2002, Volume 4, Issue 3
Strategic Study of CAE >> 2002, Volume 4, Issue 3
All Set and Artificial Intelligence
Northern Jiaotong University, Beijing 100044, China
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Abstract
This paper presents a brand new set theory, All Set theory, which is the united set form of the current set theories including crisp set, fuzzy set, extension set, vague set, rough set, set pair analysis, FHW (fuzzy gray matter - element)，FEEC(fuzzy extension economic control) and so on. The operation of the all set is also discussed in detail. A kind of style of the human being' s intelligence can be described by a kind of set form, thus all set is the united form. An all set is comprised of four parts, that is ( A, B, F, J ). A is the universe of the problem discussed. One of the elements in A can be described by an element of B. F is the map from A to B. And J restricts F. From this model, the concept of subjection that is the basic conception of human´s intelligence can be simulated. Hence the wide application of all set theory in the field of artificial intelligence including pattern recognition, clustering, logic, machine learning, intelligent decision, etc. , can be developed. Especially the relation among all set, logic and human intelligence style is illustrated in the paper. The theory of all set can not only unify and summarize the current theories but also provide the primary method for establishing new set theory and new logic.
Keywords
all set ; artificial intelligence ; set theory ; operation ; logic
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