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Solutions of composite fuzzy relational equations with triangular norms

โœ Scribed by Masaaki Miyakoshi; Masaru Shimbo

Publisher
Elsevier Science
Year
1985
Tongue
English
Weight
459 KB
Volume
16
Category
Article
ISSN
0165-0114

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โœฆ Synopsis

T-and aT-compositions , i.e., composite operations of sup-T and inf--aT, and relationships among ~-, etT-operators and t-norm are considered. It is shown that, if a composite fuzzy relational equation by T-composition has solutions, then a greatest one exists, and that if a similar equation by etr-composition has solutions, a greatest or least one exists, and unlike in T-compositions, it may have no lower solutions even if it has a greatest. Furthermore, the equivalence of the d,-and aT-operator, and the equipollence between t-norms and etr" operators are also shown. These results may be applicable to fuzzy inference under compositional rules of inference.

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