Representations of the Extensions of Many-Valued Equivalence Relations

Two fundamental questions on the extensions of many-valued equivalence relations, whose solutions have a crucial concern for the applications of many-valued equivalence relations, are explicitly stated to characterize the extensions of many-valued equivalence relations. Thereafter introducing the satisfactory solutions of these questions, the desirable characterizations of the extensions of many-valued equivalence relations are pointed out.

[1]  H. Thiele,et al.  On the mutual definability of fuzzy equivalence relations and fuzzy partitions , 1995, Proceedings of 1995 IEEE International Conference on Fuzzy Systems..

[2]  Ulrich Höhle,et al.  Many-valued equalities, singletons and fuzzy partitions , 1998, Soft Comput..

[3]  Bernard De Baets,et al.  T -partitions , 1998 .

[4]  Frank Klawonn,et al.  Equality Relations as a Basis for Fuzzy Control , 1993 .

[5]  Alexander P. Sostak,et al.  Axiomatic Foundations Of Fixed-Basis Fuzzy Topology , 1999 .

[6]  U. Höhle.  Commutative, residuated 1—monoids , 1995 .

[7]  U. Höhle.  Quotients with respect to similarity relations , 1988 .

[8]  Mustafa Demirci,et al.  Fuzzy Functions and Their Applications , 2000 .

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

[10]  Frank Klawonn,et al.  Foundations of fuzzy systems , 1994 .

[11]  Mustafa Demirci,et al.  On Many-Valued Partitions and Many-Valued Equivalence Relations , 2003, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[12]  Mustafa Demirci,et al.  Constructions of fuzzy functions based on fuzzy equalities , 2003, Soft Comput..

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

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

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

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

[17]  Mustafa Demirci,et al.  Fundamentals of M-Vague Algebra and M-Vague Arithmetic Operations , 2002, Int. J. Uncertain. Fuzziness Knowl. Based Syst..