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Solution sets of interval-valued fuzzy relational equations. (English) Zbl 1178.03071
Fuzzy Optim. Decis. Mak. 2, No. 1, 41-60 (2003); erratum ibid. 6, No. 3, 297 (2007).
Summary: This paper introduces the concepts of tolerable solution set, united solution set, and controllable solution set of interval-valued fuzzy relational equations. Given a continuous t-norm, it is proved that each of the three types of the solution sets of interval-valued fuzzy relational equations with a max-t-norm composition, if nonempty, is composed of one maximum solution and a finite number of minimal solutions. Necessary and sufficient conditions for the existence of solutions are given. Computational procedures based on the constructive proofs are proposed to generate the complete solution sets. Examples are given to illustrate the procedures.

##### MSC:
 3e+72 Theory of fuzzy sets, etc.
##### Keywords:
fuzzy relational equations; interval-valued system
Full Text:
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