Uncorrected Author Proof Journal of Intelligent & Fuzzy Systems xx (20xx) x–xx DOI:10.3233/JIFS-190711 IOS Press 1 A novel approach for solving all-pairs shortest path problem in an interval-valued fuzzy network 1 2 3 M. Enayattabr a , A. Ebrahimnejad b,∗ , H. Motameni c and H. Garg d 4 a Department of Computer Engineering, Babol Branch, Islamic Azad University, Babol, Iran 5 b Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran 6 c Department of Computer Engineering, Sari Branch, Islamic Azad University, Sari, Iran 7 d School of Mathematics, Thapar Institute of Engineering and Technology (Deemed University), Patiala, Punjab, India 8 9 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. 10 11 12 13 14 15 16 17 18 19 20 Keywords: Shortest path problem, dynamic programming, interval-valued fuzzy numbers, wireless sensor network 21 1. Introduction 22 The aim of the shortest path (SP) problem is to 23 find the best way to traverse a network to get from 24 one point to another with at least weight (time, cost 25 or length). From this point of view, researchers have 26 studied three forms of this problem classified as fol- 27 lows [1]: 28 ∗ 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 Group 1: Finding shortest paths from one node to all 29 other nodes with non-negative arc weights 30 Group 2: Finding shortest paths from one node to 31 all other nodes with arbitrary arc weights 32 Group 3: Finding shortest paths from every node 33 to every other node known as all-pairs SP 34 problem. 35 The SP problem as a network structured opti- 36 mization problem arises in numerous applications 37 settings and in different forms. This problem arises 38 in telecommunications in order to send a message 39 between two locations with at least time. Moreover, 40 ISSN 1064-1246/19/$35.00 © 2019 – IOS Press and the authors. All rights reserved