The extension principle and a decomposition of fuzzy sets

We give an algorithm to decompose a fuzzy interval u. Using this decomposition and the multilinearization of a univariate function f, we obtain an approximation of the fuzzy interval , where is obtained from f by applying the extension principle. We provide approximation bounds. Some numeric illustration is provided.

[1]  Edward R. Vrscay,et al.  Iterated fuzzy set systems: A new approach to the inverse problem for fractals and other sets , 1992 .

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

[3]  Michael Hanss,et al.  Applied Fuzzy Arithmetic: An Introduction with Engineering Applications , 2004 .

[4]  R. Bassanezi,et al.  Fuzzy modelling in population dynamics , 2000 .

[5]  J. D. Jones,et al.  Calculating functions of fuzzy numbers , 1993 .

[6]  Yurilev Chalco-Cano,et al.  Fuzzy differential equations and the extension principle , 2007, Inf. Sci..

[7]  A. Kaufmann,et al.  Introduction to fuzzy arithmetic : theory and applications , 1986 .

[8]  Michael Hanss,et al.  The transformation method for the simulation and analysis of systems with uncertain parameters , 2002, Fuzzy Sets Syst..

[9]  Chiang Kao,et al.  Solving fuzzy transportation problems based on extension principle , 2004, Eur. J. Oper. Res..

[10]  Dug Hun Hong,et al.  Fuzzy measures for a correlation coefficient of fuzzy numbers under TW(the weakest t-norm)-based fuzzy arithmetic operations , 2006, Inf. Sci..

[11]  Seyed Mahmoud Taheri,et al.  On information energy of the image fuzzy sets , 2007, Inf. Sci..

[12]  Branimir Seselja,et al.  Non-standard cut classification of fuzzy sets , 2007, Inf. Sci..

[13]  Yurilev Chalco-Cano,et al.  Solution of non-linear fuzzy systems by decomposition of incremental fuzzy numbers , 2007, Inf. Sci..

[14]  E. Antonsson,et al.  Engineering design calculations with fuzzy parameters , 1992 .

[15]  Heriberto Román-Flores,et al.  A note on Zadeh's extensions , 2001, Fuzzy Sets Syst..

[16]  Eduard Hofer,et al.  When to separate uncertainties and when not to separate , 1996 .

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

[18]  F. S. Wong,et al.  Fuzzy weighted averages and implementation of the extension principle , 1987 .

[19]  Kwong-Sak Leung,et al.  Fuzzy numbers and fuzzification of the Choquet integral , 2005, Fuzzy Sets Syst..

[20]  L. A. ZADEH,et al.  The concept of a linguistic variable and its application to approximate reasoning - I , 1975, Inf. Sci..

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

[22]  Lotfi A. Zadeh,et al.  Toward a generalized theory of uncertainty (GTU) - an outline , 2005, GrC.

[23]  Eyke Hüllermeier,et al.  An Approach to Modelling and Simulation of Uncertain Dynamical Systems , 1997, Int. J. Uncertain. Fuzziness Knowl. Based Syst..