an orthogonal approach to the fuzzification of both multisets and hybridsets is presented. in particular, we introduce $l$-multi-fuzzy and$l$-fuzzy hybrid sets, which are general enough and in spirit with thebasic concepts of fuzzy set theory. in addition, we study the properties ofthese structures. also, the usefulness of these structures is examined inthe framework of mechanical multiset proc...

background: advances in information technology and data collection methods have enabled high-speed collection and storage of huge amounts of data. data mining can be used to derive laws from large data volumes and their characteristics. similarly, fuzzy logic by facilitating the understanding of events is considered a suitable complement to scientific data mining. materials and methods: the pre...

Fuzzy semigroup theory concentrates on theoretical aspects, but also includes applications in the areas of fuzzy coding theory, fuzzy finite state machines, and fuzzy languages. In this paper, we introduce the concept of an ( , )-fuzzy filter of an ordered semigroup , where , , , , with . Since the concept of ( , )-fuzzy filter is an important and useful generalization of ordinary fuzzy filter,...

The present paper is an attempt to study the minimal BL-general fuzzy automata which realizes the given fuzzy behavior. Of two methods applied for construction of such automaton presented here, one has been based on Myhill-Nerode's theory while the other has been based on derivatives of the given fuzzy behavior. Meanwhile, the categories of BL-general fuzzy automata and fuzzy behavior, along wi...

In this paper we define intuitionistic fuzzy metric and normedspaces. We first consider finite dimensional intuitionistic fuzzy normed spacesand prove several theorems about completeness, compactness and weak convergencein these spaces. In section 3 we define the intuitionistic fuzzy quotientnorm and study completeness and review some fundamental theorems. Finally,we consider some properties of...

In the paper, logical axioms, inference rules, semantics, and some specific properties including the completeness theorems of four kinds of fuzzy type theory are presented. This theory is a higher order fuzzy logic that can be used for precise formalization, for example, of the theory of computing with words, fuzzy IF-THEN rules, approximate reasoning, and others.