Algebraic structures for fuzzy numbers from categorial point of view

Using a classic algebraic construction additive and multiplicative structures (as commutative monoids) for fuzzy numbers are obtained. Moreover, we realize here an isomorphism between these structures.

[1]  Congxin Wu,et al.  Embedding problem of noncompact fuzzy number space E∼ (I) , 1999, Fuzzy Sets Syst..

[2]  Stanisław Heilpern,et al.  The expected value of a fuzzy number , 1992 .

[3]  Milan Mares,et al.  Brief note on distributivity of triangular fuzzy numbers , 1995, Kybernetika.

[4]  Dug Hun Hong,et al.  Some algebraic properties and a distance measure for interval-valued fuzzy numbers , 2002, Inf. Sci..

[5]  R. Goetschel,et al.  Elementary fuzzy calculus , 1986 .

[6]  D. Dubois,et al.  Operations on fuzzy numbers , 1978 .

[7]  Lech Maligranda,et al.  The Continuous Case , 2006 .

[8]  Ch.-Ch Chou.  The canonical representation of multiplication operation on triangular fuzzy numbers , 2003 .

[9]  James J. Buckley.  On the algebra of interactive fuzzy numbers: the continuous case , 1990 .

[10]  M. Kovács,et al.  Algebraic structure of centered M -fuzzy numbers , 1991 .

[11]  A. Ban,et al.  Solving systems of equivalentions , 2006 .

[12]  A. Bica.  Categories and algebraical structures for real fuzzy numbers , 2002 .

[13]  James J. Buckley,et al.  On the algebra of interactive fuzzy numbers , 1989 .

[14]  Milan Mares.  Algebraic equivalences over fuzzy quantities , 1993, Kybernetika.

[15]  Milan Mares,et al.  Weak arithmetics of fuzzy numbers , 1997, Fuzzy Sets Syst..

[16]  Congxin Wu,et al.  On Henstock integral of fuzzy-number-valued functions (I) , 2001, Fuzzy Sets Syst..

[17]  Milan Mares,et al.  Multiplication of fuzzy quantities , 1992, Kybernetika.

[18]  Milan Mares,et al.  Addition of fuzzy quantities: Disjunction-conjunction approach , 1989, Kybernetika.

[19]  M. Kovács.  Stable embedding of ill-posted linear equality systems into fuzzified systems , 1992 .

[20]  Didier Dubois,et al.  Fuzzy sets and systems ' . Theory and applications , 2007 .