An optimization-based formulation for three-way decisions

A multiple attribute decision-making three-way model at four-branch fuzzy environment

Three-way decisions (TWDs) theory is one of the core ideas of decision-theoretic rough sets (DTRSs). Reviewing the existing research results, we find that TWDs provides us with more flexible decision choices. And the traditional fuzzy number does not take into account the absence of information (indifference) in the evaluation process. In order to construct a new model which can get flexible decision results in complex decision environment, we introduce four-branch fuzzy numbers (FBFNs) to describe the evaluation information, so that the decision-makers can express the evaluation information more comprehensively. In this paper, a novel TWDs model in four-branch fuzzy environment is proposed to solve multiple-attribute decision-making (MADM) problem. The first challenge is to construct a TWDs model based on FBFNs and to develop a new linguistic interpretation of the loss functions. Then, we extend a method for aggregating the loss functions obtained from the attribute evaluation values. Finally, we use the nonlinear solution to solve the threshold, and apply TOPSIS method to solve the conditional probability of FBFNs. The effectiveness of this method is illustrated by an example, and the decision results are compared with a MADM method based on OWGA operator.

Approaches to Three-Way Decisions Based on the Evaluation of Probabilistic Linguistic Terms Sets

The method of determining probability thresholds of three-way decisions (3WDs) has always been the key of research, especially in the current environment with a large number of data and uncertainties. Among these problems, there will be correlation and similarity between them. In the light of these problems, the loss function with Probabilistic Linguistic Terms Sets (PLTSs) is introduced in the paper, and then we propose a PLTS evaluation-based approach to determine the thresholds and derive 3WDs. According to the definition and characters of PLTSs, the PLTSs loss function matrix is constructed firstly. Then using the equivalent model of Decision-theoretic rough sets (DTRSs), we construct the equivalent model (i.e., the αopt-model and the βopt-model, which are symmtrical) and try to find the optimal solution to determine the thresholds. Based on that, we propose a novel three-way decision approach under PLTSs evaluations. Finally, the validity of the method is verified by an example.

Three-Way Decision for Handling Uncertainty in Machine Learning: A Narrative Review

In this work we introduce a framework, based on three-way decision (TWD) and the trisecting-acting-outcome model, to handle uncertainty in Machine Learning (ML). We distinguish between handling uncertainty affecting the input of ML models, when TWD is used to identify and properly take into account the uncertain instances; and handling the uncertainty lying in the output, where TWD is used to allow the ML model to abstain. We then present a narrative review of the state of the art of applications of TWD in regard to the different areas of concern identified by the framework, and in so doing, we will highlight both the points of strength of the three-way methodology, and the opportunities for further research.