Three-way decision for three-stage ranking pattern with criterion fuzzy concept

Abstract

The application of three-way decision models in solving multi-criteria ranking problems has been widely recognized and noticed by researchers in recent years. However, most types of three-way decision models will not be directly usable when there are individual criterion minimum requirements set by decision-maker in a multi-criteria problem. For this problem, a two-stage three-way ranking pattern oriented to criterion fuzzy concept has been proposed. But, when many objects are directly identified as accepted or rejected, using this ranking pattern, there will be some objects for which the ranking results cannot be achieved. In view of this, considering criterion fuzzy concept and three-way decision, a three-stage ranking pattern is proposed to provide a more realistic and reliable ranking in a multi-criteria environment. Firstly, a new risk-loss function is defined according to the level of risk involved in decision behavior. Then, the decision thresholds are calculated. Secondly, a fuzzy description of an object is obtained using a maximum-k-means clustering algorithm. A feasible way to calculate the conditional probability value of an object is provided by this means. Finally, a new three-way ranking rule is constructed and a feasible three-stage ranking pattern is derived. Meanwhile, the feasibility of the new ranking pattern is analyzed by a computer hardware selection problem and the definition of two ranking indices. In addition, according to the experimental results on several data sets, the ranking indices between the three-stage ranking pattern and some existing ranking patterns are mostly higher than 0.8. The effectiveness of three-stage ranking pattern in solving different types of decision problems is provided by this experiment results. Also, the advantages of the three-stage ranking pattern are demonstrated based on the qualitative analysis between several ranking patterns.