Abstract
After a survey of some known lattice results, we determine the greatest idempotent (resp. compact) solution, when it exists, of a finite square rational equation assigned over a linear lattice. Similar considerations are presented for composite relational equations.
Highlights
The theory of fuzzy relation equations is a powerful tool for applicational purposes like Fuzzy
We prove the existence in when nonempty, of compact elements of (R is compact if R> R, R is idempotent if R2 R)
We prove the thesis (a) since the thesis (b) can be proved
Summary
The theory of fuzzy relation equations is a powerful tool for applicational purposes like Fuzzy. Meet-) subsemilattice of "$ by Lemma of Shmuely [18] As it is known, ^becomes a lattice defining the sup operation "kJ" as IR R 2 R v R2, where R1,R2 R A and "_" stands for the max-min transitive closure of any. Concerning Eq (1.1), it was proved in [3] that the set "J’=Y(A,B)=n^of all max-rain transitive solutions is nonempty iff O, w e ’/being the matrix, defined as Wij Bj if Bi > Bj and Wij Sij if B R for any R E ’.
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