Effectiveness measure for TAO model of three-way decisions with interval set

Abstract

The basic idea of the three-way decisions (3WD) is ‘thinking in threes.’ The TAO (trisecting-acting-outcome) model of 3WD includes three components, trisect a whole into three reasonable regions, devise a corresponding strategy on the trisection, and measure the effectiveness of the outcome. By reviewing existing studies, we found that only a few papers touch upon the third component, i.e., measure the effect. This paper’s principal aim is to present an effectiveness measure framework consisting of three parts: a specific TAO model - Change-based TAO model, interval sets, and utility functions with unique characteristics. Specifically, the change-based TAO model provides a method to measure effectiveness based on the difference before and after applying a strategy or an action. First, we use interval sets to represent these changes when a strategy or an action is applied. These changes correspond to three different intervals. Second, we use the utility measurement method to figure out three change intervals. Namely, different utility measures correspond to the different intervals, concave utility metric, direct utility metric, and convex utility metric, respectively. Third, it aggregates the toll utility through the joint of the three utilities mentioned above. The weights among these three are adjusted by a dual expected utility function that conveys the decision-makers’ preferences. We give an example and experiment highlighting the validity and practicability of the utility measure method in the change-based TAO model of three-way decisions.

A Novel Three-Way Decision Model for Improving Computational Thinking Based on Grey Correlation Analysis

“…e outcome evaluation measures the effect of the trisection and action strategy [24][25][26]. e TAO model has merged as a new three-way decision model that promises to make the three-way decision smarter.…”

A Novel Approach for Sequential Three-Way Decision Using Chi-Square Statistic as the Assessment Metric

“…At Level 1, Universe, which stands for the "Whole," represents all of the characteristics, actions, or other things that make up the entire collection of objects [2,3]. Universe is divided into three separate and non-overlapping parts, namely Part I, Part II, and Part III, which are referred to as level 2 components such that 𝑃𝑎𝑟𝑡𝐼 𝑈 𝑃𝑎𝑟𝑡𝐼𝐼 𝑈 𝑃𝑎𝑟𝑡𝐼𝐼𝐼 = 𝑈𝑛𝑖𝑣𝑒𝑟𝑠𝑒 and 𝑃𝑎𝑟𝑡𝐼 ∩ 𝑃𝑎𝑟𝑡𝐼𝐼 = Ф, 𝑃𝑎𝑟𝑡𝐼𝐼 ∩ 𝑃𝑎𝑟𝑡𝐼𝐼𝐼 = Ф, 𝑃𝑎𝑟𝑡𝐼 ∩ 𝑃𝑎𝑟𝑡𝐼𝐼𝐼 = Ф [2]. During the phase of 'Acting', the decision-maker is required to develop a strategic plan of action and implement it to achieve the desired outcome [2].…”

“…Universe is divided into three separate and non-overlapping parts, namely Part I, Part II, and Part III, which are referred to as level 2 components such that 𝑃𝑎𝑟𝑡𝐼 𝑈 𝑃𝑎𝑟𝑡𝐼𝐼 𝑈 𝑃𝑎𝑟𝑡𝐼𝐼𝐼 = 𝑈𝑛𝑖𝑣𝑒𝑟𝑠𝑒 and 𝑃𝑎𝑟𝑡𝐼 ∩ 𝑃𝑎𝑟𝑡𝐼𝐼 = Ф, 𝑃𝑎𝑟𝑡𝐼𝐼 ∩ 𝑃𝑎𝑟𝑡𝐼𝐼𝐼 = Ф, 𝑃𝑎𝑟𝑡𝐼 ∩ 𝑃𝑎𝑟𝑡𝐼𝐼𝐼 = Ф [2]. During the phase of 'Acting', the decision-maker is required to develop a strategic plan of action and implement it to achieve the desired outcome [2]. The success of the TAO model relies on the efficient alignment of trisecting methods and strategies for actions, which presents a significant challenge in the domain of three-way decisions [2].…”

Intuitionistic Fuzzy-Based Three-Way Label Enhancement for Multi-Label Classification

“…Three-way decisions [17], also known as trisecting-acting-outcome (TAO) model [18][19][20], is an emerging decision theory for problem solving with uncertainty [21][22][23]. It originates from the semantic explanations for three regions induced by rough sets and has become an emerging theory in the soft computing community [24][25][26][27]. The sequential three steps are trisecting, acting and outcome characterizing the routines on uncertainty.…”