Note on “Optimal path selection approach for fuzzy reliable shortest path problem”

Article type: Research Article

Authors: Kumar, Ranjan^{a; d; *} | Edalatpanah, SA^b | Mohapatra, Hitesh^c

Affiliations: [a] Department of Master of Computer Applications, Jain Deemed to be University, Bengaluru, Karnataka, India | [b] Department of Applied Mathematics, Ayandegan Institute of Higher Education, Tonekabon, Iran | [c] Department of Computer Science and Engineering, Koneru Lakshmaiah Education Foundation, Vaddeswaram, Guntur, Andhra Pradesh, India | [d] Department of Mathematics, National Institute of Technology Jamshedpur, India

Correspondence: [*] Corresponding author. Ranjan Kumar. E-mail: ranjank.nit52@gmail.com.

Abstract: There are different conditions where SPP play a vital role. However, there are various conditions, where we have to face with uncertain parameters such as variation of cost, time and so on. So to remove this uncertainty, Yang et al. [1] “[Journal of Intelligent & Fuzzy Systems, 32(1), 197-205”] have proposed the fuzzy reliable shortest path problem under mixed fuzzy environment and claimed that it is better to use their proposed method as compared to the existing method i.e., “[Hassanzadeh et al.; A genetic algorithm for solving fuzzy shortest path problems with mixed fuzzy arc lengths, Mathematical and Computer Modeling, 57(2013) 84-99” [2]]. The aim of this note is, to highlight the shortcoming that is carried out in Yang et al. [1] article. They have used some mathematical incorrect assumptions under the mixed fuzzy domain, which is not true in a fuzzy environment.

Keywords: normal fuzzy number, Shortest path problem (SPP), fuzzy shortest path problem (FSPP), mixed fuzzy environment

DOI: 10.3233/JIFS-200923

Journal: Journal of Intelligent & Fuzzy Systems, vol. 39, no. 5, pp. 7653-7656, 2020