Alternating stack tree automaton
[[1] A. Bouhoula, J. P. Jouannaud and J. Meseguer, Specication and proof in membeship equa##tional logic, Theoretical Computer Science, 236 (2000), 35132.##[2] G. Birkho, Lattice theory, American Mathematical Society Colloquium Publications, New##York, 1984.##[3] S. Bozapalidis and O. L. Bozapalidoy, Fuzzy tree language recognizability, Fuzzy Sets and##Systems, 161(5) (2010), 716734.##[4] J. R. Buchi, Weak secondorder arithmetic and nite automata, Zeitschrift fur Mathematische##Logik und Grundlagen der Mathematik, 6 (1960), 6692.##[5] Y. Cao, L. Xia and M. Ying, Probabilistic automata for computing with words, Journal of##Computer and System Sciences, 79(1) (2013), 152172.##[6] A. K. Chandra, D. C. Kozen and L. J. Stockmeyer, Alternation, Journal of the ACM, 28(1)##(1981), 114133.##[7] S. R. Chaudhari and M. N. Joshi, A note on fuzzy tree automata, International Journal of##Computer Applications, 56(17) (2012), 15.##[8] H. Comon, M. Dauchet, R. Gilleron, F. Jacquemard, D. Lugiez, C. Loding, S. Ti##son and M. Tommasi, Tree automata: technigues and applications, 2007. Available:##http://tata.gforge.inria.fr.##[9] Z. Esik and G. Liu, Fuzzy tree automata, Fuzzy Sets and Systems, 158 (2007), 14501460.##[10] B. Finkbeiner and H. Sipma, Checking nite traces using alternating automata, Formal Meth##ods in System Design, 24(2) (2004), 101127.##[11] F. Gecseg and M. Steinby, Tree automata, Akademiai Kiado, Budapest, 1984. ##[12] M. Ghorani and M. M. Zahedi, Characterization of complete residuated latticevalued nite##tree automata, Fuzzy Sets and Systems, 199 (2012), 2846.##[13] M. Ghorani, M. M. Zahedi and R. Ameri, Algebraic properties of complete residuated lattice##valued tree automata, Soft Computing, 16 (2012), 17231732.##[14] J. E. Hopcroft, R. Motwani and J. D. Ullman, Introduction to automata theory, languages##and computation, 3rd edition, AddisonWesley, 2006.##[15] H. Hosoya, J. Vouillon and B. C. Pierce, Regular expression types for XML, ACM Transac##tions on Programming Languages and Systems, 27(1) (2005), 4690.##[16] J. Ignjatovic, M. Ciric and S. Bogdanovic, Determinization of fuzzy automata with member##ship values in complete residuated lattices, Information Sciences, 178 (2008), 164180.##[17] J. Jin, Q. Li and Y. Li, Algebraic properties of Lfuzzy nite automata, Information Science,##234 (2013), 182202.##[18] D. Kirsten, Alternating tree automata and parity games, In: E. Gradel (Ed.), Automata,##Logics, and Innite Games, SpringerVerlag, Berlin, 2002.##[19] R. E. Ladner, R. J. Lipton and L. J. Stockmeyer, Alternating pushdown automata, Proceeding##of 19th FOCS, IEEE Computer Society Press, Silver Spring, (1978), 92106.##[20] R. E. Ladner, R. J. Lipton and L. J. Stockmeyer, Alternating pushdown and stack automata,##SIAM Journal on Computing, 13 (1984), 135155.##[21] E. T. Lee and L. A. Zadeh, Note on fuzzy languages, Information Sciences, 1 (1969), 421434.##[22] H. X. Lei and Y. Li, Minimization of states in automata theory based on nite latticeordered##monoids, Information Sciences, 177 (2007), 14131421.##[23] Y. M. Li and W. Pedrycz, Minimization of lattice nite automata and its application to the##decomposition of lattice languages, Fuzzy Sets and Systems, 158(13) (2007), 14231436.##[24] L. Li and D. Qiu, On the state minimization of fuzzy automata, IEEE Transaction on Fuzzy##Systems, 23(3) (2015), 434  443.##[25] Y. Li and Q. Wang, The universal fuzzy automata, Fuzzy Sets and Systems, 249 (2014),##[26] F. Lin and H. Ying, Modeling and control of fuzzy discrete event systems, IEEE Trans. Syst.,##Man, Cybern. B, Cybern., 32 (2002), 408 415.##[27] J. N. Mordeson and D. S. Malik, Fuzzy automata and languages: theory and applications,##Chapman & Hall CRC, London, Boca Raton, 2002.##[28] E. Moriya, A grammatical characterization of alternating pushdown automata, Theoretical##Computer Science, 67 (1989), 7585.##[29] E. Moriya, D. Hofbauer, M. Huber and F. Otto, On statealternating contextfree grammars,##Theoretical Computer Science, 337 (2005), 183216.##[30] E. Moriya and F. Otto, Two ways of introducing alternation into contextfree grammars and##pushdown automata, IEICE Transactions on Information and Systems, E90D(6) (2007),##[31] E. Moriya and F. Otto, On alternating phrasestructure grammars, In: C. MartinVide, F.##Otto and H. Fernau (Eds.), Language and Automata Theory and Applications, Springer##Verlag Berlin, Heidelberg, 2008.##[32] C. W. Omlin, K. K. Thornber and C. L. Giles, Fuzzy nitestate automata can be determin##istically encoded in recurrent neural networks, IEEE Trans. Fuzzy Syst., 5 (1998), 7689.##[33] W. Pedrycz and A. Gacek, Learning of fuzzy automata, International Journal of Computa##tional Intelligence and Applications, 1 (2001), 1933.##[34] D. W. Qiu, Automata theory based on completed residuated latticevalued logic (I), Science##in China (Series F), 44 (2001), 419{429.##[35] D. W. Qiu, Automata theory based on completed residuated latticevalued logic (II), Science##in China (Series F), 45 (2002), 442{452.##[36] D. W. Qiu, Characterizations of fuzzy nite automata, Fuzzy Sets and Systems, 141 (2004),##[37] D. W. Qiu, Supervisory control of fuzzy discrete event systems: a formal approach, IEEE##Transactions on Systems, Man and CyberneticsPart B, 35(1) (2005), 7288. ##[38] D. W. Qiu, Pumping lemma in automata theory based on complete residuated latticevalued##logic: a note, Fuzzy Sets and Systems, 157 (2006), 21282138.##[39] E. S. Santos, Maximin automata, Inform. and Control, 12 (1968), 367377.##[40] G. Slutzki, Alternating tree automata, In: G. Goos and J. Hartmanis (Eds.), 8th colloquium##Laquila Proceeding on Trees in Algebra and Programming, SpringerVerlag, Berlin, 1983.##[41] G. Slutzki, Alternating tree automata, Theorical Computer Science, 41 (1985), 305318.##[42] J. Tang, Y. Fang and J. G. Tang, The latticevalued Turing machines and the latticevalued##type 0 grammars, Mathematical Problems in Engineering, 2014 (2014), 16.##[43] M. G. Thomason and P. N. Marinos, Deterministic acceptors of regular fuzzy languages,##IEEE Trans. Syst., Man, Cybern., 4 (1974), 228230.##[44] M. Y. Vardi, Alternating automata and program verication, In: J. Van Leeuwen (Ed.),##Computer Science Today, Recent Trends and Developments, SpringerVerlag, Berlin, 1995.##[45] M. Y. Vardi, An automatatheoretic approach to linear temporal logic, In: F. Moller and##G. Birtwistle (Eds.): Logics for Concurrency: Structure versus Automata, SpringerVerlag,##Berlin, 1996.##[46] M. Y. Vardi, Alternating automata: checking truth and validity for temporal logics, Proceding##of the 14th Int. Conference on Automated Deduction, SpringerVerlag, Berlin, 1997.##[47] K. N. Verma and J. GoubaultLarrecq, Alternating twoway ACtree automata, Information##and Computation, 205 (2007), 817869.##[48] W. G. Wee and K. S. Fu, A formulation of fuzzy automata and its application as a model of##learning systems, IEEE Trans. Systems Man Cybern., 5 (1969), 215223.##[49] T. Wilke, Alternating tree automata, parity games, and modal calculus, Bulletin of the##Belgian Mathematical SocietySimon Stevin, 8(2) (2001), 359391.##[50] L. Wu and D. W. Qiu, Automata theory based on completed residuated latticevalued logic:##reduction and minimization, Fuzzy Sets and Systems, 161 (2010), 16351656.##[51] H. Y. Xing and D. W. Qiu, Pumping lemma in contextfree grammar theory based on complete##residuated latticevalued logic, Fuzzy Sets and Systems, 160 (2009), 11411151.##[52] H. Y. Xing, D. W. Qiu and F. C. Liu, Automata theory based on complete residuated lattice##valued logic: pushdown automata, Fuzzy Sets and Systems, 160 (2009), 11251140.##[53] H. Y. Xing, D. W. Qiu, F. C. Liu and Z. J. Fan, Equivalence in automata theory based on##complete residuated latticevalued logic, Fuzzy Sets and Systems, 158 (2007), 14071422.##]
Algebraic Properties of Intuitionistic Fuzzy Residuated Lattices
2
2
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.
1

95
109


Farnaz
Ghanavizi Maroof
Department of Mathematics, Faculty of Mathematics and
Compute, Shahid Bahonar University of Kerman, 7616914111, Kerman, Iran
Department of Mathematics, Faculty of Mathematics
Iran
farnaz.ghanavizi@yahoo.com


Esfandiar
Eslami
Department of Mathematics, Faculty of Mathematics and Com
pute, Shahid Bahonar University of Kerman, 7616914111, Kerman, Iran
Department of Mathematics, Faculty of Mathematics
Iran
esfandiar.eslami@uk.ac.ir
Intuitionstic fuzzy residuated lattice
Heyting algebra
Relative Stone lattice
Glivenko residuated lattice
MV (MTL
SRL)algebra
[[1] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87{96.##[2] K. T. Atanassov and S. Stoeva, Intuitionistic Lfuzzy sets, in:R.Trapple (ed.), Elsevier##Science Publishers B.V., North Holland, 1984.##[3] K. T. Atanassov and G. Gargov, Elements of intuitionistic fuzzy logic. part I, Fuzzy Sets and##Systems, 145 (1998), 267{277.##[4] P. Burillo and H. Bustince, Intuitionistic fuzzy relations. eects of Atanassov's operators##on the properties of Intuitionistic Fuzzy relations, Mathware and Soft Computing, 2 (1995),##[5] G. Cattaneo and D. Ciucci, Basic intuitionistic principles in fuzzy set theories and its##extensions (A terminological debate on Atanassov IFS), Fuzzy Sets and Systems, 24 (2006),##3198{3219.##[6] R. Cignoli and F. Esteva, Commutative integral bounded residuated lattices with an added##involution, Annals of Pure and Applied Logic, 171 (2009), 150{170.##[7] C. Cornelis and G. Deschrijver and E. E. Kerre, Classication on intuitionistic fuzzy impli##cators: an algebraic approach, In Proceedings of the FT & T' 02, Durham, North Carolina,##[8] D. Dubois and S. Gottwald and P. Hajek and J. Kacprzyk and H. Prade, Terminological dif##culties in fuzzy set theory The case of "Intuitionistic Fuzzy Sets", Fuzzy Sets and Systems,##156 (2005), 485{491.##[9] G. Deschrijver and C. Cornelis and E. E. Kerre, Intuitionistic fuzzy connectives revisited, In##proceedings of IPMU'02, 2002.##[10] E. Eslami, An algebraic structure for Intuitionistic Fuzzy Logic, Iranian Journal of Fuzzy##Systems, 9(6) (2012), 31{41.##[11] E. Eslami and W. PengYung, More on intutionistic fuzzy residuated lattices, Journal of##MultipleValued Logic and Soft Computing, 20(3) (2013), 335{352. ##[12] E. Eslami and F. Ghanavizi Maroof, A Proposed axiomatic system for atanassov intuition##istic fuzzy logic (AIFL), Notes on Intuitionistic Fuzzy Sets, 19(3) (2013), 1{14.##[13] P. Hajek, Metamathematics of fuzzy logic, Trends in Logic, Kluwer Academic Publishers,##Drdrecht, 1998.##[14] Y. Hong and X. Ruiping and F. Xianwen, Characterizing ordered semigroups by means of##Intuitionistic Fuzzy Bi ideals, Mathware and Soft Computing, 14 (2007), 57{66.##[15] M. Kondo, Note on strict residuated lattices with an involutive negation, AAA80 Workshop##on General Algebra& Workshop on Non classical algebraic Structures, Bedlewo, Poland, 16##june, 2010.##[16] C. Muresan, Dense elements and classes of a residuated lattices, Bull. Math. Soc. Sci. Math.##Roumanie Tome, 53(1) (2010), 11{24.##[17] H. Ono, Substructural logics and residuated lattices  an introduction, Trends in Logic,##(2003), 177{212.##[18] D. Piciu, Algebras of fuzzy logic, Craiova: Ed universtaria, 2007.##[19] E. Szmidt and K. Marta, Atanassov's intuitionistic fuzzy sets in classication of imbalanced##and overlapping classes. intelligent techniques and tools for novel system architectures, Studies##in Computational Intelligence (SCI), 109 (2008), 455{471.##[20] A. Tepavcevic and M. G. Ranitovic, General form of lattice valued intuitionistic fuzzy sets,##Computational Intelligence, Theory and Applications, Springer Berlin Heidelberg, Germany,##(2006), 375{381.##[21] A. Tepavcevic and T. Gerstenkorn, Lattice valued intuitionistic fuzzy sets, Central European##Journal of Mathematics, 2(3) (2004), 388{398.##[22] G. Takeuti and S. Titani, Intuitionistic fuzzy logic and intuitionistic fuzzy set theory, Journal##of Symbolic Logic, 49(3) (1984), 851{866.##]
Width invariant approximation of fuzzy numbers
2
2
In this paper, we consider the width invariant trapezoidal and triangularapproximations of fuzzy numbers. The presented methods avoid the effortful computation of KarushKuhnTucker 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.
1

111
130


Alireza
Khastan
Department of Mathematics, Institute for Advanced Studies in
Basic Sciences, Zanjan, Iran
Department of Mathematics, Institute for
Iran
khastan@iasbs.ac.ir


Zahra
Moradi
Department of Mathematics, Institute for Advanced Studies in Basic
Sciences, Zanjan, Iran
Department of Mathematics, Institute for
Iran
zahramoradi@iasbs.ac.ir
Extended trapezoidal fuzzy numbers
Trapezoidal approximations
Triangular approximations
Width
Expected value
[[1] S. Abbasbandy and M. Amirfakhrian, The nearest approximation of a fuzzy quantity in##parametric form, Applied Mathematics and Computation, 172 (2006), 624–632.##[2] S. Abbasbandy and M. Amirfakhrian, The nearest trapezoidal form of a generalized left right##fuzzy number, International Journal of Approximate Reasoning, 43 (2006), 166–178.##[3] S. Abbasbandy and B. Asady, The nearest trapezoidal fuzzy number to a fuzzy quantity,##Applied Mathematics and Computation, 156 (2004), 381–386.##[4] S. Abbasbandy and T. Hajjari, Weighted trapezoidal approximationpreserving core of a fuzzy##number, Computers and Mathematics with Applications, 59 (2010),3066–3077.##[5] T. Allahviranloo and M. Adabitabar Firozja, Note on "Trapezoidal approximation of fuzzy##numbers", Fuzzy Sets and Systems, 158 (2007), 755–756.##[6] A. I. Ban, Approximation of fuzzy numbers by trapezoidal fuzzy numbers preserving the##expected interval, Fuzzy Sets and Systems, 159 (2008), 13271344.##[7] A. I. Ban, Trapezoidal and triangular approximations of fuzzy numbersinadvertences and##corrections, Fuzzy Sets and Systems, 160 (2009), 30483058.##[8] A. I. Ban, A. Brandas, L. Coroianu, C. Negrutiu and O. Nica, Approximations of fuzzy##numbers by trapezoidal fuzzy numbers preserving the ambiguity and value, Computers and##Mathematics with Applications, 61 (2011), 13791401.##[9] A. I. Ban and L. Coroianu, Translation invariance and scale invariance of approximations of##fuzzy numbers, in: 7th Conference of the European Society for Fuzzy Logic and Technology,##AixLesBains, 1822 July 2011.##[10] A. I. Ban and L. Coroianu, Nearest interval, triangular and trapezoidal approximation of##a fuzzy number preserving ambiguity, International Journal of Approximate Reasoning, 53##(2012), 805–836.##[11] A.I. Ban, L. Coroianu, Existence, uniqueness and continuity of trapezoidal approximations##of fuzzy numbers under a general condition, Fuzzy Sets and Systems, 257(2014), 322.##[12] A. Brandas, Approximation of fuzzy numbers by trapezoidal fuzzy numbers preserving the##core, the ambiguity and the value, Advanced Studies in Contemporary Mathematics, 21##(2011), 247259.##[13] S. Bodjanova, Median value and median interval of a fuzzy number, Information Sciences,##172 (2005), 7389.##[14] S. Chanas, On the interval approximation of a fuzzy number, Fuzzy Sets and Systems, 122##(2001), 353356.##[15] L. Coroianu, M. Gagolewski and P. Grzegorzewski, Nearset piecewise linear approximation##of fuzzy numbers, Fuzzy Sets and Systems, 233 (2013), 2651.##[16] P. Diamond and P. Kloeden, Metric spaces of fuzzy sets, theory and applications, World##Scientific, Singapore, 1994.##[17] D. Dubois and H. Prade, Operations on fuzzy numbers, Int. J. Syst. Sci., 30 (1978), 613626.##[18] D. Dubois, H. Prade, The mean value of a fuzzy number, Fuzzy Sets and Systems, 24 (1987),##[19] P. Grzegorzewski, Metrics and orders in space of fuzzy numbers, Fuzzy Sets and Systems, 97##(1998), 8394.##[20] P. Grzegorzewski, Nearest interval approximation of a fuzzy number, Fuzzy Sets and Systems,##130 (2002), 321330.##[21] P. Grzegorzewski, E. Mr´owka, Trapezoidal approximations of fuzzy numbers, Fuzzy Sets and##Systems, 153 (2005), 115135.##[22] P. Grzegorzewski, E. Mr´owka, Trapezoidal approximations of fuzzy numbersrevisited, Fuzzy##Sets and Systems, 158 (2007), 757768.##[23] S. Heilpern, The expected value of a fuzzy number, Fuzzy Sets and Systems, 47 (1992) 8186.##[24] W. Rudin, Real and Complex Analysis, McGrawHill, New York, 1986.##[25] C. T. Yeh, A note on trapezoidal approximation of fuzzy numbers, Fuzzy Sets and Systems,##158 (2007), 747754. ##[26] C. T. Yeh, On improving trapezoidal and triangular approximations of fuzzy numbers, International##Journal of Approximate Reasoning, 48 (2008), 297313.##[27] C. T. Yeh, Trapezoidal and triangular approximations preserving the expected interval, Fuzzy##Sets and Systems, 159 (2008), 1345–1353.##[28] C. T. Yeh, Weighted trapezoidal and triangular approximations of fuzzy numbers, Fuzzy Sets##and Systems, 160 (2009), 3059–3079.##[29] C. T. Yeh, Weighted semitrapezoidal approximations of fuzzy numbers, Fuzzy Sets and Systems,##165 (2011), 6180.##[30] C. T. Yeh, H. M. Chu, Approximations by LRtype fuzzy numbers, Fuzzy Sets and Systems,##257 (2014) 2340.##[31] W. Zeng, H. Li, Weighted triangular approximation of fuzzy numbers, International Journal##of Approximate Reasoning, 46 (2007), 137–150.##]
Irreducibility on General Fuzzy Automata
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2
The aim of this paper is the study of a covering of a maxmingeneral fuzzy automaton by another, admissible relations, admissiblepartitions of a maxmin general fuzzy automaton,$tilde{delta}$orthogonality of admissible partitions, irreduciblemaxmin general fuzzy automata. Then we obtain the relationshipsbetween them.
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Mohammad
Horry
Shahid Chamran University of Kerman, Kerman, Iran
Shahid Chamran University of Kerman, Kerman,
Iran
(General) Fuzzy automata
Equivalence relation
Admissible relation
Admissible partition
Irreducibility
[[1] M. Doostfatemeh and S. C. Kremer, New directions in fuzzy automata, International Journal##of Approximate Reasoning, 38 (2005), 175{214.##[2] M. Horry and M. M. Zahedi, Fuzzy subautomata of an invertible general fuzzy automaton,##Annals of fuzzy sets, fuzzy logic and fuzzy systems, 2(2) (2013), 29{47.##[3] J. Jin, Q. Li and Y. Li, Algebric properties of Lfuzzy nite automata, Information Sciences,##234 (2013), 182202.##[4] Y. Li and W. Pedrycz, Fuzzy nite automata and fuzzy regular expressions with membership##values in latticeordered monoids, Fuzzy Sets and Systems, 156 (2005), 68{92.##[5] J. N. Mordeson and D. S. Malik, Fuzzy automata and languages, theory and applications,##Chapman and Hall/CRC, London/Boca Raton, FL, 2002. ##[6] D. S. Malik, J. N. Mordeson and M. K. Sen, On subsystems of fuzzy nite state machines,##Fuzzy Sets and Systems, 68 (1994), 83{92.##[7] M. Mizumoto, J. Tanaka and K. Tanaka, Some consideration on fuzzy automata, J. Compute.##Systems Sci., 3 (1969), 409{422.##[8] W. Omlin, K. K. Giles and K. K. Thornber, Equivalence in knowledge representation: au##tomata, rnns, and dynamic fuzzy systems, Proc. IEEE, 87(9) (1999), 1623{1640.##[9] W. Omlin, K. K. Thornber and K. K. Giles, Fuzzy nitestate automata can be deterministi##cally encoded into recurrent neural networks, IEEE Trans. Fuzzy Syst., 5(1) (1998), 76{89.##[10] E. S. Santos, Realization of fuzzy languages by probabilistic, maxprod and maximin au##tomata, Inform. Sci., 8 (1975), 39{53.##[11] S. P. Tiwari, A. K. Singh, S. Sharan and V. K. Yadav Bifuzzy core of fuzzy automata, Iranian##Journal of Fuzzy Systems, 12(2) (2015), 63{73.##[12] W. G. Wee, On generalization of adaptive algorithm and application of the fuzzy sets concept##to pattern classif ication, Ph.D. dissertation Purdue University, IN, 1967.##[13] M. M. Zahedi, M. Horry and Kh. Abolpor, Bifuzzy (General) topology on maxmin general##fuzzy automata, Advanced in Fuzzy Mathematics, 3(1) (2008), 51{68.##]
On metric spaces induced by fuzzy metric spaces
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2
For a class of fuzzy metric spaces (in the sense of George and Veeramani) with an Htype tnorm, 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.
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145
160


D.
Qiu
College of Mathematics and Physics,, Chongqing University of Posts and
Telecommunications,, Nanan, Chongqing, 400065, P. R. China
College of Mathematics and Physics,, Chongqing
China


R.
Dong
College of Mathematics and Physics,, Chongqing University of Posts and
Telecommunications,, Nanan, Chongqing, 400065, P. R. China
College of Mathematics and Physics,, Chongqing
China


H.
Li
College of Mathematics and Physics,, Chongqing University of Posts and
Telecommunications,, Nanan, Chongqing, 400065, P. R. China
College of Mathematics and Physics,, Chongqing
China
Fuzzy analysis
Complete metric spaces
Fuzzy metric
Htype tnorms
[[1] T. Altun and D. Mihet, Ordered nonarchimedean fuzzy metric spaces and some xed point##results, Fixed Point Theory Appl., Article ID 782680, 2010, 11 pages.##[2] D. Burago, Y. Burago and S. Ivanov, A course in metric geometry, American Mathematical##Society, Ann Arbor, 2001.##[3] A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Set Syst., 64(2)##(1994), 395{399.##[4] A. George and P. Veeramani, On some results of analysis for fuzzy metric spaces, Fuzzy Set##Syst., 90(2) (1997), 365{368.##[5] M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Set Syst., 27(2) (1989), 385{389.##[6] V. Gregori, A. LopezCrevillen, S. Morillas and A. Sapena, On convergence in fuzzy metric##spaces, Topol. Appl., 156 (18) (2009), 3002{3006.##[7] V. Gregori, J. Mi~nana and S. Morillas, Some questions in fuzzy metric spaces, Fuzzy Set##Syst., 204(1) (2012), 71{85.##[8] V. Gregori, J. Mi~nana and S. Morillas, A note on local bases and convergence in fuzzy metric##spaces, Topol. Appl., 163 (15) (2014), 142{148.##[9] V. Gregori, S. Morillas and A. Sapena, On a class of completable fuzzy metric spaces, Fuzzy##Set Syst., 161(5) (2010), 2193{2205.##[10] V. Gregori, S. Morillas and A. Sapena, Examples of fuzzy metrics and applications, Fuzzy##Set Syst., 107(1) (2011), 95{111.##[11] V. Gregori and S. Romaguera, Some properties of fuzzy metric spaces, Fuzzy Set Syst.,##115(3) (2000), 485{489.##[12] V. Gregori and S. Romaguera, On completion of fuzzy metric spaces, Fuzzy Set Syst., 130##(3) (2002), 399{404.##[13] V. Gregori and S. Romaguera, Characterizing completable fuzzy metric spaces, Fuzzy Set##Syst., 144 (3) (2004), 411{420.##[14] V. Gregori and A. Sapena, On xed point theorems in fuzzy metric spaces, Fuzzy Set Syst.,##125 (2) (2002), 245{252.##[15] O. Hadzic and E. Pap, Fixed point theory in probabilistic metric spaces, Kluwer Academic##Publishers, Dordrecht, 2001.##[16] O. Kaleva and S. Seikkala, On fuzzy metric spaces, Fuzzy Set Syst., 12(1) (1984), 215{229.##[17] E. Klement, R. Mesiar and E. Pap, Triangular norms, Kluwer, Dordrecht (2000).##[18] I. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetika, 11(2)##(1975), 326{334.##[19] C. Li, On some results of metrics induced by a fuzzy ultrametric, Filomat, 27(6) (2013),##1133{1140.##[20] K. Menger, Statistical metrics, Proc. Natl. Acad. Sci. USA, 28(1) (1942), 535{537.##[21] D. Mihet, Fuzzy contractive mappings in nonArchimedean fuzzy metric spaces, Fuzzy Set##Syst., 159(4) (2008), 739{744.##[22] E. Pap, O. Hadzio and R. Mesiar, A xed point theorem in probabilistic metric spaces and##applications in fuzzy set theory, J. Math. Anal. Appl., 202 (2) (1996), 433{449.##[23] D. Qiu and W. Zhang, The strongest tnorm for fuzzy metric spaces, Kybernetika,49 (1)##(2013), 141{148.##[24] D. Qiu, W. Zhang and C. Li, Extension of a class of decomposable measures using fuzzy##pseudometrics, Fuzzy Set Syst., 222(1) (2013), 33{44. ##[25] V. Radu, Some suitable metrics on fuzzy metric spaces, Fixed Point Theory, 5 (2) (2004),##[26] A. Razani, A contraction theorem in fuzzy metric spaces, Fixed Point Theory Appl., 3(1)##(2005), 257{265.##[27] W. Rudin, Functional analysis, McGrawHill, New York, 1973.##[28] A. Sapena, A contribution to the study of fuzzy metric spaces, Appl. Gen. Topol., 2(1) (2001),##[29] P. Veeramani, Best approximation in fuzzy metric spaces, J. Fuzz. Math., 9(1) (2001), 75{80.##[30] L. A. Zadeh, Fuzzy sets,Inform Control., 8(2) (1965), 338{353.##]
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