Fuzzy mathematical techniques with applications
Fuzzy mathematical techniques with applications
Interval valued fuzzy sets based on normal forms
Fuzzy Sets and Systems
Interval-valued fuzzy sets and “compensatory AND”
Fuzzy Sets and Systems
Fuzzy Logic
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Based on Yin-Yang analysis, the intrinsic mechanisms among t-norms, t-conorms, negation, CNF, DNF, and axioms are analyzed in two aspects: first in the mathematical aspect, the basic root being, ''the relation and combination between the increasing functions and the decreasing ones'', 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''. Furthermore, some problems with t-norms and t-conorms are briefly studied in such fields as (1) the basic interactions in the Boolean system, the fuzzy system, and the general fuzzy system; (2) the relationship between the axioms and CNF = DNF; (3) The relationship between CNF and DNF based 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 extensive compensation principle dealing with single-valued fuzzy sets and interval-valued sets. The conclusion is that Yin-Yang analysis is a universal methodology to develop a general theory to handle the complex problems of uncertainty and find concrete approaches to them.