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Multiple Fuzzy Relation and Its Application to Coupled Fuzzy Control
Author(s) -
Feng June,
Lv Hongli,
Cheng Daizhan
Publication year - 2013
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.656
Subject(s) - defuzzification , fuzzy associative matrix , fuzzy set operations , fuzzy classification , fuzzy logic , fuzzy number , mathematics , neuro fuzzy , type 2 fuzzy sets and systems , fuzzy set , fuzzy control system , computer science , algebra over a field , artificial intelligence , pure mathematics
Using semi‐tensor product ( STP ) of matrix, this paper investigates the fuzzy relation of multiple fuzzy and uses this to design coupled fuzzy control is designed. First of all, under the assumption that the universe of discourse is finite, a fuzzy logical variable can be expressed as a vector, which unifies the expression of elements, subsets, and fuzzy subsets of a universe of discourse. Then, the matrix expression of set mappings is naturally extended to fuzzy sets. Second, based on STP, logic‐based matrix addition and product are proposed. These are particulary useful for the calculation of compounded fuzzy relations. Third, a dual fuzzy structure is introduced, which assures the finiteness of the universe of discourse, and is used for fuzzification and defuzzification. Finally, using the results obtained, a new technique is developed to design a coupled fuzzy controller for multi‐input multi‐output ( MIMO ) systems with coupled multiple fuzzy relations.