In this paper, we study fuzzy substructures in connection withHv-structures. The original idea comes from geometry, especially from thetwo dimensional Euclidean vector space. Using parameters, we obtain a largenumber of hyperstructures of the group-like or ring-like types. We connect,also, the mentioned hyperstructures with the theta-operations to obtain morestrict hyperstructures, as Hv-groups...

‎In the paper‎, ‎we study duality for vector equilibrium problems using a concept of generalized convexity in dealing with the quasi-relative interior‎. ‎Then‎, ‎their applications to optimality conditions for quasi-relative efficient solutions are obtained‎. ‎Our results are extensions of several existing ones in the literature when the ordering cones in both the objective space and the constr...

We study bisimulation and minimization for weighted automata, relying on a geometrical representation of the model, linear weighted automata (lwa). In a lwa, the state-space of the automaton is represented by a vector space, and the transitions and weighting maps by linear morphisms over this vector space. Weighted bisimulations are represented by sub-spaces that are invariant under the transit...

The study of vector optimization problems has recently been a rapidly growing area of research. See, for example, [1–5] and the references mentioned therein. In this paper, we study a class of vector minimization problems on a complete metric space such that all its bounded closed subsets are compact. This class of problems is associated with a complete metric space of continuous vector functio...

In the present paper we consider generic Sub-Riemannian structures on the co-rank 1 non-holonomic vector distributions and introduce the associated canonical volume and ”horizontal” area forms. As in the classical case, the Sub-Riemannian minimal surfaces can be defined as the critical points of the ’‘horizontal” area functional. We derive an intrinsic equation for minimal surfaces associated t...

The goal of this work is to present an extension to the vector model that accounts for the correlation among query terms, by using association rules, a popular data mining technique. In Information Retrieval, the vector model allows retrieving a set of documents from a termbased query, where both query terms and documents are vectors in a vector space. Although the vector model has been used su...

Vector couplings in the Duffin-Kemmer-Petiau theory are revised. It is shown that minimal and nonminimal vector potentials behave differently under charge-conjugation and time-reversal transformations. In particular, it is shown that nonminimal vector potentials have been erroneously applied to the description of elastic meson-nucleus scatterings and that the space component of the nonminimal v...

In this research we present new results on discrete Lagrangian methods (DLM) and extend our previous (incomplete and highly simpli ed) theory on the method. Our proposed method forms a strong mathematical foundation for solving general nonlinear discrete optimization problems. Speci cally, we show for continuous Lagrangian methods the relationship among local minimal solutions satisfying constr...