The concept of a bipolar metric space is presented in this article. In fuzzy space, the notions continuous t-norms and symmetry $$t_s$$ -conorms employs important role. Requirements triangular norms are used to extrapolate with probability density function triangle inequality. Dual processes known as conorms. Continuous define paper. Besides, number topological functional properties have been s...

The IFS is a scheme for describing and manipulating complex fractal attractors using simple mathematical models. More precisely, the most popular “fractal –based” algorithms for both representation and compression of computer images have involved some implementation of the method of Iterated Function Systems (IFS) on complete metric spaces. In this paper a new generalized space called Multi-Fuz...

Generally fuzzy sets are used to analyze the fuzzy system reliability. Here intuitionistic fuzzy set theory has been used for analyzing the fuzzy system reliability. To analyze the fuzzy system reliability, the reliability of each component of the system is considered as a triangular intuitionistic fuzzy number. At first triangular intuitionistic fuzzy number and their arithmetic operations are...

In general fuzzy sets are used to analyze the fuzzy system reliability. Here intuitionistic fuzzy set theory for analyzing the fuzzy system reliability has been used. To analyze the fuzzy system reliability, the reliability of each component of the system as a triangular intuitionistic fuzzy number is considered. Triangular intuitionistic fuzzy number and their arithmetic operations are introdu...

The theories of metric spaces and fuzzy are crucial topics in mathematics. 
 Compactness is one the most important fundamental properties that have been widely used Functional Analysis. In this paper, definition compact soft space introduced some its theorems investigated. Also, sequentially locally defined relationships between them studied. Moreover, each previous two concepts several ot...

in this paper, we give some new definitions of m-fuzzy metric spaces and we prove a common fixed point theorem for six mappings under the condition of weakly compatible mappings in complete m-fuzzy metric spaces.

In this paper, we introduce a stationary M∞-fuzzy metric on the set C B(X), where M∞-fuzzy metric can be thought of as the degree of nearness between two fuzzy sets with respect to any positive real number and C B(X) is the class of fuzzy sets with nonempty bounded closed α-cut sets. Under the φ-contraction conditions, we give some common fixed point theorems for self-mappings in the space C B(X).

In the fuzzy arithmetic, the definitions of addition and multiplication of fuzzy numbers are based on Zadeh’s extension principle. From theoretical and practical points of view, this multiplication of fuzzy numbers owns several unnatural properties. Recently, to avoid this shortcoming, a new multiplicative operation of product type is introduced, the so-called cross-product of fuzzy numbers. Th...

In this paper, we study the existence of coupled coincidence andcoupled common fixed points for single-valued and fuzzy mappingsunder a contractive condition in metric space. Presented theoremsextend and improve the main results of Abbas and$acute{C}$iri$acute{c}$ {itshape et al.} [M. Abbas, L.$acute{C}$iri$acute{c}$, {itshape et al.}, Coupled coincidenceand common fixed point theorems for hybr...