Sets With Type-2 Operations

In this paper, we examine the algebra formed by the subsets of the unit interval with operations induced by the order on the unit interval. This algebra can be obtained as a subalgebra of the truth value algebra of type-2 fuzzy sets.

[1]  Lotfi A. Zadeh,et al.  The Concepts of a Linguistic Variable and its Application to Approximate Reasoning , 1975 .

[2]  Masaharu Mizumoto,et al.  Some Properties of Fuzzy Sets of Type 2 , 1976, Inf. Control..

[3]  Didier Dubois,et al.  Operations in a Fuzzy-Valued Logic , 1979, Inf. Control..

[4]  M. Mizumoto,et al.  Fuzzy sets and type 2 under algebraic product and algebraic sum , 1981 .

[5]  Masao Mukaidono.  Algebraic Structures of Truth Values in Fuzzy Logic , 1991, Fuzzy Logic and Fuzzy Control.

[6]  Hung T. Nguyen,et al.  A First Course in Fuzzy Logic , 1996 .

[7]  Mai Gehrke,et al.  DeMorgan systems on the unit interval , 1996 .

[8]  E. Walker,et al.  Some comments on interval valued fuzzy sets , 1996 .

[9]  Masao Mukaidono,et al.  Necessary and Sufficient Conditions for fuzzy Truth Values to Form a de Morgan Algebra , 1999, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[10]  Janusz A. Brzozowski,et al.  de Morgan bisemilattices , 2000, Proceedings 30th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2000).

[11]  Zoltán Ésik,et al.  Free De Morgan Bisemigroups and Bisemilattices , 2001 .

[12]  Noboru Takagi,et al.  De Morgan bisemilattice of fuzzy truth value , 2002, Proceedings 32nd IEEE International Symposium on Multiple-Valued Logic.

[13]  Zoltán Ésik,et al.  Hazard Algebras , 2003, Formal Methods Syst. Des..

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

[15]  Elbert A. Walker,et al.  The algebra of fuzzy truth values , 2005, Fuzzy Sets Syst..

[16]  Elbert A. Walker,et al.  Automorphisms of the Algebra of Fuzzy Truth Values , 2006, Int. J. Uncertain. Fuzziness Knowl. Based Syst..