| Observation, understanding and representation, as well as analysis, synthesis and reasoning, of real world problem together with its solution at different levels of granularity, is an obvious feature in the process of human problem solving, and it also embodies the outstanding ability of human problem solving. In a sense, it is the intelligence in the process of human problem solving. Considering such ability of human, researchers of artificial intelligence have made some further investigation and presented many formal models. As an emerging research sub-field of artificial intelligence, granular computing, whole philosophy is to implement the problem solving at different levels of granularity, aims to establish much more general model reflecting the process of human problem solving.In quotient space theory, triplet (X,f,T) is proposed to describe a problem space, where X denotes the universe; f: Xâ†'Y indicates the attributes (or features) of universe X; an d T is the structure of universe X, na mely the relationship of different items at universe X. The resolving problem (X,f,T) is the process of analyzing and researching the universe X, the attributes f and the structure T.A great sort of problems can be summed up as a process of searching nodes on a corresponding and/or graphic. And/or reasoning model under quotient space solves uncertainty of information though the approach of setting different granule levels. But many times, some uncertainties of the granules which need to be studied cannot be avoided. The foregoing model needs to be extended to a new one which is capable of describing uncertain granules.This paper introduces the approach of describing granules in fuzzy set into processing and/or graphic reasoning model under quotient Space theory. Uses fuzzy definitions AF and PF instead of A and p .based on this, constructs corresponding property function fF and reasoning function gF, form the integrated fuzzy and/or reasoning model ((X, O), (fF, gF),(?), F1, F2, (AF, PF)) .Meanwhile, the paper improves fuzzy and/or graphic reasoning model is capable of projecting and combining in different quotient spaces levels. For reasoning model ((X,D),(fF,gF),(?),F1,F2,(AF,PF)), defines X1 as the quotient set of universe X ,and the projection model ((X1,D1),(fF1,gF1),(?),F1,F2,(AF1,PF1) can be built. For two reasoning models ((X1,D1),(fF1,gF1),(?),F1,F2,(AF1,PF1) and ((X2,D2),(fF2,gF2),(?)2,F1,F2,(AF2,pF2), transforms the and/or graphics to the corresponding or graphics, combines them to a new model, and transforms it into a corresponding and/or graphic, then constructs the combination model ((X3, D3), (fF3, gF3), (?)3, F1, F2,(AF3, PF3).Finally, based on fuzzy and/or graphic reasoning model under quotient. space theory, the paper solves a simulative dermal sensitivity test question. Through constructs quotient space description of the question, transforms the question into a process of searching fuzzy nodes on and/or graphic. The approach solves uncertainty by utilizing the projection and combination of fuzzy and/or graphic model between different quotient spaces. Not only testifies validity of fuzzy and/or graphic reasoning model, but also provides a new mode of disposing uncertainty in medical research on cephalosporin allergy... |
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