A path P connecting a pair of vertices in connected fuzzy graph is called detour, if its μ - length maximum among all the feasible paths between them. In this paper we establish notion detour convex sets, covering, basis, number, blocks and investigate some their properties. It has been proved that, for complete G, set any G covering. necessary sufficient condition to become block also establis...

g e y w o r d s F u z z y numbers, Convexity, Continuity, Convex fuzzy mappings, Linear ordering, Fuzzy Weirstrass theorem, Fuzzy optimization. 1. I N T R O D U C T I O N Let R n denote the n-dimensional Eucl idean space. The suppor t , supp(#) , of a fuzzy set # : R ~ I = [0, 1] is defined as supp(/~) = {x • R n I #(x) > 0}. A fuzzy set # : R n --~ I is called fuzzy convex if #(Ax + (1 A)y) _>...

The deterministic coalition game theory is based on the presumption that all expected incomes of coalitions and individual players are exactly known even befor the bargaining process If we leave this presumption then we extend the original gamemodel into the fuzzy coalition game with vague i e fuzzy pay o s The vagueness of the pay o s leads to vagueness of some other concepts and prop erties l...

Keywords--Fuzzy numbers, Convexity, Preinvexity, Generalized convexity, Fuzzy mappings. 1. I N T R O D U C T I O N Let R n deno te t he n -d imens iona l Euc l idean space. T h e suppor t , supp (p), of a fuzzy set # : R n ~ I = [0, 1] is def ined as s u p p ( # ) = { x e R n ] # ( x ) > 0} . A fuzzy set # : R n ~ I is cal led fuzzy convex if i t is quas i concave in c o m m o n sense on its su...

in this paper, we consider the production possibility set with n production units such that the following four principles that governs: inclusion observations, conceivability, immensity and convexity. our goal is to estimate the output of a same and new production unit with existing production possibility and amount of input is specified. so, initially we find the interval changes of each input...

In the present paper, we introduce and study a fuzzy vector equilibrium problem and prove some existence results with and without convexity assumptions by using some particular forms of results of textit{Kim} and textit{Lee} [W.K. Kim and K.H. Lee, Generalized fuzzy games and fuzzy equilibria, Fuzzy Sets and Systems, 122 (2001), 293-301] and textit{Tarafdar} [E. Tarafdar, Fixed point theorems i...

In this paper, a new fuzzy interpolative reasoning method is proposed for the sparse rule bases by using the highest points and slopes of the antecedent and consequent fuzzy sets. The proposed fuzzy reasoning methods are not only suitable for the four kinds of fuzzy sets in inference rules, but also can guarantee the convexity and normality of the reasoning consequence. Furthermore, the computa...

The objective of this paper is to deal with the fuzzy conic programming problems. The aim here is to derive weak and strong duality theorems for a general fuzzy conic programming. Toward this end, The convexity-like concept of fuzzy mappings is introduced and then a specific ordering cone is established based on the parameterized representation of fuzzy numbers. Under this setting, duality theo...