直觉模糊知识测度：公理、模型及应用

It is generally believed that for a fuzzy system the more entropy may always accompany the less amount of knowledge. In the context of intuitionistic fuzzy sets (IFSs), however, there is no natural logic between these two kinds of measures with the introduction of hesitancy. According to the features of IFSs at knowledge representation level, we plan to present in this research project a novel and independent knowledge measure for IFSs. More specifically, by making use of such theories & methods as fuzzy analysis, parametric equations, and personalized quantifiers, we formulate, based on the information content and the information clarity, the original axiomatic systems and parameterized modeling methods, with which to build novel non-linear parametric models and to develop a strategy for dealing with the potential knowledge related to the non-specificity of an IFS. Our aim is to provide new technique to effectively solve the problem of knowledge measurement in complex situations and further clear up the connection between the aforementioned two kinds of measures. On the other hand, aiming at such basic characteristics as the personalization of subjects as well as the uncertainty of information in real-world applications, we present, from a viewpoint of amount of knowledge, the attitudinal-based decision analysis and modeling methods. With the help of this attempt, not only can the complex information characterized by fuzziness, hybrid, and/or uncertainty, be effectively handled, but the personality characteristics of subjects are specifically considered, thus establishing personalized service models for the “satisfactory solutions” in accord with their particular attitudes, rather than the “optimal ones” in general terms. In this respect, our aim is to provide knowledge support for uncovering the characteristics and laws of complex decision-making behaviors under the guidance of personality characteristics of subjects.

一般认为，系统模糊熵越大，知识量就越小。直觉模糊系统引入犹豫度描述未知量，这使得该环境下模糊熵与知识量不具有自然的数值逻辑关系。项目针对直觉模糊集在知识表示层面的特点，提出一种全新的、独立的直觉模糊知识测度。综合应用模糊分析、参数方程、个性化语义量词等理论与方法，系统阐明基于信息清晰度与信息量的原创性公理体系及参数化建模方法，建立全新的非线性参数模型，并实现未知信息中潜在知识量的分配策略，为有效解决复杂环境下知识度量问题及进一步厘清上述两种测度之间的逻辑关系，提供新的方法和手段。在此基础上，针对实际决策环境下主体个性化及信息不确定等基本特征，从知识量的角度提出基于态度的复杂决策分析与智能化建模方法。在有效处理模糊、混合、未知等复杂信息的同时，特别考虑了主体的个性特征，为其追求“满意解”而非一般意义的“最优解”建立个性化服务模型，为揭示个性特征作用下复杂决策行为的特征与规律提供知识支持。

一般认为，系统模糊熵越大，知识量就越小。直觉模糊系统引入犹豫度描述未知量，这使得该环境下模糊熵与知识量不具有自然的数值逻辑关系。事实上，直觉模糊熵公理由经典模糊熵推广得到，对未知信息不能做出有效处理，因此现有直觉模糊熵的公理化定义及由此所得的熵模型有一定缺陷与不足。本研究针对直觉模糊集在知识表示层面的特点，原创性提出一种独立的、非依赖熵的直觉模糊知识测度，主要内容包括公理系统、建模方法及典型应用。综合应用模糊分析、参数方程、个性化语义量词等理论与方法，系统阐明基于信息清晰度与信息量的原创性公理体系及参数化、非参数化建模方法，建立全新的非线性测度模型，并实现未知信息中潜在知识量的分配策略，为有效解决复杂环境下知识度量问题及进一步厘清上述两种测度之间的逻辑关系，提供新的方法和手段。相比直觉模糊熵的不足，本研究成果在模糊系统及模糊信息处理领域具有广阔的应用前景，目前已成功应用于不确定性决策、模糊图像处理、个性化建模与推荐、网络评测等典型领域，获得优良的应用效果。未来将进一步开展关于知识测度理论在模糊聚类分析、模糊图像处理、网络流分析等典型领域的创新性研究。