On interval-valued hesitant fuzzy rough approximation operators

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• 作者：Haidong Zhang ; Lan Shu ; Shilong Liao
• 关键词：Interval ; valued hesitant fuzzy set ; Interval ; valued hesitant fuzzy relation ; Interval ; valued hesitant fuzzy rough approximation operators ; Interval ; valued hesitant fuzzy rough set
• 刊名：Soft Computing - A Fusion of Foundations, Methodologies and Applications
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：20
• 期：1
• 页码：189-209
• 全文大小：692 KB
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• 作者单位：Haidong Zhang (1) (2)
  Lan Shu (1)
  Shilong Liao (2)
  
  1. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, Sichuan, People’s Republic of China
  2. School of Mathematics and Computer Science, Northwest University for Nationalities, Lanzhou, 730030, Gansu, People’s Republic of China
  
• 刊物类别：Engineering
• 刊物主题：Numerical and Computational Methods in Engineering
  Theory of Computation
  Computing Methodologies
  Mathematical Logic and Foundations
  Control Engineering
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1433-7479

文摘

Interval-valued hesitant fuzzy set is a generalization of classical interval-valued fuzzy set by returning a family of the interval-valued membership degrees for each object in the universe. By combining interval-valued hesitant fuzzy set and rough set models, the concept of an interval-valued hesitant fuzzy rough set is explored in this paper. Both constructive and axiomatic approaches are considered for this study. In constructive approach, by employing an interval-valued hesitant fuzzy relation, a pair of lower and upper interval-valued hesitant fuzzy rough approximation operators is first defined. The connections between special interval-valued hesitant fuzzy relations and interval-valued hesitant fuzzy rough approximation operators are further established. In axiomatic approach, an operators-oriented characterization of the interval-valued hesitant fuzzy rough set is presented, that is, interval-valued hesitant fuzzy rough approximation operators are defined by axioms, and then, different axiom sets of lower and upper interval-valued hesitant fuzzy set-theoretic operators guarantee the existence of different types of interval-valued hesitant fuzzy relations producing the same operators. Finally, a practical application is provided to illustrate the validity of the interval-valued hesitant fuzzy rough set model. Keywords Interval-valued hesitant fuzzy set Interval-valued hesitant fuzzy relation Interval-valued hesitant fuzzy rough approximation operators Interval-valued hesitant fuzzy rough set