The present paper aims to introduce the concept of weak-fuzzy contraction mappings in graph structure within context fuzzy cone metric spaces. We prove some fixed point results endowed with a using contractions. By relaxing continuity condition involved, our enrich and generalize well-known theory. With help new lemmas, proofs are straight forward. furnish validity findings appropriate examples...

In this paper, following the ideas of (continuous) t-norm and interval numbers, a concept of (continuous) interval-valued t-norm is proposed. Based on the interval-valued fuzzy set and the continuous interval-valued t-norm, we propose a notion of interval-valued fuzzy metric space, which is a generalization of fuzzy metric space in the sense of George and Veeramani [Fuzzy Sets and Systems 64 (1...

We propose a new approach to assigning distance between fuzzy numbers. A pseudo-metric on the set of fuzzy numbers and a metric on the set of trapezoidal fuzzy numbers are described. The regular reducing functions and the Hausdorff metric are used to define the metric. Using this metric, we can approximate an arbitrary generalized left right fuzzy number with a trapezoidal one. Finally, powers ...

Abstract The aim of this work is to establish results in fixed point theory for a pair fuzzy dominated mappings which forms rational V -contraction modular-like metric spaces. Some via partial order and using the graph concept are also developed. We apply our ensure existence solution nonlinear Volterra-type integral equations.

Fuzzy Mathematics has seen an enormous growth since the introduction of notion of fuzzy sets by Zadeh in 1965. Kramosil and Michalek introduced the notion of fuzzy metric spaces which was later modified by George and Veeramani and others. The notion of intuitionistic fuzzy metric spaces was introduced by Park in 2004. Many authors have studied fixed point and common fixed theorems for mappings ...

In this paper, we shall establish some fixed point theorems for mappings with the contractive  condition of integrable type on complete intuitionistic fuzzy metric spaces $(X, M,N,*,lozenge)$. We also use Lebesgue-integrable mapping to obtain new results. Akram, Zafar, and Siddiqui introduced the notion of $A$-contraction mapping on metric space. In this paper by using the main idea of the work...

in this paper,  we provide two different kinds of fixed pointtheorems in  fuzzy metric spaces. the first kind is for the fuzzy$varepsilon$-contractive type mappings and  the second kind is forthe fuzzy order $psi$-contractive type mappings. they improve thecorresponding  conclusions in the literature.

Some difficulties emerging during the construction of fuzzy rule bases are inherited from the type of the applied fuzzy reasoning. The fuzzy rule base requested for many classical reasoning methods needed to be complete. In case of fetching fuzzy rules directly from expert knowledge, the way of building a complete rule base is not always straightforward. One simple solution for overcoming the n...

In this paper, we introduce a function in order to measure the distancebetween two order intervals of fuzzy numbers, and show that this function isa metric. We investigate some properties of this metric, and finally presentan application. We think that this study could provide a more generalframework for researchers studying on interval analysis, fuzzy analysis andfuzzy decision making.