We discuss some optimization problems for fuzzy variable functions and show two interesting results. First result is related to conditions for existence of global optimal solutions for some general class of optimization problems on E, the space of compacts, upper semicontinuous and normal fuzzy sets of R. The second result is about preservation of local optimality points, via Zadeh’s principle ...

DEFINITION 1.1. A fuzzy variable is characterized by a triple (X, U, R (X;u)). in which X is the name of the variable; U is a universe of discourse (finite or infinite set); u is a generic name for the elements of U; and R(X;u) is a fuzzy subset of U which represents a fuzzy restriction on the values of u imposed by X. [As in the case of nonfuzzy variables, R(X;u) will usually be abbreviated to...

1. I n t r o d u c t i o n ~ ]e concep t o f fuzzy s e t s d e f i n e d by Zadeh 1 ) g i v e s an i m p o r t a n t m a t h e m a t i c a l c l u e f o r an approach to s t u d i e s o f sys tems w i th no sha rp b o u n d a r i e s . L a t e l y , t h e fuzzy i n t e g r a l 2 ) b a s e d on t h e fuzzy s e t t h e o r y has been proposed and a p p l i e d t o t he measurement o f fuzzy o b j...

Hong [Fuzzy Optimization of Decision Making 13 (2014) 415-434, Information Sciences 228 (2013) 45-60.] considers the law of large numbers for T -independent weighted fuzzy variables whose underlying spaces are Rp. He proved T -independent fuzzy renewal theorems and renewal reward theorems with respect to the necessity measure and the expected values of fuzzy variable by using the law of large n...

This paper deals with bimatrix games in uncertainty environment based on several types of ordering, which Maeda proposed. But Maeda’s models was just made based on symmetrical triangle fuzzy variable. In this paper, we generalized Maeda’s model to the non-symmetrical environment. In other words, we investigated the fuzzy bimatrix games based on nonsymmetrical L-R fuzzy variables. Then the pseud...

In this paper, we consider the problem of solving systems of fuzzy relation equations in a space with fuzzy preorder. Two types of these systems with different compositions are considered. New solvability criteria are proposed for systems of both types. The new criteria are weaker than all the known ones that are based on the assumption that fuzzy sets on the left-hand side of a system establis...

This paper presents a method based on fuzzy regression to analyze fatigue crack growth data, where the variations of the parameters are not only due to measurement errors but also system errors. A membership function is used to describe the system errors. Crack growth data under constant and random amplitude stress are analyzed and the results are compared with conventional least-squares regres...

For theoretical fuzzy control it is a well known strategy to transform a system of control rules into a system of relation equations. Because these systems of relation equations are not always solvable, solvability criteria and approximate solutions have been discussed. We reconsider some of the results in this field and extend them using more recent results on t-norm based fuzzy logics and on ...