关键词: 多指标决策, TOPSIS, 风险偏好, 前景理论, 蛛网相似度

Abstract: Scientifically formulating a multi-criterion scheme and selecting an appropriate decision-making method are the premise of tackling multi-attribute decision-making problems and crucial factors in determining the optimal solution. The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is one of the most popular used multi-criterion decision-making methods, and it has been widely applied in various fields, including natural disasters, construction engineering, and environmental safety. While TOPSIS has undoubtedly made decision-making more convenient, most problems that require TOPSIS to solve are often based on a large amount of unclear information and subjective judgments. As a result, decision-makers often find themselves operating in a fuzzy environment full of things unknown, which can make the decision-making process challenging. In addition, it is worth noting that the results obtained via TOPSIS can be influenced by several factors, including the weighting of the indexes, the proximity algorithms, and the subjective preferences of decision-makers. As a result, the direct application of the classic TOPSIS method may be subject to certain limitations. Given the above-mentioned issues, this paper proposes a prospect interval TOPSIS method based on information cloud combination weighting and cobweb similarity improvement.
The first step in the proposed approach involves differentiating between the various types of decision indicators and considering their respective fundamental properties. An improved interval number ideal solution identification method is suggested as a result, which intends to enable decision-makers to have a more accurate and comprehensive depiction of each indicator, thereby making a more informed and reliable decision. Furthermore, recognizing the presence of limited rationality in actual decision-making behavior, a prospect interval decision matrix is constructed based on integrated prospect theory. The second step aims to address the issue of weight determination for the decision index, which is often a critical source of uncertainty in multi-attribute decision-making. To mitigate this uncertainty and balance the advantages of subjective and objective, the indicator weights are determined by utilizing an information cloud combination weighting method based on the principles of inverse cloud generator and entropy weight method. By integrating information from subjective and objective weighting, this step seeks to enhance the accuracy of multi-attribute decision-making in a fuzzy environment by reducing the impact of weight-related issues. Finally, by introducing a cobweb structure model, the approach calculates the similarity between the alternatives and the positive and negative ideal solutions. It replaces the traditional Euclidean distance with the term “cobweb similarity”, and incorporates the maximum-minimum squared sum criterion to propose a new closeness measurement method. The novel algorithm mitigates the issue of classic algorithms that tend to produce candidate solutions that are close to both the positive and negative ideal solutions simultaneously, leading to ambiguous and potentially misleading results.
To illustrate the effectiveness of this approach, it is applied to the decision-making problem of a prefabricated component supplier for an office building project in Shaanxi Province. The results of the analysis demonstrate that this approach can effectively evaluate and compare various options from several different perspectives, including shape similarity, and area similarity and proximity. Moreover, the method allows for appropriate adjustments based on the decision-makers risk preferences, which ensures that the final decision is both optimal and realistic. This differs from other methods, making itself a powerful tool for decision-makers facing complex and uncertain scenarios. Compared with traditional algorithms, the approach presented in this paper demonstrates a significantly greater level of stability. Even when uncertain factors and extreme values are present, the evaluation results of this method will remain stable and capable of producing suitable outcomes.
Even if this approach has shown itself to be highly operable in the context of multi-objective decision-making situations, there are still a few points that call for further research, for example, the proportion of subjective to objective weighing methods used to determine combination weights, as well as the influence of sensitivity and avoidance coefficients on the outcomes of decisions. The research team believes that with more study, this approach may be strengthened and applied more. Finally, we would like to express our gratitude for the invaluable guidance provided by Professor Huang Jianhua and the financial support from the China Social Science Foundation(20BGL003).

Key words: multi-attribute decision making, TOPSIS, risk preference, prospect theory, cobweb similarity