Abstract We present a first study concerning the optimization of a non linear fuzzy function f depending both on a crisp variable and a fuzzy number: therefore the function value is a fuzzy number. More specifically, given a real fuzzy number Ã and the function f(a,x), we consider the fuzzy extension induced by f. If K is a convex subset of R, the problem we consider is "maximizing" f¨(Ã,x) on K. The first problem is the meaning of the word "maximizing": in fact it is well-known that ranking fuzzy numbers is a complex matter. Following a general method, we introduce a real function (evaluation function) on real fuzzy numbers, in order to get a crisp rating, induced by the order of the real line. In such a way, the optimization problem on fuzzy numbers can be written in terms of an optimization problem for the real-valued function obtained by composition of f with a suitable evaluation function. This approach allows us to state a necessary and sufficient condition in order that it exists the maximum for f¨ in K, when f(a,x) is convex-concave .

Optimisation of a non linear fuzzy function / Facchinetti, Gisella; S., Giove; Pacchiarotti, Nicoletta. - In: SOFT COMPUTING. - ISSN 1432-7643. - STAMPA. - 6 (6):(2002), pp. 476-480.

### Optimisation of a non linear fuzzy function

#### Abstract

Abstract We present a first study concerning the optimization of a non linear fuzzy function f depending both on a crisp variable and a fuzzy number: therefore the function value is a fuzzy number. More specifically, given a real fuzzy number Ã and the function f(a,x), we consider the fuzzy extension induced by f. If K is a convex subset of R, the problem we consider is "maximizing" f¨(Ã,x) on K. The first problem is the meaning of the word "maximizing": in fact it is well-known that ranking fuzzy numbers is a complex matter. Following a general method, we introduce a real function (evaluation function) on real fuzzy numbers, in order to get a crisp rating, induced by the order of the real line. In such a way, the optimization problem on fuzzy numbers can be written in terms of an optimization problem for the real-valued function obtained by composition of f with a suitable evaluation function. This approach allows us to state a necessary and sufficient condition in order that it exists the maximum for f¨ in K, when f(a,x) is convex-concave .
##### Scheda breve Scheda completa Scheda completa (DC)
2002
6 (6)
476
480
Optimisation of a non linear fuzzy function / Facchinetti, Gisella; S., Giove; Pacchiarotti, Nicoletta. - In: SOFT COMPUTING. - ISSN 1432-7643. - STAMPA. - 6 (6):(2002), pp. 476-480.
Facchinetti, Gisella; S., Giove; Pacchiarotti, Nicoletta
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11380/310268`
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