Novel transformation methods from semi-three-way decision spaces to three-way decision spaces and their applications

Abstract

As a vital theoretical research of three-way decision (3WD), three-way decision space (3WDS) further enriches the theory on 3WD and enhances its application. In 3WDS, decision evaluation function (DEF) is an indispensable component and plays a crucial role in practical decision problems. But, a large number of valuable functions are the semi-decision evaluation functions (S-DEFs). For this problem, Hu gave many S-DEFs and presented a transformation method from S-DEFs to DEFs. Since then, it has led to a research hotspot that is the introduction of the usual aggregation functions (AFs) into the transformation method of Hu's form. This paper focuses on the new form of transformation methods from semi-three-way decision spaces (S-3WDSs) to 3WDSs and their applications. Firstly, we present a new form of transformation method with parameter σ from S-DEFs to DEFs. And, we verify both theoretically and experimentally that this introduced parameter σ provides a valid window to dynamically adjust 3WDSs by changing the parameter σ, respectively. Notably, this new form of transformation method covers all existing 3WDSs transformation methods except the representable uninorms-based methods. Secondly, we give a more general function named with F-function, which can be introduced to these construction methods in the same way as usual AFs. This enables decision-makers to select more suitable functions for solving practical problems. Thirdly, based on the new form, usual AFs and F-functions, we present some new construction methods of S-DEFs (resp. DEFs) related to fuzzy sets, interval-valued fuzzy sets and random sets. Finally, to make up for the application of the theory of 3WDSs in complex datasets, we select 7 complex datasets for experimenting and conduct comparative and sensitivity analysis to test the viability and efficacy of our methods. Notably, we also give an algorithm to calculate the thresholds α and β, which can adjust the optimal thresholds α and β according to different 3WDSs.