A discrete Sugeno integral on a bounded distributive lattice L is defined as an idempotent weighted polynomial. Another possibility for axiomatization of integrals to consider compatible aggregation functions, uniquely extending the L-valued fuzzy measures. This paper aims study mentioned unique extension property concerning possible non-distributive lattices. We show that this equivalent distr...

For a quantaloid Q, considered as a bicategory, Walters introduced categories enriched in Q. Here we extend the study of monad-quantale-enriched categories of the past fifteen years by introducing monad-quantaloid-enriched categories. We do so by making lax distributive laws of a monad T over the discrete presheaf monad of the small quantaloid Q the primary data of the theory, rather than the l...

In this paper, the concepts of L-concave structures, concave Linterior operators and concave L-neighborhood systems are introduced. It is shown that the category of L-concave spaces and the category of concave Linterior spaces are isomorphic, and they are both isomorphic to the category of concave L-neighborhood systems whenever L is a completely distributive lattice. Also, it is proved that th...

We consider advanced policy description specifications in the context of Answer Set Programming (ASP). Motivated by our application scenario, we further extend an existing policy description language, so that it allows for expressing preferences among sets of objects. This is done by extending the concept of ordered disjunctions to cardinality constraints. We demonstrate that this extension is ...

For a partially ordered set P , we denote by Co(P ) the lattice of order-convex subsets of P . We find three new lattice identities, (S), (U), and (B), such that the following result holds: Theorem. Let L be a lattice. Then L embeds into some lattice of the form Co(P ) iff L satisfies (S), (U), and (B). Furthermore, if L has an embedding into some Co(P ), then it has such an embedding that pres...

Recently the distributive equations involving various classes of aggregation operators have aroused widespread attention because of their importance in the theoretic and applied communities of fuzzy set theory. 2-uninorms and semi-t-operators are two special classes of aggregation operators and have been proved to be useful in many areas such as fuzzy decision making, approximate reasoning and ...

The category, or class of algebras, in the title is denoted by $bf W$. A hull operator (ho) in $bf W$ is a reflection in the category consisting of $bf W$ objects with only essential embeddings as morphisms. The proper class of all of these is $bf hoW$. The bounded monocoreflection in $bf W$ is denoted $B$. We classify the ho's by their interaction with $B$ as follows. A ``word'' is a function ...

The FKG inequality asserts that for a distributive lattice with logsupermodular probability measure, any two increasing functions are positively correlated. In this paper we extend this result to functions with values in partially ordered algebras, such as algebras of matrices and polynomials.

The aim of this paper is to compute Shapley’s and Banzhaf’s values of cooperative games restricted by a combinatorial structure. There have been previous models developed to study the problem of games with partial cooperation. Games restricted by a communication graph were introduced by Myerson and Owen. Another type of combinatorial structure introduced by Gilles, Owen and van den Brink is equ...

We introduce the concept of complementary elements in ordered sets. If an ordered set S is a lattice, this concept coincides with that for lattices. The connections between distributivity and the uniqueness of complements are shown and it is also shown that modular complemented ordered sets represents \geometries" which are more general than projective planes. It was shown in 2], 4] and 6] that...