Fuzzy Metric Research Articles

Fixed Point Theorems in Revised Fuzzy Metric Spaces

In this paper, we examine the existence of fixed point results for Banach and Edelstein contraction theorems in Revised fuzzy metric spaces with the assistance of Grabiec. Thus, we create a new path in Revised fuzzy theory to obtain fixed point results. We hope that this paper creates a new way to come up with several fixed point results in the Revised fuzzy metric spaces.

Strong Law of Large Numbers for Fuzzy Random Variables in Fuzzy Metric Space

Strong Law of Large Numbers for Fuzzy Random Variables in Fuzzy Metric Space

Some Fixed Point Theorems in Partial Fuzzy Metric Spaces

The aim of this study is basically to give some fundamental fixed point theorems in partial fuzzy metric spaces. Firstly, we investigate the relationships of partial metric space and fuzzy metric space with partial fuzzy metric spaces. Then we define some contractive/contraction mappings similar to the Banach contraction mappings in the classical sense. Also, we show that these mappings have a unique fixed point under some conditions. Finally, we give some examples to illustrate the validity of the obtained results and the necessity of added conditions.

Some Results on Wijsman Ideal Convergence in Intuitionistic Fuzzy Metric Spaces

In the present work, we study and extend the notion of Wijsman J –convergence and Wijsman J ∗ –convergence for the sequence of closed sets in a more general setting, i.e., in the intuitionistic fuzzy metric spaces (briefly, IFMS). Furthermore, we also examine the concept of Wijsman J ∗ –Cauchy and J –Cauchy sequence in the intuitionistic fuzzy metric space and observe some properties.

W-Distances on Fuzzy Metric Spaces and Fixed Points

We propose a notion of w-distance for fuzzy metric spaces, in the sense of Kramosil and Michalek, which allows us to obtain a characterization of complete fuzzy metric spaces via a suitable fixed point theorem that is proved here. Our main result provides a fuzzy counterpart of a renowned characterization of complete metric spaces due to Suzuki and Takahashi.

Existence of Solutions for Nonlinear Impulsive Fractional Differential Equations via Common Fixed-Point Techniques in Complex Valued Fuzzy Metric Spaces

The main purpose of this paper is to study the existence theorem for a common solution to a class of nonlinear three-point implicit boundary value problems of impulsive fractional differential equations. In this respect, we study the fuzzy version of some essential common fixed-point results from metric spaces in the newly introduced notion of complex valued fuzzy metric spaces. Also, we provide an illustrative example to demonstrate the validity of our derived results.

SOME RESULTS ON FUZZY METRIC SPACE AND SOME EXAMPLES OF FUZZY b-METRIC SPACE

Adv. Math. Sci. J. Vol. 9, No. 10 Open Access SOME RESULTS ON FUZZY METRIC SPACE AND SOME EXAMPLES OF FUZZY b-METRIC SPACE N. Kajan and K. Kannan DOI: https://doi.org/10.37418/amsj.9.10.3 Full Text Abstract Abstract The problem of constructing a satisfactory theory of fuzzy metric spaces has been investigated by several researchers from different … page AMSJ9-N10-3 Read More »

Aggregation of fuzzy quasi-metrics

In the last years fuzzy (quasi-) metrics and indistinguishability operators have been used as a mathematical tool in order to develop appropriate models useful in applied sciences as, for instance, image processing, clustering analysis and multi-criteria decision making. The both aforesaid similarities allow us to fuzzify the crisp notion of equivalence relation when a certain degree of similarity can be only provided between the compared objects. However, the applicability of fuzzy (quasi-) metrics is reduced because the difficulty of generating examples. One technique to generate new fuzzy binary relations is based on merging a collection of them into a new one by means of the use of a function. Inspired, in part, by the preceding fact, this paper is devoted to study which functions allow us to merge a collection of fuzzy (quasi-) metrics into a single one. We present a characterization of such functions in terms of ∗-triangular triplets and also in terms of isotonicity and ∗-supmultiplicativity, where ∗ is a t-norm. We also show that this characterization does not depend on the symmetry of the fuzzy quasi-metrics. The same problem for stationary fuzzy (quasi-) metrics is studied and, as a consequence, characterizations of those functions aggregating fuzzy preorders and indistinguishability operators are obtained.

On Metrization of the Topologies Induced by Fuzzy Metrics

In this paper, we focus on finding the metric functions in a fuzzy metric space. After introducing the concept of a stratified function in a fuzzy metric space, we prove that the topology generated by the family of stratified functions coincides with the topology generated by the fuzzy metric. Moreover, we get the concrete form of metric function under some special conditions.

Some Properties of Algebra Fuzzy Metric Space

Our goal in the present paper is to introduce new type of fuzzy metric space called algebra fuzzy metric space after that some examples is introduced to illustrate this notion. Then basic properties of algebra fuzzy metric space is proved.

On t-Conorm Based Fuzzy (Pseudo)metrics

We present an alternative approach to the concept of a fuzzy (pseudo)metric using t-conorms instead of t-norms and call them t-conorm based fuzzy (pseudo)metrics or just CB-fuzzy (pseudo)metrics. We develop the basics of the theory of CB-fuzzy (pseudo)metrics and compare them with “classic” fuzzy (pseudo)metrics. A method for construction CB-fuzzy (pseudo)metrics from ordinary metrics is elaborated and topology induced by CB-fuzzy (pseudo)metrics is studied. We establish interrelations between CB-fuzzy metrics and modulars, and in the process of this study, a particular role of Hamacher t-(co)norm in the theory of (CB)-fuzzy metrics is revealed. Finally, an intuitionistic version of a CB-fuzzy metric is introduced and applied in order to emphasize the roles of t-norms and a t-conorm in this context.

On the Topology Induced by C*-Algebra-Valued Fuzzy Metric Spaces

We define the notion of C * -algebra-valued fuzzy metric spaces and we study the topology induced by these spaces.

Fixed Point Theorems for Generalized Kannan-Type Mappings in a New Type of Fuzzy Metric Space

In this paper, first, we introduce a new type of S∗−fuzzy metric space which is a generalization of fuzzy metric spaces. Second, we study the topological properties of S∗−fuzzy metric spaces. Finally, we extend Kannan-type mappings to generalized Kannan-type mappings under ϕ−gauge functions introduced by Fang in S∗−fuzzy metric spaces and prove the existence and uniqueness of fixed point for this kind of mappings. Furthermore, we also obtain the common fixed point theorems for weak compatibility along with E.A. property or CLRg property. Our results extend and improve very recent theorems in the related literature.

A Characterization of Strong Completeness in Fuzzy Metric Spaces

Here, we deal with the concept of fuzzy metric space ( X , M , ∗ ) , due to George and Veeramani. Based on the fuzzy diameter for a subset of X , we introduce the notion of strong fuzzy diameter zero for a family of subsets. Then, we characterize nested sequences of subsets having strong fuzzy diameter zero using their fuzzy diameter. Examples of sequences of subsets which do or do not have strong fuzzy diameter zero are provided. Our main result is the following characterization: a fuzzy metric space is strongly complete if and only if every nested sequence of close subsets which has strong fuzzy diameter zero has a singleton intersection. Moreover, the standard fuzzy metric is studied as a particular case. Finally, this work points out a route of research in fuzzy fixed point theory.

Fuzzy metrics and cost optimization of a fault-tolerant system with vacationing and unreliable server

A finite population fuzzy model for the fault-tolerant system (FTS) is studied by considering the general distributed repair time, server vacation, and server breakdown. The concept of imperfect recovery, along with reboot process, is considered for the evaluation of fuzzy performance indices of an FTS supported by warm standbys. If the faults in the system are not detected successfully, then FTS reconfigures itself automatically by rebooting. When the system becomes free from the assigned repair jobs, the idle server can take a vacation and returns from the vacation in case a machine fails and requires repair. The single failure-prone server can provide the repair of failed machines with a slower rate in the breakdown state also. The parametric non-linear programming approach is implemented for the evaluation of performance metrics in a fuzzified environment using system parameters as a trapezoidal fuzzy number. The supplementary variable and recursive approaches are employed to obtain the system size distribution of the M/G/1 model by taking remaining repair time as a supplementary variable. The cost analysis is performed in order to determine the suitable control parameters using harmony search approach. The impacts of the sensitive system parameters on the performance of FTS are explored by evaluating numerical results for specific distributions of repair time.

Coupled Fixed Point Theorems Employing CLR-Property on V -Fuzzy Metric Spaces

The introduction of the common limit range property on V -fuzzy metric spaces is the foremost aim of this paper. Furthermore, significant results for coupled maps are proven by employing this property on V -fuzzy metric spaces. More precisely, we introduce the notion of C L R Ω -property for the mappings Θ : M × M → M and Ω : M → M . We utilize our new notion to present and prove our new fixed point results.

Fuzzy Metric Dimension of Fuzzy Hypercube Qn and Fuzzy Boolean Graphs

Let G = (V, E, ) be a fuzzy graph. Let M be a subset of V. M is said to be a fuzzy metric basis of G if for every pair of vertices x, y  V ‒ M, there exists a vertex w  M such that d (w, x)  d (w, y). The number of elements in M is said to be fuzzy metric dimension (FMD) of G and is denoted by  (G). The elements in M are called as source vertices. In this paper, we study the fuzzy metric dimension of fuzzy hypercube Qn, fuuzy Boolean Graph BG2 (G) and fuzzy Boolean Graph BG3 (G).

Some Fixed Point Theorems of Ćirić Type in Fuzzy Metric Spaces

The main aim of the current paper is the investigation of possibilities for improvements and generalizations contractive condition of Ćirić in the fuzzy metric spaces. Various versions of fuzzy contractive conditions are studied in two directions. First, motivated by recent results, more general contractive conditions in fuzzy metric spaces are achieved and secondly, quasi-contractive type of mappings are investigated in order to obtain fixed point results with a wider class of t-norms.

Fixed Point Theorem in Fuzzy Metric Space

Fixed Point Theorem in Fuzzy Metric Space

Contraction, Lebesgue and Common Fixed Point Property of Fuzzy Metric Spaces

In this paper, we using contraction and contraction functions in complete fuzzy metric space and establish sequential characterization properties of Lebesgue fuzzy metric space and common fixed on it. Then first introduce a new type of Lebesgue fuzzy metric space, which is generalization of fuzzy metric space, second we study the topological properties of Lebesgue fuzzy metric space, third a relation between Lebesgue and weak G-complete, compact fuzzy metrics and Lebesgue integral mappings finally established characterization properties on it. We prove the existence of common fixed point and contraction mapping in fuzzy metric space using the property of Lebesgue fuzzy metric space and integral type of mappings. On the basis of these properties we are getting common fixed point of two mappings, three mappings and four mappings in a easy way as compared to old method like Banach contraction fixed point. Also coincidence fixed point theorem for two mapping, three mappings and four mappings using Lebesgue fuzzy metric space and integral type of mappings. Also contraction mappings property in fuzzy metric space is helpful to determine common fixed point in Lebesgue fuzzy metric space. We also discuss the Lebesgue property of several well-known fuzzy metric spaces in this paper and conclude uniqueness of common fixed point.