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Novel Three-Way Decisions Models with Multi-Granulation Rough Intuitionistic Fuzzy Sets

1,2,*, 1,2,*, 1,2 and 1,2
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
*
Authors to whom correspondence should be addressed.
Symmetry 2018, 10(11), 662; https://doi.org/10.3390/sym10110662
Received: 27 October 2018 / Revised: 11 November 2018 / Accepted: 16 November 2018 / Published: 21 November 2018
(This article belongs to the Special Issue Discrete Mathematics and Symmetry)
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Abstract

The existing construction methods of granularity importance degree only consider the direct influence of single granularity on decision-making; however, they ignore the joint impact from other granularities when carrying out granularity selection. In this regard, we have the following improvements. First of all, we define a more reasonable granularity importance degree calculating method among multiple granularities to deal with the above problem and give a granularity reduction algorithm based on this method. Besides, this paper combines the reduction sets of optimistic and pessimistic multi-granulation rough sets with intuitionistic fuzzy sets, respectively, and their related properties are shown synchronously. Based on this, to further reduce the redundant objects in each granularity of reduction sets, four novel kinds of three-way decisions models with multi-granulation rough intuitionistic fuzzy sets are developed. Moreover, a series of concrete examples can demonstrate that these joint models not only can remove the redundant objects inside each granularity of the reduction sets, but also can generate much suitable granularity selection results using the designed comprehensive score function and comprehensive accuracy function of granularities. View Full-Text
Keywords: three-way decisions; intuitionistic fuzzy sets; multi-granulation rough intuitionistic fuzzy sets; granularity importance degree three-way decisions; intuitionistic fuzzy sets; multi-granulation rough intuitionistic fuzzy sets; granularity importance degree
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Xue, Z.-A.; Han, D.-J.; Lv, M.-J.; Zhang, M. Novel Three-Way Decisions Models with Multi-Granulation Rough Intuitionistic Fuzzy Sets. Symmetry 2018, 10, 662.

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