On the solvability of bipolar max-product fuzzy relation equations with the standard negation. (English) Zbl 1464.03053
Summary: Bipolar fuzzy relation equations arise when unknown variables together with their logical negations appear simultaneously in fuzzy relation equations. This paper gives a characterization of the solvability of bipolar max-product fuzzy (relation) equations with the standard negation. In addition, some properties associated with the existence of the greatest/least solution or maximal/minimal solutions are shown, when these (relation) equations are solvable. Different examples are included in order to clarify the developed theory.
MSC:
| 03E72 | Theory of fuzzy sets, etc. |
Keywords:
bipolar fuzzy relation equations; max-product composition; standard negation; inverse problem resolutionReferences:
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