The solution set of fuzzy relation equations with addition-min composition
This work provides a complete description of solution sets for fuzzy relation equations, which is incremental for researchers in fuzzy logic and systems theory.
The paper addresses the resolution of fuzzy relation equations using addition-min composition by proposing algorithms to find all minimal and maximal solutions, and proves that every solution lies between these extremes, thereby fully characterizing the solution set.
This paper deals with the resolutions of fuzzy relation equations with addition-min composition. When the fuzzy relation equations have a solution, we first propose an algorithm to find all minimal solutions of the fuzzy relation equations and also supply an algorithm to find all maximal solutions of the fuzzy relation equations, which will be illustrated, respectively, by numeral examples. Then we prove that every solution of the fuzzy relation equations is between a minimal solution and a maximal one, so that we describe the solution set of the fuzzy relation equations completely.