Soft computing and modelling

A short review of the recent result in the theory of ordered fuzzy numbers and their normed algebra is presented together with some interpretations. Specific applications in finance, dynamical systems and control are presented. From the classical framework known algebraic and evolution equations describing such systems are transformed to their fuzzy versions. Their solvability is shortly presented together with specially dedicated problem solutions.

[1]  L. Zadeh The role of fuzzy logic in the management of uncertainty in expert systems , 1983 .

[2]  Witold Kosiński,et al.  General mapping approximation problems solving by neural and fuzzy inference networks , 1997 .

[3]  Hung T. Nguyen,et al.  A note on the extension principle for fuzzy sets , 1978 .

[4]  James J. Buckley,et al.  Solving fuzzy equations in economics and finance , 1992 .

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

[6]  Dominik Slezak,et al.  Fuzzy Reals with Algebraic Operations: Algorithmic Approach , 2002, Intelligent Information Systems.

[7]  Witold Kosinski On Defuzzyfication of Ordered Fuzzy Numbers , 2004, ICAISC.

[8]  Madan M. Gupta,et al.  Introduction to Fuzzy Arithmetic , 1991 .

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

[10]  Dominik Slezak,et al.  Algebraic Operations on Fuzzy Numbers , 2003, IIS.

[11]  Dominik Ślęzak,et al.  Ordered fuzzy numbers , 2003 .

[12]  George J. Klir,et al.  Fuzzy arithmetic with requisite constraints , 1997, Fuzzy Sets Syst..

[13]  Lotfi A. Zadeh,et al.  The concept of a linguistic variable and its application to approximate reasoning-III , 1975, Inf. Sci..

[14]  E. Kaucher Interval Analysis in the Extended Interval Space IR , 1980 .

[15]  Witold Kosiński,et al.  On fuzzy number calculus , 2006 .

[16]  Caroline M. Eastman,et al.  Review: Introduction to fuzzy arithmetic: Theory and applications : Arnold Kaufmann and Madan M. Gupta, Van Nostrand Reinhold, New York, 1985 , 1987, Int. J. Approx. Reason..

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

[18]  Michael Wagenknecht,et al.  Computational aspects of fuzzy arithmetics based on Archimedean t-norms , 2001, Fuzzy Sets Syst..