基于信息密度的广义不确定直觉模糊集成算子及其应用

项目名称： 基于信息密度的广义不确定直觉模糊集成算子及其应用

项目编号： No.11426033

项目类型： 专项基金项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 刘金培

作者单位： 安徽大学

项目金额： 3万元

中文摘要： 直觉模糊集是传统模糊集的推广，它含有隶属度、非隶属度和犹豫度三个因素的信息，因而能更加细腻地描述模糊事物的本质。对于复杂的系统，其信息表征形式往往是区间直觉模糊数、三角直觉模糊数、梯形直觉模糊数等不确定的直觉模糊信息。本项目拟考虑不确定直觉模糊数的犹豫度对隶属度和非隶属度的交叉影响，提出新的不确定直觉模糊数运算规则，针对不确定直觉模糊数的密度结构特征和多种不确定直觉模糊信息的融合，构建信息密度赋权模型，并提出基于信息密度的广义不确定直觉模糊集成算子的概念。研究直觉模糊数的运算规则和集成算子的若干数学性质，包括单调性、幂等性、齐次性、介值性、置换不变性等。同时定义该类算子的orness测度和离散测度，用于刻画评价者的态度特征，并将其应用于生态环境的聚类和综合评价之中。本项目的研究不仅可以丰富和完善直觉模糊集的运算规则和信息集成算子相关理论，而且在实际中具有较强的应用价值。

中文关键词： 集成算子；直觉模糊数；群决策；Orness；

英文摘要： Intuitionistic fuzzy set is the generalization of traditional fuzzy set, which includes the degree of membership, the degree of non-membership and degree of indeterminancy. Thus it can describe the essence of fuzzy things in details. For complex system, it usually uses the interval intuitionistic fuzzy number, triangular intuitionistic fuzzy number or trapezoidal intuitionistic fuzzy number to characterize the fuzzy information. In view of the interactions between membership degree and non-membership degree, which is caused by indeterminancy degree of uncertain intuitionistic fuzzy number, this project proposes novel operational rules of uncertain intuitionistic fuzzy number. Aim at the density structure of uncertain intuitionistic fuzzy numbers and the fusion of various kinds of intuitionistic fuzzy numbers information, we construct an information density weighting model and propose the definition of density-based generalized unceratain intuitionistic fuzzy information aggregation operators. The operational rules of intuitionistic fuzzy numbers and the mathematic properties of aggregation operator, which includes monotonicity, idempotency, homogeneity, boundedness and commutativity, are studied. Furthermore, we define the orness measure and dispersion measure of the proposed operators, by which we can character

英文关键词： Aggregation operator；Intuitionistic fuzzy number；Group decision making；Orness；