The Criterion-Oriented Three-Way Ranking and Clustering Strategies in Fuzzy Decision Environments

Faced with any decision-making problems with fuzzy multicriteria information, decision-makers generally set a minimum requirement on each criterion for satisfying their own preferences, thereby forming a fuzzy set on the criterion universe, which is called the criterion fuzzy set. From the perspective of realistic decision, the final decision of all alternatives should be determined according to this criterion fuzzy set. In view of this, this article proposes the criterion-oriented three-way ranking and clustering strategies, which can solve the qualitative clustering and ranking problems of all alternatives from the perspective of criterion fuzzy sets. First, we define a criterion fuzzy set as a criterion-oriented fuzzy concept and propose a criterion-oriented relative risk loss model and discuss related properties accordingly. Meanwhile, we use the generalized fuzzy rough lower (upper) approximation to estimate the absolute (relative) conditional probability between the binary fuzzy class of the alternative and the criterion-oriented fuzzy concept. Then, a criterion-oriented absolute (relative) three-way clustering strategy is proposed, which can perform qualitative analysis on all alternatives. Furthermore, based on the three-way semantics and global cost function, we recommend a criterion-oriented absolute (relative) three-way ranking strategy, which can rank all alternatives. Finally, through numerical example, comparative analysis and sensitivity analysis, we test the feasibility and effectiveness of the proposed criterion-oriented three-way ranking and clustering strategies.