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...

The concept of fuzzy topological spaces was introduced in [2] and ever since this introduction much research has been done in this area. In this note we introduce the concept of extension of fuzzy topological spaces as done for topological spaces in [1,7]. Let (X, T) be a fuzzy topological space and T C T*. Then T* will be called a simple extension of T iff there exists a 6 $T such that T* = {A...

Let $$t\in {\mathbb {N}}_+$$ be given. In this article, we are interested in characterizing those $$d\in such that the congruence $$\begin{aligned}\frac{1}{t}\sum _{s=0}^{t-1}{n+d\zeta _t^s\atopwithdelims ()d-1}\equiv {n\atopwithdelims ()d-1}\pmod {d}\end{aligned}$$ is true for each $$n\in {Z}}$$ . particular, assuming d has a prime divisor greater than t, show above holds if and only $$d=p^r$$...

By the representation's theorem it is known that a fuzzy relation R is a preorder if and only if R = inf~ e so If, where -~ is the set of logical states of I~ In this paper it is shown how, in almost all cases, both for the t-norm Min and archimedean t-norms T, it is possible to consider that the fuzzy sets I~ are normalized. Furthermore a partial order between logical states, defined from the ...

The main feature of a Takagi-Sugeno (T-S) fuzzy model is to express the local dynamics of each fuzzy implication (rule) by a linear system model. The overall fuzzy model of the system is achieved by fuzzy “blending” of the linear system models. Parallel or feedback connections of T-S fuzzy systems which preserve the properties of each system are possible [1]. Thus a simple and straightforward a...

This paper presents the fuzzy-model-based control approach to synchronize two chaotic systems subject to parameter uncertainties. A fuzzy state-feedback controller using the system state of response chaotic system and the time-delayed system state of drive chaotic system is employed to realize the synchronization. The time delay which complicates the system dynamics makes the analysis difficult...

In this paper we present the N-norms/N-conorms in neutrosophic logic and set as extensions of T-norms/T-conorms in fuzzy logic and set. Also, as an extension of the Intuitionistic Fuzzy Topology we present the Neutrosophic Topologies. 1. Definition of the Neutrosophic Logic/Set: Let T, I, F be real standard or non-standard subsets of ]0, 1[, with sup T = t_sup, inf T = t_inf, sup I = i_sup, inf...

the sequential $p$-convergence in a fuzzy metric space, in the sense of george and veeramani, was introduced by d. mihet as a weaker concept than convergence. here we introduce a stronger concept called $s$-convergence, and we characterize those fuzzy metric spaces in which convergent sequences are $s$-convergent. in such a case $m$ is called an $s$-fuzzy metric. if $(n_m,ast)$ is a fuzzy metri...

Keywords: Double fuzzy topology Double neighborhood systems Double fuzzy preproximity Double fuzzy closure space a b s t r a c t In this paper, we introduce the notions of double neighborhood systems and double fuzzy preproximity in double fuzzy topological spaces. We used double neighborhoods to study the initial structure of double fuzzy topological spaces, and the joins between them and the ...

Universal approximation is the basis of theoretical research and practical applications of fuzzy systems. Studies on the universal approximation capability of fuzzy systems have achieved great progress in recent years. In this paper, linear Takagi–Sugeno (T–S) fuzzy systems that use linear functions of input variables as rule consequent and their special case named simplified fuzzy systems that...