In this paper, we present triangle algebras: residuated lattices equipped with two modal, or approximation, operators and with a third angular point u, different from 0 (false) and 1 (true), intuitively denoting ignorance about a formula’s truth value. We prove that these constructs, which bear a close relationship to several other algebraic structures including rough approximation spaces, prov...

In this paper,  the concept of fuzzy metric-like spaces is introduced which generalizes  the notion of fuzzy metric spaces given by George and Veeramani cite{Vee1}. Some fixed point results for fuzzy contractive mappings on fuzzy metric-like spaces are derived. These results generalize several comparable results from the current literature. We also provide illustrative examples in support of ou...

In this paper we investigate the algebraic properties of dimension of fuzzy hypervector spaces. Also, we prove that two isomorphic fuzzy hypervector spaces have the same dimension.

In this paper, we propose a new definition of intuitionistic fuzzyquasi-metric and pseudo-metric spaces based on intuitionistic fuzzy points. Weprove some properties of intuitionistic fuzzy quasi- metric and pseudo-metricspaces, and show that every intuitionistic fuzzy pseudo-metric space is intuitionisticfuzzy regular and intuitionistic fuzzy completely normal and henceintuitionistic fuzzy nor...

In this paper, fuzzy syntopogenous spaces is introduced. First, the *-increasing and *-decreasing spaces have been studied. Second,order-convexity on syntopogenous structures (X,S,≤ ) has been defined. Third, the equivalent description of orderconvexity has been given. Finally, some important properties of order-convexity have been obtained.

In this paper we discuss several characterizations of fuzzy P-spaces and the conditions under which fuzzy topological spaces become fuzzy P-spaces, are investigated.

This paper presents a general framework for the study of rough fuzzy sets in which fuzzy sets are approximated in a crisp approximation space. By the constructive approach, a pair of lower and upper generalized rough fuzzy approximation operators is first defined. The rough fuzzy approximation operators are represented by a class of generalized crisp approximation operators. Properties of rough...

In this work, we introduce notion of connectedness on fuzzy soft topological spaces and present fundamentals properties. We also investigate effect to fuzzy soft connectedness. Moreover, $C_i$-connectedness which plays an important role in fuzzy topological space extend to fuzzy soft topological spaces.

In this paper, rstly, it is proved that, for a fuzzy vector space, the set of its fuzzy bases de ned by Shi and Huang, is equivalent to the family of its bases de ned by P. Lubczonok. Secondly, for two fuzzy vector spaces, it is proved that they are isomorphic if and only if they have the same fuzzy dimension, and if their fuzzy dimensions are equal, then their dimensions are the same, however,...