Aiming at the decision-making problem in heterogeneous information environment and considering the influence of decision makers' psychological behavior on decision-making results, this paper proposes a multi-attribute decision-making method based on prospect theory in heterogeneous information environment. The heterogeneous information in this paper indicates that the decision attribute value is represented by various types of data forms, including exact number, interval number, linguistic term, intuitionistic fuzzy number, interval intuitionistic fuzzy number, neutrosophic numbers, and trapezoidal fuzzy neutrosophic numbers, and so on. Firstly, the distance and similarity measure of various heterogeneous data are introduced, and the heterogeneous information attribute weights are obtained using the deviation maximization method. Then, the psychological expectation value of each attribute given by the decision maker is used as a reference point, thereby calculating the gain and loss of each attribute value relative to the reference point, and establishing a gain matrix and a loss matrix. On this basis, the prospect theory is used to obtain the comprehensive prospect value of each alternative, so as to obtain the alternative ordering result and optimal alternative. Finally, an illustrative example about typhoon disaster assessment is presented to show the feasibility and effectiveness of the proposed method, and the advantages of the proposed method are illustrated by comparison with other methods.
The shortest path problem (SPP) is considerably important in several fields. After typhoons, the resulting damage leads to uncertainty regarding the path weight that can be expressed accurately. A neutrosophic set is a collection of the truth membership, indeterminacy membership, and falsity membership degrees of the elements. In an uncertain environment, neutrosophic numbers can express the edge distance more effectively. Based on the theories of interval valued neutrosophy and neutrosophic graphs, this paper proposes a shortest path solution method of interval valued neutrosophic graphs using the ant colony algorithm. Further, an analysis comparing the proposed algorithm with the Dijkstra algorithm was used to probe the potential shortcomings and advantages of the proposed method. In addition, this approach confirmed the effectiveness of the proposed algorithm. Furthermore, we investigated the convergence processes of the ant colony algorithm with different parameter settings, analyzed their results, and used different score functions to solve the SPP and analyze the results. INDEX TERMS Ant colony algorithm, interval valued neutrosophic numbers, neutrosophic graph, shortest path problem.
The shortest path problem is a topic of increasing interest in various scientific fields. The damage to roads and bridges caused by disasters makes traffic routes that can be accurately expressed become indeterminate. A neutrosophic set is a collection of the truth membership, indeterminacy membership, and falsity membership of the constituent elements. It has a symmetric form and indeterminacy membership is their axis of symmetry. In uncertain environments, the neutrosophic number can more effectively express the edge distance. The objectives in this study are to solve the shortest path problem of the neutrosophic graph with an edge distance expressed using trapezoidal fuzzy neutrosophic numbers (TrFNN) and resolve the edge distance according to the score and exact functions based on the TrFNN. Accordingly, the use of a circle-breaking algorithm is proposed to solve the shortest path problem and estimate the shortest distance. The feasibility of this method is verified based on two examples, and the rationality and effectiveness of the approach are evaluated by comparing it with the Dijkstra and Bellman algorithms.
PurposeThe Chinese believe that “man will conquer the sky” and “fighting with the sky brings endless joy”. Considering that disaster assessment can be regarded as a two-person, zero-sum game problem between nature and human beings, this paper proposes a multi-attribute decision-making method based on game theory and grey theory in a single-value neutrosophic set environment. Due to the complexity and uncertainty of the decision-making environment, the method builds a decision matrix based on single-valued neutrosophic numbers.Design/methodology/approachFirst, the authors use the single-value neutrosophic information entropy to calculate the attribute weights and the weighted decision matrix. Second, the optimal mixed strategy method based on linear programming solves the optimal mixed strategy for both sides of the game so that the expected payoff matrix can be obtained. Finally, grey correlation analysis is used to obtain the closeness coefficient of each alternative based on the expectation payoff matrix to identify the ranking result of the alternative.FindingsAn example is used to verify the effectiveness of the proposed method, and its rationality is verified through a comprehensive comparison and analysis of the various aspects.Practical implicationsThe proposed decision-making method can be applied to typhoon disaster assessment. Such assessment results can provide intelligent decision support to the relevant disaster management departments, thereby reducing the negative impact of typhoon disasters on society, stabilizing society and improving people's happiness. Further, the method can be used for decision-making, recommendation and evaluation in other fields.Originality/valueThe proposed method uses single-value neutrosophic numbers to solve the information representation problem of decision-making in a complex environment. Under a new perspective, game theory is used to handle the decision matrix, while grey relational analysis converts inexact numbers to exact numbers for comparison and sorting. Thus, the proposed method can be used to make reasonable decisions while preserving information to the extent possible.
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