An Intuitionistic Fuzzy Dominance-Based Rough Set

The dominance---based rough set approach plays an important role in the development of the rough set theory. It can be used to describe the inconsistencies coming from consideration of the preference---ordered domains of the attributes. The purpose of this paper is to further generalize the dominance---based rough set model to fuzzy environment. The constructive approach is used to define the intuitionistic fuzzy dominance---based lower and upper approximations, respectively. Basic properties of the intuitionistic fuzzy dominance---based rough approximations are then examined.

[1]  Masahiro Inuiguchi,et al.  Variable-precision dominance-based rough set approach and attribute reduction , 2009, Int. J. Approx. Reason..

[2]  Krassimir T. Atanassov,et al.  Intuitionistic fuzzy sets , 1986 .

[3]  Francisco Herrera,et al.  Fuzzy Sets and Their Extensions: Representation, Aggregation and Models , 2008 .

[4]  Andrzej Skowron,et al.  Rough sets and Boolean reasoning , 2007, Inf. Sci..

[5]  Salvatore Greco,et al.  On Variable Consistency Dominance-Based Rough Set Approaches , 2006, RSCTC.

[6]  Wojciech Kotlowski,et al.  Stochastic dominance-based rough set model for ordinal classification , 2008, Inf. Sci..

[7]  Jing-Yu Yang,et al.  Dominance-based rough set approach and knowledge reductions in incomplete ordered information system , 2008, Inf. Sci..

[8]  Krassimir T. Atanassov,et al.  Intuitionistic Fuzzy Sets - Theory and Applications , 1999, Studies in Fuzziness and Soft Computing.

[9]  Salvatore Greco,et al.  Fuzzy Set Extensions of the Dominance-Based Rough Set Approach , 2021, Fuzzy Sets and Their Extensions: Representation, Aggregation and Models.

[10]  Masahiro Inuiguchi,et al.  Fuzzy rough sets and multiple-premise gradual decision rules , 2006, Int. J. Approx. Reason..

[11]  Sadaaki Miyamoto,et al.  Rough Sets and Current Trends in Computing , 2012, Lecture Notes in Computer Science.

[12]  Salvatore Greco,et al.  Monotonic Variable Consistency Rough Set Approaches , 2009, Int. J. Approx. Reason..

[13]  Z. Pawlak Rough Sets: Theoretical Aspects of Reasoning about Data , 1991 .

[14]  Salvatore Greco,et al.  Rough approximation by dominance relations , 2002, Int. J. Intell. Syst..

[15]  Andrzej Skowron,et al.  Rough sets: Some extensions , 2007, Inf. Sci..

[16]  Ming-Wen Shao,et al.  Dominance relation and rules in an incomplete ordered information system , 2005 .

[17]  Andrzej Skowron,et al.  Rudiments of rough sets , 2007, Inf. Sci..

[18]  Salvatore Greco,et al.  Rough sets theory for multicriteria decision analysis , 2001, Eur. J. Oper. Res..