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Solving fuzzy equations: A new solution concept. (English) Zbl 0723.04005
Authors’ abstract: “We have previously shown that many fuzzy equations do not have solutions when the solution concept is based on the extension principle. We therefore introduce two new solution procedures, one based on the unified extension and the other based on possibility theory, after we solve the non-fuzzy equation for the unknown variable. We show, for many types of equations, that (1) the two new solutions are identical; (2) the solution is either a real, or generalized complex, fuzzy number (all uncertain parameters are modeled as real fuzzy numbers); and (3) the previous solution based on the extension principle (when it exists) is a subset of the new solution. In particular, we show that the fuzzy quadratic equation with real fuzzy number coefficients, always has a (new) solution.”

03E72Fuzzy set theory
Full Text: DOI
[1] Buckley, J. J.: Fuzzy complex numbers. Fuzzy sets and systems 33, 333-345 (1989) · Zbl 0739.30038
[2] Buckley, J. J.; Qu, Y.: Solving linear and quadratic fuzzy equations. Fuzzy sets and systems 38, 43-59 (1990) · Zbl 0713.04004
[3] Dubois, D.; Prade, H.: Fuzzy numbers: an overview. Analysis of fuzzy information 1, 3-40 (1987) · Zbl 0663.94028
[4] Goetschel, R.; Voxman, W.: Topological properties of fuzzy numbers. Fuzzy sets and systems 10, 87-99 (1983) · Zbl 0521.54001
[5] Goetschel, R.; Voxman, W.: Elementary fuzzy calculus. Fuzzy sets and systems 18, 31-43 (1986) · Zbl 0626.26014
[6] Moore, R. E.: Methods and applications of interval analysis. (1979) · Zbl 0417.65022
[7] Taylor, A. E.: General theory of functions and integration. (1965) · Zbl 0135.11301
[8] Ougang, H.: Topological properties of the spaces of regular fuzzy sets. J. math. Anal. appl. 192, 346-361 (1988)
[9] Wilansky, A.: Functional analysis. (1964) · Zbl 0136.10603
[10] Zadeh, L.: The concept of a linguistic variable and its application to approximate reasoning-I. Inform. sci. 8, 199-249 (1975) · Zbl 0397.68071
[11] Zadeh, L.: Fuzzy sets as a basis for a theory of possibility. Fuzzy sets and systems 1, 3-28 (1978) · Zbl 0377.04002