Affiliations: [a] Department of Computer Engineering, Babol Branch, Islamic Azad University, Babol, Iran
| [b] Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran
| [c] Department of Computer Engineering, Sari Branch, Islamic Azad University, Sari, Iran
| [d] School of Mathematics, Thapar Institute of Engineering and Technology (Deemed University), Patiala, Punjab, India
Correspondence:
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Corresponding author. Ali Ebrahimnejad, Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr Branch, Qaemshahr, Iran. E-mails: a.ebrahimnejad@qaemiau.ac.ir and aemarzoun@gmail.com.
Abstract: Researchers have studied several different types of directed shortest path (SP) problems under fuzzy environment. However, few researchers have focused on solving this problem in an interval-valued fuzzy network. Thus, in order to light these, we investigate a generalized kind of the SP problem under interval-valued fuzzy environment namely all pairs shortest path (APSP) problem. The main contributions of the present study are fivefold: (1) In the interval-valued fuzzy network under consideration, each arc weight is represented in terms of interval-valued fuzzy number. (2) We seek the shortest weights between every pair of nodes in a given interval-valued fuzzy network based on a dynamic approach. (3) In contrast to most existing approaches, which provide the shortest path between two predetermined nodes, the proposed approach provides the interval-valued fuzzy shortest path between every pair of nodes. (4) Similarly to the competing methods in the literature, the proposed approach not only gives the interval-valued fuzzy weights of all pairs shortest path but also provides the corresponding interval-valued fuzzy APSP. (5) The efficiency of the proposed approach is illustrated through two applications of APSP problems in wireless sensor networks and robot path planning problems.
