In this paper, three types of (philosophical, optimistic and pessimistic) multigranulation single valued neutrosophic (SVN) covering-based rough set models are presented, and these three models are applied to the problem of multi-criteria group decision making (MCGDM).Firstly, a type of SVN covering-based rough set model is proposed.Based on this rough set model, three types of mult...

The Conditional Covering Problem (CCP) aims to locate facilities on a graph, where the vertex set represents both the demand points and the potential facility locations. The problem has a constraint that each vertex can cover only those vertices that lie within its covering radius and no vertex can cover itself. The objective of the problem is to find a set that minimizes the sum of the facilit...

In the previous lecture, we covered a series of online/offline edge-weighted Steiner tree/forest problems. This lecture extends the discussion to the node-weighted scope. In particular, we will study the nodeweighted Steiner tree/forest problem and introduce an offline O(logn)−approximation polynomial-time algorithm[KR95]. It is well known there is no polynormial-time algorithm that achieves o(...

An important endeavor in computer science is to understand the expressive power of logical formalisms over discrete structures, such as words. Naturally,"understanding"is not a mathematical notion. This investigation requires therefore a concrete objective to capture this understanding. In the literature, the standard choice for this objective is the membership problem, whose aim is to find a p...

in this paper we present the problem of designing a three level hub center network. in our network, the top level consists of a complete network where a direct link is between all central hubs.  the second and third levels consist of star networks that connect the hubs to central hubs and the demand nodes to hubs and thus to central hubs, respectively. we model this problem in an incomplete net...

In this paper an uncapacitated multiple allocation p-hub median problem is discussed. The model minimizes the transportation cost based on inventory service level at hubs through double paths between hubs. Inventory service level is defined as the percent of inventory shortage of vehicles at hubs according to passengers demand and replenishment time of vehicles. A real data from 25 nodes of mun...

in this paper, a hierarchical p-hub median problem is considered that all the nodes and arcs on the network have limited capacities. proposed model has three-level where the complete network at the top level consists of the central hubs. the second and third levels consist of hub and demand nodes respectively, which are connected through star networks. also, delivery time restriction is taken i...

Transportation networks frequently employ hub-and-spoke network architectures to route flows between many origin and destination pairs. In this paper, we deal with a problem, called the single allocation hub-and-spoke network design problem. In the single allocation hub-andspoke network design problem, the goal is to allocate each non-hub node to exactly one of given hub nodes so as to minimize...