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Fuzzy relational equations on complete Brouwerian lattices. (English) Zbl 1248.03073
Summary: This paper deals with the problem of solving fuzzy relational equations with inf-\(\alpha _{\mathcal T}\) composition on complete Brouwerian lattices under finite domains (resp. countably infinite domains). When the right-hand sides of fuzzy relational equations are meet-irreducible elements or have irredundant finite meet-decompositions, some necessary and sufficient conditions for attainable solutions (resp. unattainable solutions) are formulated and some properties of the attainable solutions (resp. the unattainable solutions) are shown. Further, the solution sets are given when they are nonempty.

03E72 Theory of fuzzy sets, etc.
06B23 Complete lattices, completions
06D20 Heyting algebras (lattice-theoretic aspects)
Full Text: DOI
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