Informatics and Applications

2024, Volume 18, Issue 1, pp 92-99

ANALYSIS OF APPROACHES TO DEFINING FUZZY RESOLVENT

T. M. Ledeneva
M. V. Leshchinskaya

Abstract

The article presents the results of a study concerning various definitions of the resolvent in fuzzy logic. Conditions are defined under which the Lee resolvent is a significant logical consequence in the case of the classical definition of fuzzy logical connectives. It is shown that when using triangular norms and conorms for their formalization, it is impossible to obtain a logically significant Lee resolvent. However, if the triangular conorm is defined as max, then the Lee resolvent exists for any triangular norm. Conditions are defined under which the Mukaidano resolvent is a significant logical consequence for classical min and max operations. When using triangular norms and conorms other than classical ones, further research is required. An illustrative example is provided demonstrating the process of constructing the Mukaidano resolvent.

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