用单一公理刻画由复合直觉模糊关系生成的(S,T)-直觉模糊粗糙近似算子  

On Single Axioms for(S,T)-intuitionistic Fuzzy Rough Approximation Operators Generated by Compositive Intuitionistic Fuzzy Relations

作　　者：吴伟志 WU Weizhi(School of Mathematics,Physics and Information Science,Zhejiang Ocean University,Zhoushan 316022,Zhejiang;Key Laboratory of Oceanographic Big Data Mining&Application of Zhejiang Province,Zhejiang Ocean University,Zhoushan 316022,Zhejiang)

机构地区：[1]浙江海洋大学数理与信息学院,浙江舟山316022 [2]浙江海洋大学浙江省海洋大数据挖掘与应用重点实验室,浙江舟山316022

出　　处：《四川师范大学学报（自然科学版）》2020年第6期727-738,F0002,共13页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(61976194和41631179);浙江省自然科学基金(LY18F030017)。

摘　　要：粗糙集理论中的下近似算子和上近似算子是粗糙集理论基础研究和应用发展最重要的概念之一.粗糙近似算子的公理刻画是粗糙集理论研究的一个重要方向.基于[0,1]×[0,1]上的一个直觉模糊三角模T及其对偶直觉模糊三角余模S,给出由直觉模糊关系生成的直觉模糊近似算子的公理方法.证明了由串行、自反、对称、传递等合成的各种直觉模糊关系生成的S-下直觉模糊近似算子与T-上直觉模糊近似算子都可以用一条公理来刻画.Lower and upper approximation operators are the foundation in the study of theoretic aspect of rough set theory as well as its practical applications.One of the main directions of the theoretic study of rough sets is the axiomatic characterization of rough approximation operators.In this paper,axiomatic approach for relation based intuitionistic fuzzy rough approximation operators,determined by an intuitionistic fuzzy triangular norm T and its dual intuitionistic fuzzy triangular conorm S on [0,1] ×[0,1],are presented.We examine that S-lower and T-upper intuitionistic fuzzy rough approximation operators generated by various compositive special intuitionistic fuzzy relations,namely,serial/reflexive,symmetric,and transitive intuitionistic fuzzy relations,can be characterized by single axioms.

关 键 词：近似算子 直觉模糊粗糙集 直觉模糊集 直觉模糊三角模 粗糙集 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]