it is well known fact that binary relations are generalized mathematical functions. contrary to functions from domain to range, binary relations may assign to each element of domain two or more elements of range. some basic operations on functions such as the inverse and composition are applicable to binary relations as well. depending on the domain or range or both are fuzzy value fuzzy set, i...

‎in this paper, a new class of fuzzy sets called fuzzy strongly ${{g}^{*}}$-closed sets is introduced and its properties are investigated. moreover, we study some more properties of this type of closed spaces.

In this study, we present an integrated method of Analytical Hierarchy Process based on interval type-2 fuzzy sets (IT2FAHP) and Technique for Order Performance by Similarity to Ideal Solution based on on interval type-2 fuzzy sets (IT2FTOPSIS). The applicability of the proposed integrated method was performed on a case study of evaluation of life quality for 28 European Union Countries and oth...

Interval-valued intuitionistic fuzzy sets (IVIFSs), a generalization of fuzzy sets, is characterized by an interval-valued membership function, an interval-valued non-membership function.The objective of this paper is to deal with criteria aggregation problems using IVIFSs where there exists a prioritization relationship over the criteria.Based on the ${L}$ukasiewicz triangular norm, we first p...

Type-II fuzzy sets are used to convey the uncertainties in the membership function of type-I fuzzy sets. Linguistic information in expert rules does not give any information about the geometry of the membership functions. These membership functions are mostly constructed through numerical data or range of classes. But there exists an uncertainty about the shape of the membership, that is, wheth...

Nonlinear inter-symbol interference leads to significant error rate in nonlinear communication and digital storage channel. In this paper, therefore, a novel recurrent interval type-2 fuzzy neural network with asymmetric membership functions (RT2FNN-A) is proposed for nonlinear channel equalization. The RT2FNN-A uses the interval asymmetric type-2 fuzzy sets and it implements the fuzzy logic sy...

Monotonicity is a major property of entropy measures. In this paper, we focus on measures for intuitionistic fuzzy sets and interval-valued sets. We consider their polar representation which provides an easy interpretation monotonicity several introduced in the literature. Moreover, enables us to propose two new kinds such entropies, that offer more understandable way explain differences entrop...

In this paper, we propose a novel recurrent interval type-2 fuzzy neural network with asymmetric membership functions (RT2FNN-A). The RT2FNN-A uses the interval asymmetric type-2 fuzzy sets and it implements the fuzzy logic system (FLS) in a five-layer neural network structure. The RT2FNN-A is modified from the type-2 fuzzy neural network to provide memory elements for capturing the system’s dy...

This study presents vibration control using actively tunable vibration absorbers (ATVA) to suppress vibration of a thin plate. The ATVA is made of a sandwich hollow structure embedded with electrorheological fluid (ERF). ERF is considered to be one of the most important smart fluids and it is suitable to be embedded in a smart structure due to its controllable rheological property. ERF’s appare...

Rough set theory is an important approach to granular computing. Type-1 fuzzy set theory permits the gradual assessment of the memberships of elements in a set. Hybridization of these assessments results in a fuzzy rough set theory. Type-2 fuzzy sets possess many advantages over type-1 fuzzy sets because their membership functions are themselves fuzzy, which makes it possible to model and minim...