In this paper, an interval-valued Pythagorean triangular fuzzy number (IVPTFN) as a useful tool to handle decision-making problems with vague quantities is defined. Then, their operational laws are developed. By introducing a novel method of making a decision on the concept of possibility theory, a multi-attribute group decision-making (MAGDM) problem is considered, in which the attribute value...

Fermatean fuzzy sets are more powerful than sets, intuitionistic and Pythagorean in handling various problems involving uncertainty. The distance measures the non-standard frameworks have got their applicability areas such as pattern analysis, clustering, medical diagnosis, etc. Also, knowledge played a vital role computing criteria weights multicriteria decision-making problems. As there is no...

Uncertainty always exists in nature and real systems. It is known that probability has been used traditionally in modeling uncertainty. Since a belief function was proposed as an another type of measuring uncertainty, Dempster-Shafer theory (DST) has been widely studied and applied in diverse areas. Because of the advent of computer technology, the representation of human knowledge can be proce...

In this paper, we first use a fuzzy preference relation with a membership function representing preference degree forcomparing two interval-valued fuzzy numbers and then utilize a relative preference relation improved from the fuzzypreference relation to rank a set of interval-valued fuzzy numbers. Since the fuzzy preference relation is a total orderingrelation that satisfies reciprocal and tra...

in this paper we introduce the notions of fuzzy transposition hypergroupsand fuzzy regular relations and investigate their basic properties.we also study fuzzy quotient hypergroups of a fuzzy transposition hypergroup.

Fuzzy relational models have been widely investigated and found to be an efficient tool for the identification of complex systems. However, little attention has been given to the linguistic interpretation of these models. The use of relational models is recommended since their development follows a natural sequence based on the original ideas about fuzzy sets and fuzzy logic, involving the esti...

in this paper, our focus of attention is the proper propagationof fuzzy degrees in determinization of $nondeterministic$ $fuzzy$$finite$ $tree$ $automata$ (nffta). initially, two determinizationmethods are introduced which have some limitations (one inbehavior preserving and other in type of fuzzy operations). inorder to eliminate these limitations and increasing theefficiency of ffta, we defin...

Fuzzy Set Theory and Rough Set Theory are the most popular mathematical tools for dealing with uncertainties. During past decades, these set theories are being applied successfully in several areas for solving many complex tasks. This paper is concerned with the application of hybrid Fuzzy-Rough set based approach for feature subset selection. Keywords— Fuzzy set theory, Rough Set theory, Fuzzy...

The backing of the fuzzy ideal is normal ideal in some ring and in same time there fuzzy set whose is not fuzzy ideal and it backing set is ideal, i.e., it crisp is normal ideal. Consequently, in this paper we constructing a fuzziness function which defined on fuzzy sets and assigns membership grade for every fuzzy set whose it backing set are crisp ideal. Now, Let  be collection of all fuzzy s...

The aim of this paper is to introduce and study the notions of fuzzy upper $e$-limit set, fuzzy lower $e$-limit set and fuzzy $e$-continuously convergent functions. Properties and basic relationships among fuzzy upper $e$-limit set, fuzzy lower $e$- limit set and fuzzy $e$-continuity are investigated via fuzzy $e$-open sets.