Shortest Path Solution of Trapezoidal Fuzzy Neutrosophic Graph Based on Circle-Breaking Algorithm

Some aggregation operators of credibility trapezoidal fuzzy neutrosophic values and their decision-making application in the selection of slope design schemes

Modern decision-making (DM) systems are becoming more and more complex and sophisticated in their demands for information expressions and credibility levels. In the existing literature, a trapezoidal fuzzy neutrosophic value (TFNV) that combines trapezoidal fuzzy numbers with neutrosophic values can be better depicted by truth, indeterminacy, and falsity membership functions. Unfortunately, TFNV implies its defect since it lacks a measure of credibility. To make TFNV more creditable, TFNV should be related to its credibility level. Regarding the motivation for combining TFNV with its credibility level, this paper first proposes the concept of a credibility TFNV (C-TFNV) as a new framework of TFNV associated with the measure of credibility. The advantage of its information expression is that C-TFNV has a more creditable ability to describe indeterminate and inconsistent knowledge and judgments of human beings by the mixed information of a TFNV and a related credibility level (an ordered pair of TFNVs). Next, we propose the operational laws of C-TFNVs and the score function of C-TFNV. Furthermore, we present a C-TFNV weighted arithmetic averaging (C-TFNVWAA) and a C-TFNV weighted geometric averaging (C-TFNVWGA) operators and their properties. Then, a multicriteria DM model based on the C-TFNVWAA and C-TFNVWGA operators and the score function is established in the case of C-TFNVs. Finally, an actual DM example of slope decision schemes is provided to show the applicability and efficiency of the established DM model in the case of C-TFNVs.

Particle swarm optimization for the shortest path problem

Solving the shortest path problem is very difficult in situations such as emergency rescue after a typhoon: road-damage caused by a typhoon causes the weight of the rescue path to be uncertain and impossible to represent using single, precise numbers. In such uncertain environments, neutrosophic numbers can express the edge distance more effectively: membership in a neutrosophic set has different degrees of truth, indeterminacy, and falsity. This paper proposes a shortest path solution method for interval-valued neutrosophic graphs using the particle swarm optimization algorithm. Furthermore, by comparing the proposed algorithm with the Dijkstra, Bellman, and ant colony algorithms, potential shortcomings and advantages of the proposed method are deeply explored, and its effectiveness is verified. Sensitivity analysis performed using a 2020 typhoon as a case study is presented, as well as an investigation on the efficiency of the algorithm under different parameter settings to determine the most reasonable settings. Particle swarm optimization is a promising method for dealing with neutrosophic graphs and thus with uncertain real-world situations.

An Efficient Shortest Path Algorithm: Multi-Destinations in an Indoor Environment

The shortest path-searching with the minimal weight for multiple destinations is a crucial need in an indoor applications, especially in supermarkets, warehouses, libraries, etc. However, when it is used for multiple item searches, its weight becomes higher as it searches only the shortest path between the single sources to each destination item separately. If the conventional Dijkstra algorithm is modified to multi-destination mode then the weight is decreased, but the output path is not considered as the real shortest path among multiple destinations items. Our proposed algorithm is more efficient for finding the shortest path among multiple destination items with minimum weight, compared to the single source single destination and modified multi-destinations of Dijkstra’s algorithm. In this research, our proposed method has been validated by real-world data as well as by simulated random solutions. Our advancement is more applicable in indoor environment applications based on multiple items or destinations searching.