基于改進前景理論的直覺模糊隨機多準則決策方法

摘要： 針對方案準則值為直覺模糊數(shù)、準則權重信息部分已知的隨機多準則決策問題,提出一種基于改進前景理論的決策分析方法.首先,定義一個新的記分函數(shù),據(jù)此可將直覺模糊數(shù)轉化為實數(shù).其次,考慮到?jīng)Q策者并非完全理性及決策者風險態(tài)度的差異性,將決策者分為保守型、中間型及冒險型,引入改進前景理論,根據(jù)不同決策者類型調整參數(shù),構建改進前景決策矩陣.再次,建立以準則值總差異最大化且準則權重差異最小化為目標的非線性二次偏差優(yōu)化定權模型,計算準則權重.進而,結合改進前景決策矩陣及準則權重計算各方案的綜合效用值,并以此確定方案的順序排列.最后,通過算例驗證所提出直覺模糊隨機多準則決策方法的有效性和合理性.
This paper provides an approach based on the modified prospect theory solving the intuitionistic fuzzy stochastic multi-criteria decision-making problem where the information of criteria weights is partially known. Firstly, a new score function is defined, by which the intuitionistic fuzzy numbers can be transformed into the real numbers. Then,considering that decision-makers are not completely rational and there are differences among them, the types of decisionmakers attitudes towards risk can be classified into risk-seeking, risk-neutral and risk-averse. The modified prospect value decision-making matrix is constructed by applying the modified prospect theory and adjusting its parameters to fit different types of decision-makers. In addition, a nonlinear quadratic deviation optimization model is established,whose goal is maximizing the total difference of criteria values and at the same time minimizing the difference between criteria weights. Furthermore, the order of alternatives is listed on the basis of the integrated utility values, which are derived by the modified prospect decision-making matrix and criteria weights. Finally, an example is given to illustrate the effectiveness and rationality of the proposed method.