a shortest path problem is a practical issue in networks for real-world situations. this paper addresses the fuzzy shortest path (fsp) problem to obtain the best fuzzy path among fuzzy paths sets. for this purpose, a new efficient algorithm is introduced based on a new definition of ideal fuzzy sets (ifss) in order to determine the fuzzy shortest path. moreover, this algorithm is developed for ...

In this paper, the order, size and degree of the nodes of the isomorphic fuzzy graphs are discussed. Isomorphism between fuzzy graphs is proved to be an equivalence relation. Some properties of self complementary and self weak complementary fuzzy graphs are discussed. Keywords—complementary fuzzy graphs, co-weak isomorphism, equivalence relation, fuzzy relation, weak isomorphism.

In the theory of fuzzy relations the properties of reflexiv-ity, symmetry, antisymmetry, transitivity, etc. are intensely studied. The indicators of fuzzy relations measure the degree to which such a fuzzy relation verifies such a property. The purpose of this paper is to characterize indicators of fuzzy relations in terms of fuzzy modal operators.

We have already introduced many fuzzy concepts to scheduling problem and discussed so called fuzzy scheduling problems. In this paper, we introduce fuzzy allowable time concept newly to two identical machine problem, which is a fuzzy version of M. R. Garey and D. S. Johnson. That is, there are two identical machines and fuzzy ready times and deadlines are associated to each job, i.e., membershi...

The well-known generalisation of hard Cmeans (HCM) clustering is fuzzy C-means (FCM) clustering where a weight exponent on each fuzzy membership is introduced as the degree of fuzziness. An alternative generalisation of HCM clustering is proposed in this paper. This is called fuzzy entropy (FE) clustering where a weight factor of the fuzzy entropy function is introduced as the degree of fuzzy e...

Let G be an intuitionistic fuzzy graph. Let u and v be two vertices of G. A subset D of V is called a fuzzy equitable dominating set if every v ∈ V − Dthere exist a vertex u ∈ D such that uv ∈ E(G) and |deg(u) − deg(v)| = 1 where deg(u) denotes the degree of vertex u and deg(v) denotes the degree of vertex v and μ2(vi, vj ) = μ1(vi) ∧ μ1(vj ), γ2(vi, vj ) = γ1(vi) ∨ γ1(vj ). The minimum cardina...

This article introduces interior and closure operators with inclusion degree considered within a crisp or fuzzy topological framework. First, inclusion degree is introduced in an extension of the interior and closure operators in crisp topology. This idea is then introduced in fuzzy topology by incorporating a relaxed version of fuzzy subsethood. The introduction of inclusion degree leads to a ...