각종 대수에서의 하이퍼 및 소프트집합 이론의 응용에 관한 연구

Abstract

Using the notion of bipolar-valued fuzzy sets, the concepts of bipolar fuzzy (weak, -weak, strong) hyper -ideals are introduced, and their relations are discussed. Moreover, several related properties are investigated. Bipolar-valued fuzzification of the notion of implicative hyper -ideals is considered. Using the concepts of positive and negative level sets, a characterization of a bipolar fuzzy implicative hyper -ideal is provided. A relation between a bipolar fuzzy hyper -ideal and a bipolar fuzzy implicative hyper -ideal is established. A condition for a bipolar fuzzy hyper -ideal to be a bipolar fuzzy implicative hyper -ideal is given. By using a collection of implicative hyper -ideals, a bipolar fuzzy implicative hyper -ideal is established. The notions of (weak) hyper -deductive systems and (weak) implicative hyper -deductive systems are introduced, and several properties are investigated. Relations among hyper -deductive systems, weak hyper -deductive systems, implicative hyper -deductive systems and weak implicative hyper -deductive systems are discussed. A characterization of a hyper -deductive system is provided. A condition for a weak hyper -deductive system to be a weak implicative hyper -deductive system is given. The notions of fuzzy hyper -subalgebras, (weak, strong) fuzzy hyper -deductive systems and previously weak fuzzy hyper -deductive systems are introduced, and their relations/properties are investigated. We apply the notion of soft sets introduced by Molodtsov to the theory of -algebras. Soft -subalgebras and homomorphisms in soft -algebras are discussed.