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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
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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
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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. 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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. 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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
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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. 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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
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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
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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
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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
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