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Fuzzy relation equations. (Chinese) Zbl 0534.15002

The paper is basically a survey paper which describes some basic concepts and methods of solving fuzzy relation equations. Similar to concepts widely employed in linear algebra, the fuzzy relation equation is represented by the fuzzy matrices and their product. With such representation, the solution of the fuzzy relation equation is reduced to finding fuzzy matrix that satisfies the fuzzy linear equation. The paper starts with the discussions of solving the one-variable one-degree fuzzy equation. It then extends the idea to the case of n variable, one-degree fuzzy equation. It discussed the Tsukamoto method of solving the fuzzy equation and two other simplified methods for problems with higher order matrix. The paper also points out the non-uniqueness of the minimal solutions and gives guidelines for selecting the minimal solution when they are repeated solutions. The paper is well presented. It familiarizes readers quickly on the important question of solving the fuzzy relation equation. It is a good exposition paper.
Reviewer: M.-Y.Wu

MSC:

15A06 Linear equations (linear algebraic aspects)
03B52 Fuzzy logic; logic of vagueness
03E72 Theory of fuzzy sets, etc.
94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
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