Theory And Applications Of Fuzzy Set FSCOM

After fuzzy mathematical theory proposed by Zadeh in 1965, fuzzy mathematics has made great achievements in mathematical theory and applications research. It has become an important branch of mathematics. With the put forward of definition of fuzzy set, fuzzy mathematics broke the shackles of accuracy classical mathematics, making today’s mathematics become a scientific theory to processing accuracy, randomness and fuzzy objects.In computer and artificial intelligence theory and applications, knowledge represents and reasoning is a key research field, especially in the research of fuzzy knowledge representation and reasoning, the negative concept plays an important and special role. With the development of knowledge research, the new requirements of different negative concepts in fuzzy knowledge (information) are proposed in theoretical research and practical research.In real world, different negation relations always exist. However, there was only one kind of negation concept and negation representation not matter in Zadeh fuzzy set, vague set or rough set. And this kind of classical negation cannot satisfy the research requirement of knowledge representation and processing. In order to study different negative relations, recently. Pan Zhenghua distinguished negative concept on the basis of concept, studied and determined three kinds of different negative relations, namely opposite negative relation, medium negative relation and contradictory negative relation existed in fuzzy information, put forward fuzzy set FSCOM based on these. FSCOM provides a new theoretical basis for the study of the different negative problems in practical applications. The paper mainly study cut set of fuzzy set FSCOM, and applications of FSCOM fuzzy comprehensive evaluation and formal concept analysis.Chapter 1 introduces the background and development of fuzzy sets, and the research of negation in fuzzy knowledge;Chapter 2 focuses on the importance of distinguishing different kinds of negations. Further expounds five negative relations in knowledge process. Fuzzy logic FLCOM and FSCOM are proposed by these theories.Chapter 3 introduces the flaws in traditional fuzzy comprehensive evaluation methods based on Zadeh set. Application of FSCOM in practical problems is given by one dimensional Euclidean distance formula, different membership function are set up. Comprehensive evaluation matrix is established by FSCOM with different negative relations. And slope stability and water level evaluations are solved. The advantages of this method are obtained compared with traditional methods. Finally principles and general steps of FSCOM comprehensive evaluation are summarized.Chapter 4 cut set is an important concept in fuzzy system theory; it’s also an important key bridge between fuzzy set and Zadeh set. This chapter defines a-up cut set, α-strong up cut set, a-down cut set and a-strong down cut set and corresponding properties and theorem in FSCOM theory. Different relations among cut sets are presented as well. These works enrich the fuzzy sets FSCOM theory effectively.Chapter 5 FCA (formal concept analysis) proposed by German famous scholar Wille in 1992 uses formal context to present data, FCA is a powerful tool dealing with data analysis in formal context and rule extraction.Its core data construction is concept lattice. FCA has been widely used in many fields such as medicine, data mining, pattern recognition and engineering management-However, in data extraction and analysis most data process systems use classical two value logic to deal with negative knowledge presentation. With the increase complexity in information processing field, the traditional negation is no longer widely used, in order to adapt to negative knowledge processing technology development, many domestic and foreign scholars are working to give different notions of negation. This chapter mainly introduces the formal concept analysis of FSCOM and logical concept analysis.