In this paper, we introduce intuitionistic fuzzy incline (IFI), intuitionistic fuzzy incline matrix (IFIM) and its determinant. Also the transitive closure, power of convergent, nilpotence of IFIM and adjoint of an IFIM are considered here. Some properties of determinant of IFIM and triangular IFIM are also introduced here. 2010 AMS Classification: 03E72, 15A15, 15B15

In this paper, we consider the problem of solving systems of fuzzy relation equations in a space with fuzzy preorder. Two types of these systems with different compositions are considered. New solvability criteria are proposed for systems of both types. The new criteria are weaker than all the known ones that are based on the assumption that fuzzy sets on the left-hand side of a system establis...

This article introduces interior and closure operators with inclusion degree considered within a crisp or fuzzy topological framework. First, inclusion degree is introduced in an extension of the interior and closure operators in crisp topology. This idea is then introduced in fuzzy topology by incorporating a relaxed version of fuzzy subsethood. The introduction of inclusion degree leads to a ...

Berstel and Pin have characterized local languages by introducing local automaton. In this paper fuzzy local language is introduced and the fuzzy local languages recognized by partial fuzzy local automata in max-min and min-max compositions are studied. Some closure properties of fuzzy local languages are provided. Mathematics Subject Classification: 68Q45

In this paper, we introduce some important properties of intuitionistic fuzzy soft topological spaces and define the intuitionistic fuzzy soft closure and interior of an intuitionistic fuzzy soft set. Furthermore, intuitionistic fuzzy soft continuous mapping are given and structural characteristics are discussed and studied.

in this paper we present a method for solving fuzzy linear systemsby two crisp linear systems. also necessary and sufficient conditions for existenceof solution are given. some numerical examples illustrate the efficiencyof the method.

We study a Lindenmayer-like parallel rewriting system to model the growth of filaments (arrays of cells) in which developmental errors may occur. In essence this model is the fuzzy analogue of the derivation-controlled iteration grammar. Under minor assumptions on the family of control languages and on the family of fuzzy languages in the underlying iteration grammar, we show that (i) regular c...

Vagueness and high dimensional space data are usual features of current data. The paper is an approach to identify conceptual structures among fuzzy three dimensional data sets in order to get conceptual hierarchy. We propose a fuzzy extension of the Galois connections that allows to demonstrate an isomorphism theorem between fuzzy sets closures which is the basis for generating lattices ordere...

Galois connection in category theory play an important role inestablish the relationships between different spatial structures. Inthis paper, we prove that there exist many interesting Galoisconnections between the category of Alexandroff $L$-fuzzytopological spaces, the category of reflexive $L$-fuzzyapproximation spaces and the category of Alexandroff $L$-fuzzyinterior (closure) spaces. This ...

In this paper, we present a general framework for the study of interval type-2 rough fuzzy sets by using both constructive and axiomatic approaches. First, several concepts and properties of interval type-2 fuzzy sets are introduced. Then, a pair of lower and upper interval type-2 rough fuzzy approximation operators with respect to a crisp binary relation is proposed. Classical representations ...