踌躇模糊环境下的近似推理算子理论

Hesitant fuzzy sets, as a new extension of fuzzy sets, have gained extensive attention from the academic circles and the circles of engineering and technology, since it had been introduced by Torra in 2009, for its stronger ability to express uncertainty than ordinary fuzzy sets. At present, hesitant fuzzy sets have been successfully used in the field of decision making, and lots of remarkable results had been obtained. With the successful use of fuzzy control technology in many fields, as the core of fuzzy control, approximate reasoning plays an important role in fuzzy system theory. However, there are few works on the research of approximate reasoning under hesitant fuzzy environments so far. By introducing hesitant fuzzy sets to approximate reasoning, fuzzy system can be designed properly. On the one hand, missing of fuzzy information can be avoided, on the other hand, it seemed reasonable to express the fuzziness and uncertainty of reasoning results by hesitant fuzzy sets. In this project, operators in approximate reasoning under hesitant fuzzy environments are investigated systematically from both theory and application level, which aims at the foundation of operation theory. This project provides not only a lager operation choice space, but also a more rational theoretical basis for the fields of both intelligent control and decision making.

踌躇模糊集（hesitant fuzzy sets），作为传统模糊集的又一新的推广形式，较传统模糊集具有更强的表达不确定性的能力，因而自2009年由Torra提出以来，受到了学术界和工程技术界的广泛关注。目前，踌躇模糊集已成功应用于决策领域，并取得了丰富的研究成果。随着模糊控制技术在诸多领域的成功应用，作为模糊控制的核心，近似推理在模糊系统理论的研究中占有重要的地位。但踌躇模糊环境下的近似推理的研究工作迄今却很少。将踌躇模糊集引入到近似推理中，一方面可以减少推理过程中模糊信息的丢失，另一方面，模糊推理的结果用踌躇模糊集来表示更能反映日常推理的模糊性和不确定性，有利于模糊系统的合理设计。本项目拟在踌躇模糊环境下对近似推理中的算子进行从理论到应用两个层面的系统性研究，以期建立较完整的算子理论体系，为智能控制以及决策等应用领域提供更大的算子选择空间和更合理的理论依据。

踌躇模糊集已成功应用于决策领域，并取得了丰富的研究成果。同时，随着模糊控制技术在诸多领域的成功应用，作为模糊控制的核心，近似推理在模糊系统理论的研究中占有重要的地位。本项目重点研究了踌躇模糊环境下的近似推理算子理论。另外，还做了一些拓展性的研究工作。主要研究内容包括：(1) 踌躇模糊推理算子及其性质；(2) 一致模(半一致模)算子和Mayor聚合算子之间的分配性；(3) 2-一致模上连续三角模和三角余模的分配性。重要结果有：提出了一类踌躇模糊三角模，研究了这一类三角模的代数性质，刻画了阿基米德性和极限性质；刻画了满足分配性方程的一致模(半一致模)和Mayor聚合算子；给出了连续三角模和三角余模在2-一致模上满足分配性方程的充要条件。本项目的研究结果为智能控制和决策等应用领域提供了更大的算子选择空间和更合理的理论依据。