A model for type-2 fuzzy rough sets

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• 作者：Juan Lu^a ; ^b ; ^{nancylu0312@163.com" class="auth_mail" title="E-mail the corresponding author} ; De-Yu Li ; ^a ; ^{lidy@sxu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; ^{lidysxu@163.com" class="auth_mail" title="E-mail the corresponding author} ; Yan-Hui Zhai^a ; ^{chai_yanhui@163.com" class="auth_mail" title="E-mail the corresponding author} ; Hua Li^a ; ^{hualisjzri@sina.com" class="auth_mail" title="E-mail the corresponding author} ; He-Xiang Bai^a ; ^{baihx@sxu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Type-2 fuzzy rough set ; Representation Theorem ; Granular type-2 fuzzy set ; Lower approximation operator ; Upper approximation operator
• 刊名：Information Sciences
• 出版年：2016
• 出版时间：20 January 2016
• 年：2016
• 卷：328
• 期：Complete
• 页码：359-377
• 全文大小：466 K

文摘

Rough set theory is an important approach to granular computing. Type-1 fuzzy set theory permits the gradual assessment of the memberships of elements in a set. Hybridization of these assessments results in a fuzzy rough set theory. Type-2 fuzzy sets possess many advantages over type-1 fuzzy sets because their membership functions are themselves fuzzy, which makes it possible to model and minimize the effects of uncertainty in type-1 fuzzy logic systems. Existing definitions of type-2 fuzzy rough sets are based on vertical-slice or 伪-plane representations of type-2 fuzzy sets, and the granular structure of type-2 fuzzy rough sets has not been discussed. In this paper, a definition of type-2 fuzzy rough sets based on a wavy-slice representation of type-2 fuzzy sets is given. Then the concepts of granular type-2 fuzzy sets are proposed, and their properties are investigated. Finally, granular type-2 fuzzy sets are used to describe the granular structures of the lower and upper approximations of a type-2 fuzzy set, and an example of attribute reduction is given.