Since its original formulation, the theory of fuzzy sets has spawned a number of extensions where the role of membership values in the real unit interval $[0, 1]$ is handed over to more complex mathematical entities. Amongst the many existing extensions, two similar ones, the fuzzy multisets and the hesitant fuzzy sets, rely on collections of several distinct values to represent fuzzy membershi...

In this work, we shall present some novel process to measure the similarity between picture fuzzy sets. Firstly, we adopt the concept of intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets and picture fuzzy sets. Secondly, we develop some similarity measures between picture fuzzy sets, such as, cosine similarity measure, weighted cosine similarity measure, set-theoretic similar...

Several specific types of generalized sets (briefly, g-T_g-sets in topological spaces T_g-spaces have been defined and investigated for various purposes from time to the literature T_g-spaces. Our recent research field a new class is reported herein as starting point more classes. It shown that superclass those whose elements are called open, closed, semi-open, semi-closed, pre-open, pre-closed...

Fourier analysis is a powerful tool for many problems, and especially for solving various differential equations of interest in science and engineering. In the present paper since the utilization of Zadeh's Extension principle is quite difficult in practice, we prefer the idea of level sets in order to construct a fuzzy-valued function on a closed interval via related membership function. We de...

We address the problem of identifying a useful set of mutually compatible separation axioms for each category T-FNS of T-neighbourhood spaces. It should contain one of T-complete regularity that characterizes T-uniformizability, as indeed we achieve here. This seems to necessitate the parameterization of most separation axioms by the triangular norm T, with the exception of the two axioms T0 an...

Bijective transformations play an important role in generating fuzzy implications from fuzzy implications. In [Representations through a Monoid on the set of Fuzzy Implications, Fuzzy Sets and Systems, 247, 5167], Vemuri and Jayaram proposed a monoid structure on the set of fuzzy implications, which is denoted by I, and using the largest subgroup S of this monoid discussed some group actions on...

When 60 years ago Shannon established “A Mathematical Theory of Communication” nobody could know the consequences for science and technology in the second half of the century. Shannon published his article in two parts in the July and October 1948 editions of the Bell System Technical Journal. However, it is very probable that this article wouldn’t have become famous without the help of Weaver,...

Carlsson and Fuller [C. Carlsson, R. Fuller, On possibilistic mean value and variance of fuzzy numbers, Fuzzy Sets and Systems 122 (2001) 315–326] have introduced possibilisticmean, variance and covariance of fuzzy numbers and Fuller andMajlender [R. Fuller, P. Majlender, On weighted possibilistic mean and variance of fuzzy numbers, Fuzzy Sets and Systems 136 (2003) 363–374] have introduced the...

in this paper we study two important concepts, i.e. the direct andthe inverse limit of hyperstructures associated with fuzzy sets of type 2, andshow that the direct and the inverse limit of hyperstructures associated withfuzzy sets of type 2 are also hyperstructures associated with fuzzy sets of type 2.