Issue:About the intuitionistic fuzzy set generators

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Title of paper: About the intuitionistic fuzzy set generators Author(s): Humberto Bustince Departamento de Automatica y Computación, Public University of Navarra, 31006, Campus Arrosadía, Pamplona, Spain bustince@si.upna.es Victoria Mohedano Departamento de Automatica y Computación, Public University of Navarra Presented at: 5th ICIFS, Sofia, 18—19 Oct. 1997 Published in: "Notes on Intuitionistic Fuzzy Sets", Volume 3 (1997) Number 4, pages 21—27 Download:  PDF (301  Kb, File info) Abstract: In this paper form the definition of Intuitionistic Fuzzy Sets we analyze the Intuitionistic fuzzy Generators and the Complementation in these sets. We start by defining the intuitionistic fuzzy generators in order to then study the particular cases for which this definition coincides with the fuzzy complementation. Afterwards, we analyse the existence of equilibrium points, dual points and we present characterization theorems of intuitionistic fuzzy generators. Lastly, we study a manner of constructing intuitionistic fuzzy sets and analyse the structure of the complementary of intuitionistic fuzzy sets built. Keywords: Intuitionistic fuzzy set, Intuitionistic fuzzy complementary, Fuzzy negation, Intuitionistic fuzzy generator References: C. Alsina, E. Trillas, L. Valverde, On some logical connectives for Fuzzy Sets Theory, J. Math. An. and Appl., 93 (1983) 15-26. K. Atanassov, Intuitionistic fuzzy sets, Fuzzy sets and Systems, 20 (1986), 87-96. K. Atanassov, Review and new results on intuitionistic fuzzy sets, IM-MFAIS, 1 (1988). K. Atanassov, Two operators on intuitionistic fuzzy sets, Comptes rendus de l'Academi bulgare des Sciences, Tome 41, 5 (1988). P. Burillo, H. Bustince , Construction theorems for intuitionistic fuzzy sets, will be published in Fuzzy Sets and Systems, 84 (1996) P. Burillo, H. Bustince, Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets, Fuzzy Sets and Systems, 78 (1996) 305-316. P. Burillo, H. Bustince , Intuitionistic fuzzy relations (Part I), Mathware and Soft Computing, 2 (1995) 5-38. P. Burillo and H. Bustince, Estructuras algebraicas en conjuntos IFS, II Congreso Nacional de Lógica y Tecnologia Fuzzy, Boadilla del Monte, Madrid, Spain (1992) 135-147. H. Bustince, Conjuntos Intuicionistas e Intervalo valorados Difusos: Propiedades y Construcción. Relaciones Intuicionistas Fuzzy. Thesis, Universidad Publica de Navarra (1994). H. Bustince, P. Burillo, Correlation of interval-valued intuitionistic fuzzy sets, Fuzzy sets and Systems, 74 (1995) 237-244. H. Bustince, P. Burillo, Structures on intuitionistic fuzzy relations, Fuzzy sets and Systems, 78 (1996) 293-303. M. Sugeno, Theory of fuzzy integrals and its applications. Thesis. Tokyo Institute of Technology (1974). E. Trillas, Sobre funciones de negacion en la teoria de conjuntos difusos, Stochasstica, III-1 (1979) 47-59. E. Trillas, C. Alsina, J.M. Terricabras, Introducción a la lógica borrosa, Ariel Matematica, (1995). R. Yager, On On a general class of fuzzy connectives, Fuzzy Sets and Systems, 4 (1980) 338-353. R. Yager, On the measure of fuzziness and negation. Part I: Membership in the unit interval, Intern. J. of General Systems, 5 (1979) 221-229. Citations: The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.