Maji et al. introduced the concept of intuitionistic fuzzy soft sets, which is an extension to the soft set and intuitionistic fuzzy set. In this paper, we apply the concept of intuitionistic fuzzy soft sets to semigroup theory. The notion of intuitionistic fuzzy soft ideals over a semigroup is introduced and their basic properties are investigated. Some lattice structures of the set of all int...

We have defined fuzzy bipolar soft sets and basic operations of union, intersection and complementation for fuzzy bipolar soft sets. The algebraic properties of fuzzy bipolar soft sets are discussed. The concept of bipolar fuzzy soft set is also given and the equivalence of both structures is established. An application of fuzzy bipolar soft sets in decision making problems is presented with th...

Firstly, soft hyperideals of hyperlattices are introduced and several interesting examples of them are given. Secondly, fuzzy soft hyperideals are proposed, which are generalizations of hyperideals and soft hyperideals in hyperlattices. After that, equivalent conditions of fuzzy soft hyperideals are given by using level soft sets. Finally, under the fuzzy soft homomorphism of hyperlattices, the...

An n× n fuzzy matrix A is called regular if there is an n× n fuzzy matrix G such that AGA = A. We study the problem of characterizing those linear operators T on the fuzzy matrices such that T (X) is regular if and only if X is. Consequently, we obtain that T strongly preserves regularity of fuzzy matrices if and only if there are permutation matrices P and Q such that it has the form T (X) = P...

We propose a new MCDM method based on fuzzy pair-wise comparisons and a feedback between the criteria. The evaluation of the weights of criteria, the variants as well as the feedback between the criteria is based on the data given in pair-wise comparison matrices. Extended arithmetic operations with fuzzy numbers are used as well as ordering fuzzy relations to compare fuzzy outcomes. An illustr...

Fuzzy algebra is an algebraic structure in which classical addition and multiplication are replaced by ⊕ and ⊗, where a⊕ b = max{a,b}, a⊗ b = min{a,b}. Fuzzy discrete dynamic systems can be introduced by fuzzy matrices and are useful for describing knowledge engineering, scheduling, cluster analysis, fuzzy logic programs, diagnosis of technical devices or medical diagnosis. The paper deals with...

Soft Computing techniques play an important role for decision in applications with imprecise and uncertain knowledge. The application of soft computing disciplines is rapidly emerging for the diagnosis and prognosis in medical applications. Between various soft computing techniques, fuzzy expert system takes advantage of fuzzy set theory to provide computing with uncertain words. In a fuzzy exp...