A fuzzy graph is a symmetric binary fuzzy relation on a fuzzy subset. The concept of fuzzy sets and fuzzy relations was introduced by L.A.Zadeh in 1965cite{zl} and further studiedcite{ka}. It was Rosenfeldcite{ra} who considered fuzzy relations on fuzzy sets and developed the theory of fuzzy graphs in 1975. The concepts of fuzzy trees, blocks, bridges and cut nodes in fuzzy graph has been studi...

The objective of this paper is to finds the lower and upper bounds Nordhaus-Gaddum inequalities fuzzy chromatic number for anti-fuzzy graph. This analyzes index complementary anti graphs in some cases. A theorem proved graph be k-critical. Examples are provided derive vertex coloring these graphs.

This paper studies some relationships between fuzzy relations, fuzzy graphs and fuzzy measure. It is shown that a fundamental theorem of Discrete Convex Analysis is derived from the theory of fuzzy measures and the Choquet integral.

We describe the basics of fuzzy sets and fuzzy logic. Based upon the concept of linguistic values, which describe imprecise concepts using words, the basics of fuzzy rules and fuzzy inference are introduced. In the second part we briefly explain applications of fuzzy rules for function approximation using fuzzy graphs, clustering using fuzzy algorithms, and classification under uncertainty usin...