An elongation of the single-valued neutrosophic set is an interval-valued neutrosophic set. It has been demonstrated to deal indeterminacy in a decision-making problem. Real-world problems have some kind of uncertainty in nature and among them; one of the influential problems is solving the shortest path problem (SPP) in interconnections. In this contribution, we consider SPP through Bellman's algorithm for a network using interval-valued neutrosophic numbers (IVNNs). We proposed a novel algorithm to obtain the neutrosophic shortest path between each pair of nodes. Length of all the edges is accredited an IVNN. Moreover, for the validation of the proposed algorithm, a numerical example has been offered. Also, a comparative analysis has been done with the existing methods which exhibit the advantages of the new algorithm.Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
In the last decade, concealed by uncertain atmosphere, many algorithms have been studied deeply to workout the shortest path problem. In this paper, we compared the shortest path problem with various existing algorithms. Finally, we concluded the best algorithm for certain environment.
Real-life decision-making problem has been demonstrated to cover the indeterminacy through single valued neutrosophic set. It is the extension of interval valued neutrosophic set. Most of the problems of real life involve some sort of uncertainty in it among which, one of the famous problem is finding a shortest path of the network. In this paper, a new score function is proposed for interval valued neutrosophic numbers and SPP is solved using interval valued neutrosophic numbers. Additionally, novel algorithms are proposed to find the neutrosophic shortest path by considering interval valued neutrosophic number, trapezoidal and triangular interval valued neutrosophic numbers for the length of the path in a network with illustrative example. Further, comparative analysis has been done for the proposed algorithm with the existing method with the shortcoming and advantage of the proposed method and it shows the effectiveness of the proposed algorithm.Keywords Interval valued triangular neutrosophic number · Interval valued trapezoidal neutrosophic number · Ranking methods · Deneutrosophication · Neutrosophic shortest path problem · Network
Introduction and literature of reviewIn this part, introduction to the objective of the paper is given by presenting basic concepts and procedure of the shortest path problem (SPP) and the literature of review have been collected to know the recent work related to the presented concept which shows the novelty of the presented work * Said Broumi Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
To avoid mathematical complexity, Interval T2FSs (IT2FSs) have been pertained in majority of the fields. Type-2 fuzzy sets (T2FSs) handle a greater modeling and uncertainties that exist in the real world applications especially in control systems. One of the important components that influence the fuzzy controller is the triangular norm, which is the aggregation operator. For getting the stability of a control system T-norm operator can be preferred. Gaussian Interval Type-2 Membership Function (GIT2MF) has been used in this research. Mathematical properties of aggregation operator also proved using Gaussian Interval Type-2 Weighted Arithmetic (GIT2WA) operator. The aim of this research is analyzing the stability of an inverted pendulum using Interval Type-2 Fuzzy Logic Controller (IT2FLC) and the results are compared with traditional Proportional Integrated Derivative (PID) controller. It is observed that IT2FL controller gives better stability under imprecise condition.
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