基于AFS结构和AFS代数的模糊理论

作者简介

《基于AFS结构和AFS代数的模糊理论(英文版)》内容简介：It is well known that, "fuzziness" is one of the important characteristics of human cognizanceand thinking. And fuzzy phenomena exist throughout nature and extensively within humansociety. The theory of fuzzy sets and systems has been rapidly developed and applied in manyfields since it was proposed by professor L.A. Zadeh, an expert of control theory, 1965. Manymathematicians, engineers and technicians have achieved many important results by using andapplying fuzzy theory.

This book is a systematic introduction to the AFS theory, which was first studied on theeleven research papers （[12]～[22]） published in the USA, North-holland and China by theauthor between 1994 and 1998, In these papers some new mathematical objects, such as AFSstructure, AFS algebras and cognitive field were proposed. Using regular mathematicallanguage, a new axiomatic system based on AFS structure and AFS algebras has beenestablished. In this system, membership functions are described by strict and uniformmathematical methods. It is proved that each fuzzy concept can be represented by an elementof the AFS algebras in some AFS structure and AFS algebras are mathematical abstractionsof the compositions and the operators of concepts. The topological molecular lattice structuresand topological structures are established on AFS structures, thus the relations betweenconcepts and some other variable properties of concepts are described by modernmathematical language, using such mathematical tools as topological molecular lattices andtopology. Thus a kind of the abstractions of human cognitive activities is obtained through theAFS theory.

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