data obtained in association with many real-life random experiments from different fields cannot be perfectly/exactly quantified.hspace{.1cm}often the underlying imprecision can be suitably described in terms of fuzzy numbers/values. for these random experiments, the scale of fuzzy numbers/values enables to capture more variability and subjectivity than that of categorical data, and more accura...

In this paper, we investigate the properties of some recently pro-posed fuzzy distance measures. We find out some shortcomings for these dis-tances and then the obtained results are illustrated by solving several examplesand compared with the other fuzzy distances.

In this paper, we firstly invoke gradual Hausdorff metric to define a new additive fuzzy-valued measure on the ordinary measurable space. Then, from the view of a fuzzy number as a crisp interval of gradual numbers, we show that the new fuzzy-valued measure can be characterized by two gradual number-valued measures. Finally, we investigate some of its properties and structural characterizations.

‎In this study‎, ‎we investigate topological properties of fuzzy strong‎ b-metric spaces defined in [13]‎. ‎Firstly‎, ‎we prove Baire's theorem for‎ ‎these spaces‎. ‎Then we define the product of two fuzzy strong b-metric spaces‎ ‎defined with same continuous t-norms and show that $X_{1}times X_{2}$ is a‎ ‎complete fuzzy strong b-metric space if and only if $X_{1}$ and $X_{2}$ are‎ ‎complete fu...

We consider the concept of fuzzy quasi-contractions initiated by '{C}iri'{c} in the setting of fuzzy metric spaces and establish fixed point theorems for quasi-contractive mappings and for fuzzy $mathcal{H}$-contractive mappings on M-complete fuzzy metric spaces in the sense of George and Veeramani.The results are illustrated by a representative example.

When handling fuzzy number data, it is a common practice to make use of a metric to quantify distances between fuzzy numbers. Several metrics have been suggested in the literature for this purpose. When statistically analyzing fuzzy number-valued data, L metrics become especially useful. This paper introduces a new family of generalized L metrics which take into account key features of the invo...

In this paper, we introduce a new fuzzy metric based on gradual numbers. Firstly, the concept of gradual metric spaces is introduced. And then, basic topological concepts in gradual metric spaces are presented and their properties are investigated. Mathematics Subject Classification: 54E35, 03E72

In this paper, we introduce the notions of fuzzy $alpha$-Geraghty contraction type mapping and fuzzy $beta$-$varphi$-contractive mapping and establish some interesting results on the existence and uniqueness of fixed points for these two types of mappings in the setting of fuzzy metric spaces and non-Archimedean fuzzy metric spaces. The main results of our work generalize and extend some known ...

In this paper, we first use a fuzzy preference relation with a membership function representing preference degree forcomparing two interval-valued fuzzy numbers and then utilize a relative preference relation improved from the fuzzypreference relation to rank a set of interval-valued fuzzy numbers. Since the fuzzy preference relation is a total orderingrelation that satisfies reciprocal and tra...

in this paper, a novel method for ranking of fuzzy numbers are proposed. in this method, decision maker is defined based on the center of mass at some cuts of a pair of fuzzy numbers in discreet version and center of mass on all of cuts of a pair of fuzzy numbers in continuous version. our method can rank more than two fuzzy numbers simultaneously. also, some properties of methods are described...