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From Trillas’ Negations and Antonyms to a Set Representation of Contradiction Within Bipolar and Other Extensions of Fuzzy Sets

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Abstract
In 1979, Enric Trillas started to interest in in fuzzy connectives. His first paper on this topic was ”Funciones de negacin en la teora de subconjuntos difusos” ([9]) (Negation functions in the theory of fuzzy subsets), which appeared in Spanish in the Stochastica journal. This work, focused on the characterization of strong negations, has been so relevant for the development of fuzzy theory that it was translated into English and widely cited in the last 35 years
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A Festschrift book to Enric Trillas Ruiz
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Aisbett, J., Rickard, J.T., Morgenthaler, D.G.: Type-2 Fuzzy Sets as Functions on Spaces. IEEE Transactions on Fuzzy Systems 18(4), 841–844 (2010) Atanassov, K.T.: Intuitionistic fuzzy sets, VII ITKR’s Session, Sofia, (deposed in Central Science-Technical Library of Bulgarian academy of Science, 1697/1984) (1983) Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets and Systems 20, 87–96 (1986) Atanassov, K.T., Gargov, G.: Interval valued intuitionistic fuzzy sets. Fuzzy Sets and Systems 31(3), 343–349 (1989) Atanassov, K.T.: Answer to D. Dubois, S. Gottwald, P. Hajek, J. Kacprzyk and H. Prade’s paper Terminological difficulties in fuzzy set theory - the case of Intuitionistic fuzzy sets. Fuzzy Sets and Systems 156(3), 496–499 (2005) Bustince, H., Burillo, P.: Vague sets are intuitionistic fuzzy sets. Fuzzy Sets and Systems 79, 403–405 (1996) Bustince, H., Barrenechea, E., Pagola, M.: Generation of interval-valued fuzzy and Atanassov’s intuitionistic fuzzy connectives from fuzzy connectives and from K(alpha) operators. Laws for conjunctions and disjunctions. Amplitude. International Journal of Intelligent Systems 23, 680–714 (2008) Bustince, H., Montero, J., Pagola, M., Barrenechea, E., Gómez, D.: A survey on interval-valued fuzzy sets. In: Pedrycz, W., Skowron, A., Kreinovichedrycz, V. (eds.) Handbook of Granular Computing, ch. 22. John Wiley and Sons, New York (2008) Bustince, H., Herrera, F., Montero, J.: Fuzzy Sets and Their Extensions: Representation, Aggregation and Models. STUDFUZZ, vol. 220. Springer, Heidelberg (2008) Cacioppo, J.T., Gardner, W.L., Bernston, G.G.: Beyond bipolar conceptualization and measures The case of attitudes and evaluative space. Personality and Social Psychology Review 1(1), 3–25 (1997) Cornelis, C., Arieli, O., Deschrijver, G., Kerre, E.E.: Uncertainty modeling by bilattice-based squares and triangles. IEEE Transactions on Fuzzy Systems 15(2), 161–175 (2007) Deng, J.L.: Introduction to grey system theory. Journal of Grey Systems 1, 1–24 (1989) Deschrijver, G., Kerre, E.E.: On the position of Intuitionistic fuzzy set theory in the framework of theories modelling imprecision. Information Sciences 177, 1860–1866 (2007) Dubois, D., Prade, H.: An introduction to bipolar representations of information and preference. International Journal of Intelligent Systems 23, 866–877 (2008) Dubois, D., Ostasiewicz, W., Prade, H.: Fuzzy sets: history and basic notions. In: Dubois, D., Prade, H. (eds.) Fundamentals of Fuzzy Sets, pp. 80–93. Kluwer Academic Publishers, Dordrecht (2000) Dubois, D., Gottwald, S., Hajek, P., Kacprzyk, J., Prade, H.: Terminological difficulties in fuzzy set theory – The case of “Intuitionistic Fuzzy Sets”. Fuzzy sets and Systems 156(3), 485–491 (2005) Gau, W.L., Buehrer, D.J.: Vague sets. IEEE Transactions on Systems Man and Cybernetics 23(2), 610–614 (1993) Goguen, J.: L-fuzzy sets. Journal of Mathematical Analysis and Applications 18, 145–174 (1967 ) Harding, J., Walker, C., Walker, E.: The variety generated by the truth value algebra of type-2 fuzzy sets. Fuzzy Sets and Systems 161(5), 735–749 (2010)View ArticleMATHMathSciNet Karnik, N.N., Mendel, J.M.: Operations on type-2 fuzzy sets. Fuzzy Sets Systems 122, 327–348 (2001) Klir, G., Yuan, B.: Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice Hall, Upper Saddle River (1995)MATH Lee, K.M.: Bipolar-valued fuzzy sets and their operations. In: Proc. Int. Conf. on Intelligent Technologies, Bangkok, Thailand, pp. 307–312 (2000) Lee, K.M.: Comparison of interval-valued fuzzy sets, intuitionistic fuzzy sets, and bipolar-valued fuzzy sets. J. Fuzzy Logic Intelligent Systems 14, 125–129 (2004) Mendel, J.M.: Advances in type-2 fuzzy sets and systems. Information Sciences 177, 84–110 (2007) Mizumoto, M., Tanaka, K.: Some properties of fuzzy sets of type 2. Information and Control 31, 312–340 (1976) Montero, J., Gomez, D., Bustince, H.: On the relevance of some families of fuzzy sets. Fuzzy Sets Systems 158, 2429–2442 (2007) Osgood, C.E., Suci, G.J., Tannenbaum, P.H.: The measurement of meaning. University of Illinois Press, Urbana (1957) Öztürk, M., Tsoukiás, A.: Modelling uncertain positive and negative reasons in decision aiding. Decision Support Systems 43(4), 1512–1526 (2007) Patrascu, V.: Multi-valued Color Representation Based on Frank t-norm Properties. In: Proc. IPMU 2008, Málaga, Spain, June 22-27, pp. 1215–1222 (2008) Pradea, A., Trillas, E.: Aggregation, Non-Contradiction and Excluded-Middle. Mathware and Soft Computing XIII, 189–201 (2006) Pradea, A., Trillas, E.: A Aggregation operators from the ancient NC and EM point of view. Kybernetika 42, 243–260 (2006) Sambuc, R.: Fonctions ϕ-flues. Application á l’aide au diagnostic en pathologie thryoidienne. PhD. Thesis, Université de Marseille, France (1975) Slovic, P., Peters, E., Finucane, M.L., MacGregor, D.G.: Affect, risk, and decision making. Health Psychology 24(4), S35–S40 (2005) Smarandache, F.: A unifying field in logics: neutrosophic logic. Multiple-Valued Logic 8(3), 385–438 (2002) Szmidt, E., Kacprzyk, J.: Using intuitionistic fuzzy sets in group decision making. Control and Cybernetics 31(4), 1037–1053 (2002) Torra, V., Miyamoto, S., Endo, Y.: On intuitionistic fuzzy clustering for its application to privacy. In: Conference Information: IEEE International Conference on Fuzzy Systems, Hong Kong, Peoples R China, IEEE International Conference on Fuzzy Systems, 1–5, 1042–1048 (2008) Xu, Z.S., Chen, J.A., Wu, J.J.: Clustering algorithm for intuitionistic fuzzy sets. Information Sciences 178(19), 3775–3790 (2008) Torres-Blanc, C., Cubillo, S., Castineira, E.: An axiomatic model for measuring contradiction and N-contradiction between two AIFSs. Information Sciences 180(6), 834–845 (2010) Trillas, E.: Sobre funciones de negación en la teoria de los conjuntos difusos. Stochastica 3(1), 47–59 (1979) Turksen, I.B., Bilgic, T.: Interval valued strict preference with Zadeh triples. Fuzzy Sets and Systems 78(2), 183–195 (1996) Ye, J.: Fuzzy decision-making method based on the weighted correlation coefficient under intuitionistic fuzzy environment. European Journal of Operational Research 205(1), 202–204 (2010) Zhang, W.R.: NPN Fuzzy Sets and NPN Qualitative Algebra: A Computational Framework for Bipolar Cognitive Modeling and Multiagerit Decision Analysis. IEEE Transactions on Systems, Man, and Cybernetics-part B: Cybernetics 26(4),561–574 (1996) Zhang, W.R.: Bipolar logic and bipolar fuzzy partial orderings for clustering and coordination. In: Proc. of 6th Joint Conference on Information Sciences, North Carolina, USA, March 8-13, pp. 85–88 (2002) Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–353 (1965) Zadeh, L.A.: Quantitative fuzzy semantics. Information Sciences 3, 159–176 (1971b