Research On Theories And Applications Of Fuzzy Set FS_COM With Three Kinds Of Negation

Negative concept plays an important role in knowledge representation and reasoning,especially in fuzzy knowledge representation and reasoning. The negation of Zadeh fuzzy setand its extentions theories can’t be able to fulfill the need of negation of fuzzy information inthe field of fuzzy information processing. How to distinguish, express and compute differentkinds of negative fuzzy information are important basic problems in the field of fuzzyinformation processing. In recent years, many scholars at home and foreign come up with alot of methods of thinking to slove these problems. Pan Zhenghua distinguishes contradictorynegative relation, medium negative relation and opposite negative relation in fuzzyknowledge from the angle of concept, and puts forward a fuzzy set FSCOM with three kinds ofnegation. This paper further studies on theories and applications of fuzzy set FSCOM.Theories and relationships of fuzzy set and its development of fuzzy set are introduced,the situation of the studies of negative relation of fuzzy information in the word is analyzed inthe first chapter. The second chapter mainly introduces the five kinds of different negativerelations of clear knowledge and fuzzy knowledge, the definition and operate nature of fuzzyset FSCOM are introduced.The ability of FSCOM and other fuzzy sets deal with negative fuzzyinformation is compared. The relations between FSCOM with Zadeh fuzzy set, Intuitionisticfuzzy sets and Vague sets are discussed.Chapter3defines fuzzy degree and close degree of FSCOM, and discusses the relations offuzzy degree of three kinds of negative fuzzy sets. Different calculation formulas of closedegree are given. In aplication, fuzzy information and their negative relations are representedby fuzzy set FSCOM, and formulas of close degree with three kinds of negation are reasonableby computing.Chapter4defines the concept of λ–medium negation on the base of FSCOM set, and alsopoints out the characteristic of its extention relationship. In order to make the maximummembership degree principle of traditional fuzzy set can be applied in FSCOM set, soλ–interval function is defined. The fuzzy comprehensive evaluation of FSCOM is given andthis theory is applied in disaster loss grade assessment, and also the comprehensive evaluationmethod of FSCOM is reasonable by comparing the results with raditional fuzzy set’s.The fuzzy inclusion degree of FSCOM set is defined from the angle of three kinds ofnegation of fuzzy set: contradictory negation, medium negation and opposite negation, andcomes up with three kinds of calculation formulas, and also discusses its application inchapter5.