We studied here on some simple examples the interaction between valuation family, parameters and ranking result. The ranking method studied is based upon the idea of associating with a fuzzy number a scalar value, its valuation, and using this valuation to compare and order fuzzy numbers. The valuation method considered was introduced initially by the Yager and Filev. This valuation consists in...

We propose three methods for obtaining solutions in fuzzy constraint networks and study their application to the problem of ordering fuzzy numbers. The techniques proposed may be classified as defuzzification functions which are applicable to any set of mutually dependent fuzzy numbers in which the dependence relationships are represented by means of metric constraints. We suggest the use of th...

The importance and difficulty of the problem of ranking fuzzy numbers is pointed out. Here we consider approaches to the ranking of fuzzy numbers based upon the idea of associating with a fuzzy number a scalar value, its valuation, and using this valuation to compare and order fuzzy numbers. Specifically we focus on expected value type valuations which are based upon the transformation of a fuz...

A fuzzy random variable is viewed as the imprecise observation of the outcomes in a random experiment. Since randomness and vagueness coexist in the same framework, it seems reasonable to integrate fuzzy random variables into imprecise probabilities theory. Nevertheless, fuzzy random variables are commonly presented in the literature as classical measurable functions associated to a classical p...

In this paper a linear Fuzzy Fredholm Integral Equation(FFIE) with arbitrary Fuzzy Function input and symmetric triangular (Fuzzy Interval) output is considered. For each variable, output is the nearest triangular fuzzy number (fuzzy interval) to the exact fuzzy solution of (FFIE).

Fuzzy variables are functions from credibility spaces to the set of real numbers. Based on the expected value of a fuzzy variable, the expected value of function of a simple fuzzy variable is studied. In order further to discuss the mathematical properties of fuzzy variables, some inequalities for fuzzy variables are derived based on the concepts of credibility measures and expected value opera...

* Department of Teacher Training in Electrical Engineering, Faculty of Technical Education, King’s Mongkut Institute of Technology North Bangkok. Abstract This paper describes fuzzy sliding-mode control (FSMC), a fuzzy logic control based upon variable structure techniques. A variable structure approach is designed with guaranteed stability properties. A ball and beam system is used here as an ...

There are various types of uncertainty in the real world. This is a motivation to investigate the behavior of uncertain phenomena. Random phenomena is one class of objective uncertain phenomena which has been well studied. Probability theory is an efficient tool to study the behavior of random phenomena. Besides randomness, fuzziness is a basic type of subjective uncertainty initiated by Zadeh....

in this paper, we consider portfolio selection problem in which security returns are regarded as fuzzy variables rather than random variables. we first introduce a concept of absolute deviation for fuzzy variables and prove some useful properties, which imply that absolute deviation may be used to measure risk well. then we propose two mean-absolute deviation models by defining risk as abs...

The concept of (fuzzy) probability density function of fuzzy random variable is proposed in this paper. Due to the "resolution identity", we can construct a closed fuzzy number from a family of closed intervals. Using the same technique, we can construct the (fuzzy) probability density function of fuzzy random variable from the known probability density function. The basic idea of the new metho...