Comparison of Different Algorithms of Approximation by Extensional Fuzzy Subsets

How to approximate an arbitrary fuzzy subset by an adequate extensional one is a key question within the theory of Extensional Fuzzy Subsets. In a recent paper by the authors [19] different methods were provided to find good approximations. In this work these methods are compared in order to understand better the performance and improvement they give.

[1]  Jordi Recasens,et al.  Dualities and isomorphisms between indistinguishabilities and related concepts , 2011, 2011 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2011).

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

[3]  Jordi Recasens Indistinguishability Operators - Modelling Fuzzy Equalities and Fuzzy Equivalence Relations , 2011, Studies in Fuzziness and Soft Computing.

[4]  Jorge Elorza,et al.  On the relation between fuzzy closing morphological operators, fuzzy consequence operators induced by fuzzy preorders and fuzzy closure and co-closure systems , 2013, Fuzzy Sets Syst..

[5]  R. Belohlávek Fuzzy Relational Systems: Foundations and Principles , 2002 .

[6]  F. Mora-Camino,et al.  Studies in Fuzziness and Soft Computing , 2011 .

[7]  J. Aczél,et al.  Lectures on Functional Equations and Their Applications , 1968 .

[8]  T. H. Hildebrandt Lebesgue on Integration , 1930 .

[9]  Jordi Recasens,et al.  Maps and isometries between indistinguishability operators , 2002, Soft Comput..

[10]  Lotfi A. Zadeh,et al.  Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic , 1997, Fuzzy Sets Syst..

[11]  Mokhtar S. Bazaraa,et al.  Nonlinear Programming: Theory and Algorithms , 1993 .

[12]  Hans-Paul Schwefel,et al.  Introduction to Evolutionary Computing , 2004, Natural Computing Series.

[13]  Jordi Recasens,et al.  Aggregating non-finite families of T-transitive relations , 2003, EUSFLAT Conf..

[14]  Jordi Recasens,et al.  Structural analysis of indistinguishability operators and related concepts , 2013, Inf. Sci..

[15]  M. K. Luhandjula Studies in Fuzziness and Soft Computing , 2013 .

[16]  Jordi Recasens,et al.  How to Make $T$-Transitive a Proximity Relation , 2009, IEEE Transactions on Fuzzy Systems.

[17]  Joan Jacas,et al.  Fixed Points and Generators of Fuzzy Relations , 1994 .

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

[19]  Radim Bělohlávek,et al.  Fuzzy Relational Systems: Foundations and Principles , 2002 .

[20]  Jordi Recasens,et al.  Approximating Arbitrary Fuzzy Subsets by Extensional Ones , 2015, IEEE Transactions on Fuzzy Systems.

[21]  Vijay K. Rohatgi,et al.  Advances in Fuzzy Set Theory and Applications , 1980 .

[22]  Lotfi A. Zadeh,et al.  Fuzzy sets and information granularity , 1996 .

[23]  D. Dubois,et al.  Fundamentals of fuzzy sets , 2000 .

[24]  L. Valverde On the structure of F-indistinguishability operators , 1985 .

[25]  Lotfi A. Zadeh,et al.  Similarity relations and fuzzy orderings , 1971, Inf. Sci..

[26]  Lluis Godo,et al.  On the Minimum Many-Valued Modal Logic over a Finite Residuated Lattice , 2008, J. Log. Comput..

[27]  Jordi Recasens,et al.  Natural Means of Indistinguishability Operators , 2012, IPMU.

[28]  J. Recasens,et al.  Fuzzy T-transitive relations: eigenvectors and generators , 1995 .

[29]  Harley Flanders,et al.  Differentiation Under the Integral Sign , 1973 .

[30]  J. Recasens,et al.  UPPER AND LOWER APPROXIMATIONS OF FUZZY SETS , 2000 .

[31]  Nehad N. Morsi,et al.  Axiomatics for fuzzy rough sets , 1998, Fuzzy Sets Syst..

[32]  Frank Klawonn,et al.  Similarity in fuzzy reasoning , 1995 .

[33]  J. Recasens,et al.  Fuzzy Equivalence Relations: Advanced Material , 2000 .