‎in this paper first we define the morphism between geometric spaces in two different types‎. ‎we construct two categories of $uu$ and $l$ from geometric spaces then investigate some properties of the two categories‎, ‎for instance $uu$ is topological‎. ‎the relation between hypergroups and geometric spaces is studied‎. ‎by constructing the category $qh$ of $h_{v}$-groups we answer the question...

We apply the classical theory of hyperrings to vague soft sets to derive the concepts of vague soft hyperrings, vague soft hyperideals, and vague soft hyperring homomorphism. The properties and structural characteristics of these concepts are also studied and discussed. Furthermore, the relationship between the concepts introduced here and the corresponding concepts in classical hyperring theor...

‡ Partially supported by FCT/PRAXIS XXI, Portugal, grant number BD/21595/99. ¥ Partially supported by CNPq, Brazil, grant number 301041/95-4, and by project MAPPEL (PROTEM-CC, CNPq/NSF), grant number 680033/99-8. Abstract. In this paper we propose an emergence-driven software process for agent-based simulation that clarifies the traceability of micro and macro observations to micro and macro sp...

We introduce and study category of $(m, n)$-ary hypermodules as a generalization of the category of $(m, n)$-modules as well as the category of classical modules. Also, we study various kinds of morphisms. Especially, we characterize monomorphisms and epimorphisms in this category. We will proceed to study the fundamental relation on $(m, n)$-hypermodules, as an important tool in the study of a...

The concept of algebraic hyperstructures introduced by Marty as a generalization of ordinary algebraic structures. In an ordinary algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two elements is a set. The concept of ?-semihyperrings is a generalization of semirings, a generalization of semihyper‌rings and a generalizat...

Hyperoperations are mappings that assign a non-void subset of a set to each n-tuple of elements from the set. They present a fundamental notion for modeling non deterministic processes. Even though for each non deterministic automaton there is a language equivalent deterministic automaton, they do not have the same behavior. As behavior of concurrent processes took place in emerging fields of t...

The study of BCK-algebras was initiated by Iséki [7] as a generalization of the concept of set-theoretic difference and propositional calculus. Iséki posed an interesting problem; whether the class of BCK-algebras is a variety. In connection with this problem Komori introduced in [9] a notion of BCC-algebra which is a generalization of a BCK-algebra and proved that the class of all BCC-algebras...

‡ Partially supported by FCT/PRAXIS XXI, Portugal, grant number BD/21595/99. ¥ Partially supported by CNPq, Brazil, grant number 301041/95-4, and by project MAPPEL (PROTEM -CC, CNPq/NSF), grant number 680033/99-8. Abstract. In this paper we propose an emergence-driven software process for agent-based simulation that clarifies the traceability of micro and macro observations to micro and macro s...