Uncorrected Author Proof Journal of Intelligent & Fuzzy Systems xx (20xx) x–xx DOI:10.3233/JIFS-181751 IOS Press 1 A new approach to compute measures of connectivity in rough fuzzy network models 1 2 Muhammad Akram ∗ and Fariha Zafar 3 Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan 4 Abstract. Connectivity incorporates a significant role in various abstract and applied mathematical modeling and decision analysis. Graphical networks can be studied more precisely in connection with directed influenced flows, emphasizing the need of a mathematical approach for connectivity analysis. Our main focus in this research study is to generalize the concept of connectivity of fuzzy graphs to rough fuzzy digraphs (RFDs). We introduce the strength of connectedness between vertices, present different types of arcs in RFDs and investigate their properties. Moreover, we discuss the measures of connectivity, connectivity index, average connectivity index and isomorphism properties of partial rough fuzzy subdigraphs and spanning rough fuzzy subdigraphs. We apply various measures of connectivity to real world networks and with the help of connectivity reducing vertices, connectivity enhancing vertices and neutral vertices, we identify the most effective countries for human trafficking. Finally, we design an algorithm to describe the method discussed in the real world problem. 5 6 7 8 9 10 11 12 13 Keywords: Rough fuzzy digraph, strength of connectedness, connectivity index, average connectivity index. Mathematics Subject Classification 2010: 03E72, 68R10, 68R05 14 15 1. Introduction 16 The notion of fuzzy set proposed by Zadeh [31] 17 is the first mathematical approach to deal with 18 vagueness. After successful introduction of fuzzy 19 set theory, Zadeh [32] introduced fuzzy relations. 20 Fuzziness in crisp graphs based on Zadeh’s fuzzy 21 relation was introduced by Kaufmann [16] in 1975. 22 Structures of both crisp graph and fuzzy graph are 23 similar but fuzzy graphs deal with uncertainty on 24 vertices and/or edges. Fuzzy graphs occur when 25 the uncertainty is observed in real life situations. 26 Fuzzy graphs have many applications in all fields of 27 engineering, medicine, and science, e.g., clustering, 28 ∗ Corresponding author. Muhammad Akram, Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan. E-mail: makrammath@yahoo.com. communication, data mining, image capturing, image 29 segmentation, networking, planning and scheduling. 30 Many researchers imparted their contributions to 31 the success of fuzzy graphs. Several graph-theoretic 32 concepts like paths, connectedness, bridges, cycles 33 and trees were obtained by Rosenfeld [29]. He also 34 discussed some of their characteristics. Some connec- 35 tivity concepts like fuzzy cutnodes and fuzzy bridges 36 were established by Bhattacharya [6]. Some oper- 37 ations on fuzzy graphs were studied by Mordeson 38 and Peng [23]. Mordeson and Nair [22] discussed 39 fuzzy graphs and fuzzy hypergraphs in detail. Bhutani 40 and Battou [7] introduced M-strong fuzzy graphs. 41 Bhutani et al. [8] discussed degrees of end nodes and 42 cut nodes in fuzzy graphs. Bhutani and Rosenfeld 43 [9] introduced strong arcs in fuzzy graphs. Mathew 44 and Sunitha [20] classified the types of arcs in fuzzy 45 1064-1246/18/$35.00 © 2018 – IOS Press and the authors. All rights reserved