A Novel Dynamic Multi-Criteria Decision Making Method Based on Generalized Dynamic Interval-Valued Neutrosophic Set

Dynamic nonlinear simplified neutrosophic sets for multiple-attribute group decision making

In this paper, the concept of a dynamic nonlinear simplified neutrosophic set (DNSNS) is proposed for describing the real-time changing expert preference information. Furthermore, the DNSNS aggregation model and decision algorithm are provided to solve the actual multiple-attribute group decision making (MAGDM) problems. The basic notions, the similarity measure, the entropy measure, and the index of distance of DNSNS are presented first. Secondly, the univariate time series of DNSNS are projected into dynamic nonlinear simplified neutrosophic curves in three-dimensional space. The areas of the surface enclosed by the curves represent the variance among the DNSNSs. Thus, the DNSNS aggregation model is established correctly without preprocessing the original data. Afterward, the aggregation algorithm extended from the plant growth simulation algorithm (PGSA) is proposed for calculating the optimal aggregation preference curve and constructing the collective matrix. Additionally, a novel corresponding decision algorithm based on TOPSIS and projection theory is proposed for obtaining the overall ranking of alternatives in the actual MAGDM problem. Finally, a typical example is presented to illustrate the feasibility and effectiveness of the proposed model and algorithm.

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.

Arccosine and arctangent similarity measures of refined simplified neutrosophic indeterminate sets and their multicriteria decision-making method

In indeterminate and inconsistent setting, existing simplified neutrosophic indeterminate set (SNIS) can be depicted by the neutrosophic number (NN) functions of the truth, falsity and indeterminacy. Then, the three NN functions in SNIS lack their refined expressions and then the simplified neutrosophic indeterminate decision making (DM) method cannot carry out the multicriteria DM problems with both criteria and sub-criteria in the setting of SNISs. To overcome the flaws, this study first proposes a new notion of a refined simplified neutrosophic indeterminate set (RSNIS), which is described by the refined truth, falsity and indeterminate NN information regarding both elements and sub-elements in a universe set, as the extension of SNIS. Next, we propose the arccosine and arctangent similarity measures of RSNISs and their multicriteria DM method with various indeterminate risk ranges so as to carry out multicriteria DM problems with weight values of both criteria and sub-criteria in RSNIS setting. Lastly, the proposed DM method is applied to a multicriteria DM example of slope design schemes for an open pit mine to illustrate its application in the indeterminate DM problem with RSNISs. The decision results and comparative analysis indicate the rationality and efficiency of the proposed DM method with different indeterminate risk ranges.

A neutrosophic folding and retraction on a single-valued neutrosophic graph

The main aim of this article is to present neutrosophic folding and neutrosophic retractions on a single-valued neutrosophic graph Ğ from the viewpoint of geometry and topology. For this reason, we use a sequence of neutrosophic transformations on Ğ to obtain a new single-valued neutrosophic graph G ˇ 1 which contains different parameters under new conditions. We deduce the isometric neutrosophic folding on neutrosophic spheres and neutrosophic torii. Also, we determine the relationship between the limit neutrosophic folding and the limit of neutrosophic retraction on Ğ. Theorems regulating these relations are attained.

Multi-criteria collaborative filtering using rough sets theory

Recommender systems have recently become a significant part of e-commerce applications. Through the different types of recommender systems, collaborative filtering is the most popular and successful recommender system for providing recommendations. Recent studies have shown that using multi-criteria ratings helps the system to know the customers better. However, bringing multi aspects to collaborative filtering causes new challenges such as scalability and sparsity. Additionally, revealing the relation between criteria is yet another optimization problem. Hence, increasing the accuracy in prediction is a challenge. In this paper, an aggregation-function based multi-criteria collaborative filtering system using Rough Sets Theory is proposed as a novel approach. Rough Sets Theory is used to uncover the relationship between the overall criterion and the individual criteria. Experimental results show that the proposed model (RoughMCCF) successfully improves the predictive accuracy without compromising on online performance.