On matrix equations in a class of complete and completely distributive lattices
Fuzzy Sets and Systems
Further contributions to the study of finite fuzzy relations equations
Fuzzy Sets and Systems
Finite fuzzy relation equations with unique solution in complete brouwerian lattices
Fuzzy Sets and Systems
Fuzzy sets and fuzzy logic: the foundations of application—from a mathematical point of view
Fuzzy sets and fuzzy logic: the foundations of application—from a mathematical point of view
Fuzzy sets and fuzzy logic: theory and applications
Fuzzy sets and fuzzy logic: theory and applications
Fuzzy Relation Equations and Their Applications to Knowledge Engineering
Fuzzy Relation Equations and Their Applications to Knowledge Engineering
Some properties of infinite fuzzy relational equations on complete Brouwerian lattices
Fuzzy Sets and Systems
Resolution of matrix equations over arbitrary Brouwerian lattices
Fuzzy Sets and Systems
Using concept lattice theory to obtain the set of solutions of multi-adjoint relation equations
Information Sciences: an International Journal
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It is well known that the solution set of a fuzzy relational equation with sup-inf composition is a join semilattice, in general, not a meet semilattice. This paper investigates the conditions under which the solution sets of fuzzy relational equations with sup-inf composition over complete Brouwerian lattices form lattices. We first give some properties of the decompositions of elements in complete lattices, then present a necessary and sufficient condition that the meet of a solution with any other solution is again a solution. Finally, we show some necessary and sufficient conditions that the solution sets are lattices.