INTRINSIC MECHANISMS AND APPLICATION PRINCIPLES OF GENERAL FUZZY-LOGIC THROUGH YIN-YANG ANALYSIS

Based on Yin-Yang analysis, the intrinsic mechanisms among t-norms, t- conorms, negation, CNF, DNF, and axioms are analyzed in two aspects: f irst in the mathematical aspect, the basic root being, ''the relation and combination between the increasing functions and the decreasing on es'', and second in the philosophical aspect, the fundamental Yin-Yang principle being, ''the compensatory and dialectical thinking methods combining the positive analysis and the negative analysis''. Furthermo re, some problems with t-norms and t-conorms are briefly studied in su ch fields as (1) the basic interactions in the Boolean system, the fuz zy system, and the general fuzzy system; (2) the relationship between the axioms and CNF = DNF; (3) The relationship between CNF and DNF bas ed on the 16 fuzzy compositions (4) the construction of the uncertain map which is an extension of the fuzzy map or Karnaugh map; (5) the ex tensive compensation principle dealing with single-valued fuzzy sets a nd interval-valued sets. The conclusion is that Yin-Yang analysis is a universal methodology to develop a general theory to handle the compl ex problems of uncertainty and find concrete approaches to them. (C) 1 998 Elsevier Science Inc. All rights reserved.