Fuzzy programming technique for solving the shortest path problem on networks under triangular and trapezoidal fuzzy environment

The authors present a new algorithm for solving the shortest path problem (SPP) in a mixed fuzzy environment. With this algorithm, the authors can solve the problems with different sets of fuzzy numbers e.g., normal, trapezoidal, triangular, and LR-flat fuzzy membership functions. Moreover, the authors can solve the fuzzy shortest path problem (FSPP) with two different membership functions such as normal and a fuzzy membership function under real-life situations. The transformation of the fuzzy linear programming (FLP) model into a crisp linear programming model by using a score function is also investigated. Furthermore, the shortcomings of some existing methods are discussed and compared with the algorithm. The objective of the proposed method is to find the fuzzy shortest path (FSP) for the given network; however, this is also capable of predicting the fuzzy shortest path length (FSPL) and crisp shortest path length (CSPL). Finally, some numerical experiments are given to show the effectiveness and robustness of the new model. Numerical results show that this method is superior to the existing methods.

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

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-200923 ◽

2020 ◽

Vol 39 (5) ◽

pp. 7653-7656

Author(s):

Ranjan Kumar ◽

SA Edalatpanah ◽

Hitesh Mohapatra

Keyword(s):

Shortest Path ◽

Fuzzy Systems ◽

Optimal Path ◽

Vital Role ◽

Path Selection ◽

Shortest Path Problem ◽

Shortest Path Problems ◽

Fuzzy Environment ◽

Selection Approach ◽

Arc Lengths

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.

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Bellman–Ford algorithm for solving shortest path problem of a network under picture fuzzy environment

Complex & Intelligent Systems ◽

10.1007/s40747-021-00430-w ◽

2021 ◽

Author(s):

Mani Parimala ◽

Said Broumi ◽

Karthikeyan Prakash ◽

Selçuk Topal

Keyword(s):

Decision Making ◽

Shortest Path ◽

Fuzzy Set ◽

Intuitionistic Fuzzy Set ◽

Shortest Path Problem ◽

Point Of View ◽

The Novel ◽

Fuzzy Environment ◽

Picture Fuzzy Set ◽

Decision Making Problem

AbstractAn elongation of the novel intuitionistic fuzzy set is a picture fuzzy set theory. The demonstration of this has been used to deal with the abstinence criteria in a decision-making problem. The uncertainty in nature occurs sometimes in real-world problems and amidst them, the prominent one is the shortest path problem (SPP) solving. In the last few years, one of the best algorithms on the network for finding SPP is Bellman–Ford. Due to uncertainty in the decision-making process, it becomes difficult for decision-makers for communicating their point of view and judgment with certainty. We conceive of SPP in this contribution via Bellman's algorithm (BA) for a network with trapezoidal picture fuzzy numbers (TPFNs). We introduce a new algorithm to stand the shortest picture fuzzy path between each pair of nodes. A TPFN is considered for the length of all edges. A numerical example for the validation of the presented algorithm has also been proposed. There has also been relative research with existing techniques showing the benefits of the new algorithm.

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