Abstract
Through this study, the authors treat two kinds of fuzzy logical operators, that is, non-commutative conjunctions and their residual implications which include almost all of already-known functions in the field of fuzzy logic. Corresponding to such operators, two kinds of generalized compositions of fuzzy relations are introduced, and the solutions of new composite relational equations are given. This work reveals that the solutions include the results of the past researches in the field of fuzzy relational equations as special cases. Some specific numerical examples of the solutions of a given equation illustrate the mechanism of these compositions.
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