In this article, Hamacher operations of Picture Fuzzy Matrices are proposed, which direct extensions Intuitionistic Matrices. By using these scalar multiplication and exponentiation constructed for a picture fuzzy matrix certain new relations established

Abstract In this study, the notions of picture fuzzy tolerance graphs, interval containment graphs and $$\phi $$ ϕ -tolerance are established. Three special types having bounded representations introduced studied corresponding properties them taking as max, min sum functions. Also, proper unit established som...

lthough fuzzy set theory and  sheaf theory have been developed and studied independently,  ulrich hohle shows that a large part of fuzzy set  theory  is in fact a subfield of sheaf theory. many authors have studied mathematical structures, in particular, algebraic structures, in both  categories of these generalized (multi)sets. using hohle's idea, we show that for a (universal) algebra $a$, th...

The main purpose of this article is to highlight the fact that there are some drawbacks in the existing definition of complementation of fuzzy sets and hence the geometrical representation of fuzzy sets on the basis of such definition which itself is defective would have no meaning. As a result the theorems or formulas which were rooted in the geometrical representation would become unacceptabl...

a flood warning system is a non-structural measure for flood mitigation. several parameters are responsible for flood related disasters. this work  illustrates an ordered intuitionistic fuzzy analysis that has the capability to simulate the unknown relations between a set of meteorological and hydrological parameters. in this paper, we first define ordered intuitionistic fuzzy soft sets and est...

To tackle the problem with inexact, uncertainty and vague knowl- edge, constructive method is utilized to formulate lower and upper approx- imation sets. Rough set model over dual-universes in fuzzy approximation space is constructed. In this paper, we introduce the concept of rough set over dual-universes in fuzzy approximation space by means of cut set. Then, we discuss properties of rough se...

Picture fuzzy set is a direct generalization of intuitionistic and therefore more capable dealing with uncertainty while working on real life problems. The concept inclusion subject that frequently studied in family sets has many applications Therefore, this work, the measuring degree between picture introduced. For purpose, firstly axioms for subsethood measure are given then based distance pr...