각종 대수에서의 하이퍼 및 소프트집합 이론의 응용에 관한 연구
- Title
- 각종 대수에서의 하이퍼 및 소프트집합 이론의 응용에 관한 연구
- Other Titles
- Some Applications of Hyper and Soft Set Theory to Several Algebras
- Author
- 강민수
- Alternative Author(s)
- Min Su Kang
- Advisor(s)
- 김희식
- Issue Date
- 2010-02
- Publisher
- 한양대학교
- Degree
- Doctor
- 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.
- URI
- https://repository.hanyang.ac.kr/handle/20.500.11754/142702http://hanyang.dcollection.net/common/orgView/200000413357
- Appears in Collections:
- GRADUATE SCHOOL[S](대학원) > MATHEMATICS(수학과) > Theses (Ph.D.)
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