A fuzzy graph (f-graph) is a pair G : (σ, μ) where σ is a fuzzy subset of a set S and μ is a fuzzy relation on σ. A fuzzy graph H : (τ, υ) is called a partial fuzzy subgraph of G : (σ, μ) if τ (u) ≤ σ(u) for every u and υ (u, v) ≤ μ(u, v) for every u and v . In particular we call a partial fuzzy subgraph H : (τ, υ) a fuzzy subgraph of G : (σ, μ ) if τ (u) = σ(u) for every u in τ * and υ (u, v) ...

In order to analyze the logical foundation of fuzzy reasoning, this paper first introduces the concept of generalized roots of theories in Łukasiewicz propositional fuzzy logic Łuk, Gödel propositional fuzzy logic Göd, Product propositional fuzzy logic P, and nilpotent minimum logic NM (the R0-propositional fuzzy logic L ). Next, it is proved that all consequences of a theory C, named D(C), are...

The π-derivative for fuzzy function is considered. Consequently, using this π-derivative we study fuzzy differentuial equations. In particular, we build a solution for a fuzzy differential equation with the help of a system of ordinary differential equations which is generates of the π-derivative. Keywords— π-derivative for set valued functions, derivative for fuzzy functions, fuzzy differentia...

In this paper ,we fuzzify the new class of algebraic structure introduced by Kim[5].In this fuzzification(called fuzzy KS-semigroups),we introduce the notions of fuzzy sub KS-semigroups,fuzzy KS-ideal,fuzzy KS-p-ideal and investigate some of their related properties.The purpose of this study is to implement the fuzzy set theory and ideal theory in the KS-semigroups.This fuzzification leads to d...