基于区间值相似度的模糊推理算法  

Fuzzy Inference Method Based on Interval-Valued Similarity Measure

作　　者：史宏艳 罗敏霞 SHI Hong-yan;LUO Min-xia(College of Sciences,China Jiliang University,Hangzhou,Zhejiang 310018,China)

机构地区：[1]中国计量大学理学院,浙江杭州310018

出　　处：《电子学报》2022年第11期2738-2745,共8页Acta Electronica Sinica

基　　金：国家自然科学基金(No.12171445,No.61773019)。

摘　　要：模糊推理最基本的模型是模糊假言推理和模糊反驳推理.本文是在区间值模糊集层面解决区间值模糊假言推理和区间值模糊反驳推理问题,给出基于区间值相似度的模糊推理算法.首先,基于区间值t-可表示三角范数诱导的区间值剩余蕴涵,给出一种区间值相似度;其次,研究基于区间值相似度的模糊推理算法,给出算法解的表示形式;证明基于区间值相似度的模糊推理算法具有还原性;最后,研究基于区间值相似度的广义模糊推理算法.本文提出的基于区间值相似度的模糊推理算法可应用于模式识别与多属性决策等领域.The basic models of fuzzy reasoning are fuzzy modus ponens and fuzzy modus tollens.The paper studies the problems of interval-valued fuzzy modus ponens and interval-valued fuzzy modus tollens at the level of interval-valued fuzzy sets,and propose fuzzy reasoning algorithms based on interval-valued similarity measure.Based on the interval-valued residuated implication induced by left-continuous interval-valued t-representable triangular norm,the interval-valued similarity measure is given.The fuzzy reasoning algorithms based on interval-valued similarity are further studied,and the representation of the algorithm solutions are given.Meanwhile,the fuzzy reasoning algorithms based on interval-valued similarity are proved to be reductive.Finally,the generalized fuzzy reasoning algorithms based on interval-valued similarity measure are studied.The fuzzy reasoning algorithms based on interval-valued similarity measure can be applied to the fields of pattern recognition and multi-attribute decision-making.

关 键 词：区间值模糊集 区间值三角范数 区间值剩余蕴涵 区间值相似度 t-可表示三角范数 模糊推理算法 

分 类 号：O141.1[理学—数学]