We consider a multiple-rule, generalized modus ponens inference scheme, with an interpretation based on compositional rule of inference (CRI) and a residuated implication. We show that such a system is equivalent, as far as CRI is concerned, to a system that satis5es the “basic requirement for fuzzy reasoning”, proposed by Turksen and Tian (Fuzzy Sets and Systems 58 (1993) 3–40). We establish a...

In this paper, a new definition of fuzzy bounded sets and totallyfuzzy bounded sets is introduced and properties of such sets are studied. Thena relation between totally fuzzy bounded sets and N-compactness is discussed.Finally, a geometric characterization for fuzzy totally bounded sets in I- topologicalvector spaces is derived.

Recently, Carlsson and Fuller [C. Carlsson, R. Fuller, On possibilistic mean value and variance of fuzzy numbers, Fuzzy Sets and Systems 122 (2001) 315–326] have introduced possibilistic mean, variance and covariance of fuzzy numbers and Fuller and Majlender [R. Fuller, P. Majlender, On weighted possibilistic mean and variance of fuzzy numbers, Fuzzy Sets and Systems 136 (2003) 363–374] have in...

In this paper, the concept of fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) of an ordered group (resp. lattice-ordered group) is introduced and some properties, characterizations and related results are given. Also, the fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) generated by a fuzzy subgroup (resp. fuzzy subsemigroup) is characterized. Furthermore,...

Fuzzy Logic Systems are widely recognized to be successful at modelling uncertainty in a large variety of applications. While recently interval type-2 fuzzy logic has been credited for the ability to better deal with large amounts of uncertainty, general type2 fuzzy logic has been a steadily growing research area. All fuzzy logic systems require the accurate specification of the membership func...

In this paper, a characterization of convex fuzzy mappings is obtained. SupposeF C : ® F is a fuzzy mapping, whereC is a non-empty convex subset ofR andF is the set of all fuzzy numbers. With respect to the fuzzy-max order, F is convex if and only if it is both quasi-convex and intermediate-point convex. In this paper, a characterization of convex fuzzy mappings will be given. Specifically, it ...

A defuzzification function assigns to each fuzzy set a crisp value in a way that this value may intuitively be understood as the “centre” of the fuzzy set. In the present paper, this vague concept is put into a mathematically rigorous form. To this end, we proceed analogously to the case of sharply bordered subsets, for which the Steiner point is frequently used. The function assigning to each ...