Title: The hierarchical structure analysis of intuitionistic fuzzy tolerance relations

Authors: Xiufang Jia; Liangtu Song; Wei Li; Haiying Hu

Addresses: Department of Automation, University of Science and Technology of China, No. 96 JinZhai Road, Hefei, Anhui Province, 230000, China; Institute of Intelligent Machines, Chinese Academy of Sciences, No. 350 Shushanghu Road, HeFei, Anhui Province, 230031, China ' Department of Automation, University of Science and Technology of China, No. 96 JinZhai Road, Hefei, Anhui Province, 230000, China; Institute of Intelligent Machines, Chinese Academy of Sciences, No. 350 Shushanghu Road, HeFei, Anhui Province, 230031, China ' Department of Automation, University of Science and Technology of China, No. 96 JinZhai Road, Hefei, Anhui Province, 230000, China; Institute of Intelligent Machines, Chinese Academy of Sciences, No. 350 Shushanghu Road, HeFei, Anhui Province, 230031, China ' Department of Automation, University of Science and Technology of China, No. 96 JinZhai Road, Hefei, Anhui Province, 230000, China; Institute of Intelligent Machines, Chinese Academy of Sciences, No. 350 Shushanghu Road, HeFei, Anhui Province, 230031, China

Abstract: In this paper, on the basis of quotient space theory, a theoretical framework of hierarchical structures is proposed by intuitionistic fuzzy tolerance matrices based on intuitionistic fuzzy tolerance relations. It also generalises classic quotient space induced by equivalent relations. The first, some new definitions on intuitionistic fuzzy tolerance relation are presented. We then propose and prove some interesting properties which describe the same hierarchical structure induced in two ways of composition by the intuitionistic fuzzy tolerance relations. Finally, the effective algorithm of getting their hierarchical structures by matrices is proposed. The algorithm has been validated by an example.

Keywords: quotient space; intuitionistic fuzzy tolerance relations; IFTR; hierarchical structure; intuitionistic fuzzy tolerance matrix; cut matrix; transitive closure; granular computing; GrC.

DOI: 10.1504/IJGCRSIS.2013.057240

International Journal of Granular Computing, Rough Sets and Intelligent Systems, 2013 Vol.3 No.2, pp.117 - 129

Available online: 18 Oct 2013 *

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