The concept of the strongest path plays a crucial role in fuzzy graph theory. In classical graph theory, all paths in a graph are strongest, with a strength value of one. In this article, we introduce Menger’s theorem for fuzzy graphs and discuss the concepts of strengthreducing sets and t-connected fuzzy graphs. We also characterize t-connected and t-arc connected fuzzy graphs. 2012 Elsevier I...

Myhill-Nerode Theorem is regarded as a basic theorem in the theories of languages and automata and is used to prove the equivalence between automata and their languages. The significance of this theorem has stimulated researchers to develop that on different automata thus leading to optimizing computational models. In this article, we aim at developing the concept of congruence in general fuzzy...

In practice, some special LR fuzzy numbers, like the triangular fuzzy number, the Gaussian fuzzy number and the Cauchy fuzzy number, are widely used in many areas to deal with various vague information. With regard to these special LR fuzzy numbers, called regular LR fuzzy numbers in this paper, an operational law is proposed for fuzzy arithmetic, providing a novel approach to analytically and ...

In this paper, we introduce intuitionistic fuzzy contraction mappingand prove a fixed point theorem in intuitionistic fuzzy metric spaces.

The definitions of new type separated subsets are given in ideal topological spaces. By using these definitions, we introduce types connectedness. It is shown that connectedness more general than some previously defined concepts compared with well-known point-set topology. Then, the intermediate value theorem for spaces given. Also, special cases, it and coincide.

‎in this article we introduce $mu$-filtered fuzzy module with a family of fuzzy submodules.  it shows the relation between $mu$-filtered fuzzy modules and crisp filtered modules by level sets. we investigate fuzzy topology on the $mu$-filtered fuzzy module and apply that to introduce fuzzy completion. finally we extend krull's intersection theorem of fuzzy ideals by using concept $mu$-adic...

‎In this article we introduce $mu$-filtered fuzzy module with a family of fuzzy submodules.  It shows the relation between $mu$-filtered fuzzy modules and crisp filtered modules by level sets. We investigate fuzzy topology on the $mu$-filtered fuzzy module and apply that to introduce fuzzy completion. Finally we extend Krull's intersection theorem of fuzzy ideals by using concept $mu$-adic comp...

Several diierent basic properties are used for developing a system of calculus for subdiierentials. They are a nonlocal fuzzy sum rule in 5, 25], a multidirectional mean value theorem in 7, 8], local fuzzy sum rules in 14, 15] and an extremal principle in 19, 21]. We show that all these basic results are equivalent and discuss some interesting consequences of this equivalence.