论文信息 - Supplementarity measures on fuzzy sets

Supplementarity measures on fuzzy sets

In this paper, we commence the study of the so called supplementarity measures. They are introduced axiomatically and are then related to incompatibility measures by antonyms. To do this, we have to establish what we mean by antonymous measure. We then prove that, under certain conditions, supplementarity and incompatibility measuresare antonymous. Besides, with the aim of constructing antonymous measures, we introduce the concept of involution on the set made up of all the ordered pairs of fuzzy sets. Finally, we obtain some antonymous supplementarity measures from incompatibility measures by means of involutions.

[1] M. J. Frank,et al. Associative Functions: Triangular Norms And Copulas , 2006 .

[2] Francesc Esteva,et al. Sobre funciones de negación en [0,1]. , 1980 .

[3] Lotfi A. Zadeh,et al. Fuzzy Sets , 1996, Inf. Control..

[4] Elena Castiñeira,et al. Measuring incompatibility between Atanassov's intuitionistic fuzzy sets , 2010, Inf. Sci..

[5] C. A. Català. A reflection on what is a membership function , 1999 .

[6] Radko Mesiar,et al. Triangular Norms , 2000, Trends in Logic.

[7] Elena Castiñeira,et al. Measuring contradiction in fuzzy logic , 2005, Int. J. Gen. Syst..

[8] S. Weber. A general concept of fuzzy connectives, negations and implications based on t-norms and t-conorms , 1983 .

[9] Enric Trillas,et al. On antonym and negate in fuzzy logic , 1999, Int. J. Intell. Syst..

[10] S. Ovchinnikov. Involutions in fuzzy set theory. , 1980 .

[11] Berthold Schweizer,et al. Probabilistic Metric Spaces , 2011 .

[12] S. Ovchinnikov. Representarions of synonymy and antonymy by automorphisms in fuzzy set theory. , 1981 .

[13] Claudio Moraga,et al. Computing with Antonyms , 2007 .

[14] Francesc Esteva,et al. Review of Triangular norms by E. P. Klement, R. Mesiar and E. Pap. Kluwer Academic Publishers , 2003 .

[15] E. Trillas. Sobre funciones de negación en la teoría de conjuntos difusos. , 1979 .