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Infinite fuzzy relation equations with continuous t-norms. (English) Zbl 1135.03346
Summary: This study develops a concept of infinite fuzzy relation equations with a continuous t-norm. It extends the work by Q. Xiong and X. Wang [“Some properties of sup-min fuzzy relational equations on infinite domains”, Fuzzy Sets Syst. 151, 393–402 (2005; Zbl 1062.03053)]. We describe attainable (respectively, unattainable) solutions, which are closely related to minimal solutions to the equations. It is shown that a solution set comprises both attainable and unattainable solutions. The study offers a characterization of these solutions. Under some assumptions, the solution set is presented and discussed. Two applications are also given.

MSC:
03E72 Theory of fuzzy sets, etc.
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