On Modeling and Analysis of MIMO Wireless Mesh Networks with Triangular Overlay Topology

Multiple input multiple output (MIMO) wireless mesh networks (WMNs) aim to provide the last-mile broadband wireless access to the Internet. Along with the algorithmic development for WMNs, some fundamental mathematical problems also emerge in various aspects such as routing, scheduling, and channel assignment, all of which require an effective mathematical model and rigorous analysis of network properties. In this paper, we propose to employ Cartesian product of graphs (CPG) as a multichannel modeling approach and explore a set of unique properties of triangular WMNs. In each layer of CPG with a single channel, we design a node coordinate scheme that retains the symmetric property of triangular meshes and develop a function for the assignment of node identity numbers based on their coordinates. We also derive a necessary-sufficient condition for interference-free links and combinatorial formulas to determine the number of the shortest paths for channel realization in triangular WMNs

Semantic operations of multiple soft sets under conflict

AbstractMolodtsov initiated the concept of soft set theory, which can be used as a generic mathematical tool for dealing with uncertainty. Description Logics (DLs) are a family of knowledge representation languages which can be used to represent the terminological knowledge of an application domain in a structured and formally well-understood way. Nowadays, properties and semantics of ontology constructs mainly are determined by DLs. In this paper we investigate semantic operations of multiple standard soft sets by using domain ontologies (i.e., DL intensional knowledge bases). Concretely, we give some semantic operations such as complement, restricted difference, extended union, restricted intersection, restricted union, extended intersection, AND, and OR for (multiple) standard soft sets from a semantic point of view. Especially, we also present an approach to deal with conflict from a semantic point of view when we define these semantic operations. Moreover, the basic properties and implementation methods of these semantic operations under conflict are also presented and discussed

semantic operations of multiple soft sets under conflict

Molodtsov initiated the concept of soft set theory, which can be used as a generic mathematical tool for dealing with uncertainty. Description Logics (DLs) are a family of knowledge representation languages which can be used to represent the terminological knowledge of an application domain in a structured and formally well-understood way. Nowadays, properties and semantics of ontology constructs mainly are determined by DLs. In this paper we investigate semantic operations of multiple standard soft sets by using domain ontologies (i.e., DL intensional knowledge bases). Concretely, we give some semantic operations such as complement, restricted difference, extended union, restricted intersection, restricted union, extended intersection, AND, and OR for (multiple) standard soft sets from a semantic point of view. Especially, we also present an approach to deal with conflict from a semantic point of view when we define these semantic operations. Moreover, the basic properties and implementation methods of these semantic operations under conflict are also presented and discussed. © 2011 Elsevier Ltd. All rights reserved

On Modeling and Analysis of MIMO Wireless Mesh Networks with Triangular Overlay Topology

Multiple input multiple output (MIMO) wireless mesh networks (WMNs) aim to provide the last-mile broadband wireless access to the Internet. Along with the algorithmic development for WMNs, some fundamental mathematical problems also emerge in various aspects such as routing, scheduling, and channel assignment, all of which require an effective mathematical model and rigorous analysis of network properties. In this paper, we propose to employ Cartesian product of graphs (CPG) as a multichannel modeling approach and explore a set of unique properties of triangular WMNs. In each layer of CPG with a single channel, we design a node coordinate scheme that retains the symmetric property of triangular meshes and develop a function for the assignment of node identity numbers based on their coordinates. We also derive a necessary-sufficient condition for interference-free links and combinatorial formulas to determine the number of the shortest paths for channel realization in triangular WMNs