Geodesic
Fuzzy sets (in)equations with a complete codomain lattice
Kybernetika, Tome 58 (2022) no. 2, pp. 145-162
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The paper applies some properties of the monotonous operators on the complete lattices to problems of the existence and the construction of the solutions to some fuzzy relational equations, inequations, and their systems, taking a complete lattice for the codomain lattice. The existing solutions are extremal - the least or the greatest, thus we prove some extremal problems related to fuzzy sets (in)equations. Also, some properties of upper-continuous lattices are proved and applied to systems of fuzzy sets (in)equations, in a special case of a meet-continuous complete codomain lattice.
The paper applies some properties of the monotonous operators on the complete lattices to problems of the existence and the construction of the solutions to some fuzzy relational equations, inequations, and their systems, taking a complete lattice for the codomain lattice. The existing solutions are extremal - the least or the greatest, thus we prove some extremal problems related to fuzzy sets (in)equations. Also, some properties of upper-continuous lattices are proved and applied to systems of fuzzy sets (in)equations, in a special case of a meet-continuous complete codomain lattice.
DOI : 10.14736/kyb-2022-2-0145
Classification : 03B52, 03E72, 06B23
Keywords: fuzzy relations; fuzzy set equations; fuzzy set inequations; monotonous operator; upper continuous lattice 
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Stepanović, Vanja; Tepavčević, Andreja. Fuzzy sets (in)equations with a complete codomain lattice. Kybernetika, Tome 58 (2022) no. 2, pp. 145-162. doi: 10.14736/kyb-2022-2-0145

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