In the process of decision making, the decision makers usually provide inconsistent fuzzy preference relations, and it is unreasonable to get the priority from an inconsistent preference relation. In this paper, we propose a method to derive the multiplicative consistent fuzzy preference relation from an inconsistent fuzzy preference relation. The fundamental characteristic of the method is tha...

This paper further investigates the data compression of fuzzy relation information systems. First, we introduce an algorithm for constructing the homomorphism between fuzzy relation information systems. Then, we discuss that how to compress the dynamic fuzzy relation information systems by utilizing the compression of the original systems. Afterwards, several illustrative examples are employed ...

This paper introduces a novel real-time Fuzzy Supervised Learning with Binary Meta-Feature (FSL-BM) for big data classification task. The study of real-time algorithms addresses several major concerns, which are namely: accuracy, memory consumption, and ability to stretch assumptions and time complexity. Attaining a fast computational model providing fuzzy logic and supervised learning is one o...

In this paper, we propose a novel design of evolving fuzzy classifiers in case of multi-class classification problems. Therefore, we exploit the concept of all-pairs aka all-versus-all classification using binary classifiers for each pair of classes, which has some advantages over direct multi-class as well as one-versus-rest classification variants. Regressionbased as well as singleton class l...

This  paper extends the notion of fuzzy $BCK$-subalgebras to fuzzy hyper $BCK$-subalgebras and defines an extended fuzzy $BCK$-subalgebras. This study  considers  a type of fuzzy hyper  $BCK$-ideals  in this  hyperstructure  and  describes   the  relationship  between hyper  $BCK$-ideals and  fuzzy hyper  $BCK$-ideals.  In fact, it tries to introduce   a  strongly  regular  relation  on hyper $...

In this paper, the order, size and degree of the nodes of the isomorphic fuzzy graphs are discussed. Isomorphism between fuzzy graphs is proved to be an equivalence relation. Some properties of self complementary and self weak complementary fuzzy graphs are discussed. Keywords—complementary fuzzy graphs, co-weak isomorphism, equivalence relation, fuzzy relation, weak isomorphism.

Systems of fuzzy relation equations are considered as models of fuzzy inference systems. A proper use of an inference mechanism connected to a fuzzy relation modelling a fuzzy rule base is certified by keeping the fundamental interpolation condition. The paper aims at new solutions of systems of fuzzy relation equations and introduces new solvability criteria.

We define an extended fuzzy equivalence relation, discuss some basic properties of extended fuzzy equivalence relations, find the extended fuzzy equivalence relation generated by a fuzzy relation in a set, and give some lattice theoretic properties of extended fuzzy equivalence relations.

In 1965, Zadeh [30] introduced a concept of a fuzzy set as the generalization of a crisp set. Also, in 1971, he introduced a fuzzy relation naturally, as a generalization of a crisp relation in [31]. Nel [27] introduced the notion of a topological universe which implies concrete quasitopos [1]. Every topological universe satisfies all the properties of a topos except one condition on the subobj...

The paper dealswith systems of fuzzy relation equations known in the literature as eigen fuzzy set equations, aswell aswith systems of related fuzzy relation inequalities.Ourmain results are algorithms for computing the greatest and the smallest solutions to the considered systems of fuzzy relation inequalities, and algorithms for computing the greatest solutions to the considered systems of fu...