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Multi-Granulation Graded Rough Intuitionistic Fuzzy Sets Models Based on Dominance Relation

1
College of Computer and Information Engineering, Henan Normal University, Xinxiang 453007, China
2
Engineering Lab of Henan Province for Intelligence Business & Internet of Things, Henan Normal University, Xinxiang 453007, China
*
Author to whom correspondence should be addressed.
Symmetry 2018, 10(10), 446; https://doi.org/10.3390/sym10100446
Received: 7 August 2018 / Revised: 22 September 2018 / Accepted: 26 September 2018 / Published: 28 September 2018
(This article belongs to the Special Issue Discrete Mathematics and Symmetry)
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Abstract

From the perspective of the degrees of classification error, we proposed graded rough intuitionistic fuzzy sets as the extension of classic rough intuitionistic fuzzy sets. Firstly, combining dominance relation of graded rough sets with dominance relation in intuitionistic fuzzy ordered information systems, we designed type-I dominance relation and type-II dominance relation. Type-I dominance relation reduces the errors caused by single theory and improves the precision of ordering. Type-II dominance relation decreases the limitation of ordering by single theory. After that, we proposed graded rough intuitionistic fuzzy sets based on type-I dominance relation and type-II dominance relation. Furthermore, from the viewpoint of multi-granulation, we further established multi-granulation graded rough intuitionistic fuzzy sets models based on type-I dominance relation and type-II dominance relation. Meanwhile, some properties of these models were discussed. Finally, the validity of these models was verified by an algorithm and some relative examples. View Full-Text
Keywords: graded rough sets; rough intuitionistic fuzzy sets; dominance relation; logical conjunction operation; logical disjunction operation; multi-granulation graded rough sets; rough intuitionistic fuzzy sets; dominance relation; logical conjunction operation; logical disjunction operation; multi-granulation
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Xue, Z.-A.; Lv, M.-J.; Han, D.-J.; Xin, X.-W. Multi-Granulation Graded Rough Intuitionistic Fuzzy Sets Models Based on Dominance Relation. Symmetry 2018, 10, 446.

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