On an algebraic structure induced by a fuzzy bi-partially ordered space
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We introduce an algebraic structure induced by a fuzzy bi-partial order space on a complete residuated lattice. We establish that the two families of $f$-stable and $g$-stable fuzzy sets are complete lattices and that they are isomorphic. Additionally, we demonstrate that the composition map $gf$, when the two maps $f$ and $g$ are restricted to suitable Alexandrov topologies, can be regarded as an interior operator, while the map $fg$ can be viewed as a closure operator.
Abstract
We introduce an algebraic structure induced by a fuzzy bi-partial order space on a complete residuated lattice. We establish that the two families of $f$-stable and $g$-stable fuzzy sets are complete lattices and that they are isomorphic. Additionally, we demonstrate that the composition map $gf$, when the two maps $f$ and $g$ are restricted to suitable Alexandrov topologies, can be regarded as an interior operator, while the map $fg$ can be viewed as a closure operator.
참고문헌 (10)
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