On Fuzzy Number Calculus and Some Application

The concept of ordered fuzzy numbers (OFN) is revised in order to handle with general fuzzy inputs in a quantitative way, exactly in the same way as with real numbers. Referring to a cuts and interval arithmetic method the algebraic structure is introduced to allow counting with more general type of membership curves (relations). Application is given to a problem of economics and finance in which fuzzy equation appears.

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

[2]  Esfandiar Eslami,et al.  Advances in soft computing: an introduction to fuzzy logic and fuzzy sets , 2002 .

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

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

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

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

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

[8]  Piotr Prokopowicz,et al.  Fuzzy Calculator - Useful Tool for Programming with Fuzzy Algebra , 2004, ICAISC.

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

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

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

[12]  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..

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

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

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

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

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

[18]  Bela Martos,et al.  Nonlinear programming theory and methods , 1977 .

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

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