基于三角直觉模糊数的多属性群决策理论与方法及其应用研究

项目名称： 基于三角直觉模糊数的多属性群决策理论与方法及其应用研究

项目编号： No.61263018

项目类型： 地区科学基金项目

立项/批准年度： 2013

项目学科： 自动化技术、计算机技术

项目作者： 万树平

作者单位： 江西财经大学

项目金额： 44万元

中文摘要： 由于客观事物的复杂性和模糊不确定性，实际的系统管理决策优化问题涉及大量的模糊"数量"概念，使得决策者对所做的判断、估计不能完全肯定，即存在一定的犹豫度。直觉模糊数可以很好地描述这些模糊"数量"的大小，反映出决策者对其所做判断、估计的犹豫不确定性。三角直觉模糊数(TIFN)是一种特殊的直觉模糊集，比直觉模糊集更具有吸引人的解释并且能被决策者容易地量化和执行。本项目将根据模糊数可能性理论，定义TIFN的可能性均值、方差、协方差和相关系数，据此给出TIFN的合理排序方法。研究TIFN的算术集成算子、几何集成算子、Choquet积分算子、幂均融合算子和点算子并探讨其有关性质。建立不同情形下的TIFN多属性群决策系统模型，探讨属性权重、专家权重的确定,进而提出相应的群决策方法，结合投资组合、金融工程管理等实际应用问题进行分析或仿真模拟，为决策者存在犹豫度的系统管理决策优化问题提供技术指导与方法支持。

中文关键词： 多属性决策；多属性群决策；直觉模糊集；三角直觉模糊数；可能性理论

英文摘要： Due to the complexity and fuzzy uncertainty of objective things,the problems of systemic management decision optimization invlove lots of notions of fuzzy "quantity". The judgement and estimation given by decision makers may be not completely affirmative, that is, there exsit some hesitation. The intuitionistic fuzzy number can better describe the sizes of these fuzzy "quantity" and reflect the hesitant uncertainty of the judgement and estimation given by the decision makers. Triangular intuitionistic fuzzy number is a special intutionistic fuzzy set, which has appealing interpretations than intuitionistic fuzzy set and can be easily specified and implemented by the decision maker.According to the possibility theory of fuzzy numbers, this project defines the possibility mean, variance, covariance and correlative coefficient of TIFN. Hereby, the ranking method of TIFN is given.Some aggregation operators for TIFNs are developed, such as arithmetic aggregation operators, geometric aggregation operators, Choquet integral operators, power average operators and point operator.The desirable properties of these operators are also investigated. The systemic models using TIFN for multi-attribute group decsion making are constructed under different circumstances. The approaches to determining the attribute weight and exper

英文关键词： Multi-attribute decision making；Multi-attribute group decision making；Intuitionistic fuzzy set；Triangular intuitionistic fuzzy number；Possibility theory