Effectiveness measures in movement-based three-way decisions

Two-Way Concept-Cognitive Learning via Concept Movement Viewpoint

Representation and learning of concepts are critical problems in data science and cognitive science. However, the existing research about concept learning has one prevalent disadvantage: incomplete and complex cognitive. Meanwhile, as a practical mathematical tool for concept representation and concept learning, two-way learning (2WL) also has some issues leading to the stagnation of its related research: the concept can only learn from specific information granules and lacks a concept evolution mechanism. To overcome these challenges, we propose the two-way concept-cognitive learning (TCCL) method for enhancing the flexibility and evolution ability of 2WL for concept learning. We first analyze the fundamental relationship between two-way granule concepts in the cognitive system to build a novel cognitive mechanism. Furthermore, the movement three-way decision (M-3WD) method is introduced to 2WL to study the concept evolution mechanism via the concept movement viewpoint. Unlike the existing 2WL method, the primary consideration of TCCL is two-way concept evolution rather than information granules transformation. Finally, to interpret and help understand TCCL, an example analysis and some experiments on various datasets are carried out to demonstrate our method's effectiveness. The results show that TCCL is more flexible and less time-consuming than 2WL, and meanwhile, TCCL can also learn the same concept as the latter method in concept learning. In addition, from the perspective of concept learning ability, TCCL is more generalization of concepts than the granule concept cognitive learning model (CCLM).

Three-way decision theory based on interval type-2 fuzzy linguistic term sets

This study examines decision theory based on interval type-2 fuzzy sets with linguistic information for the three-way decision approach by addressing the challenge of uncertainty for information analysis and fusion in subjective decision-making processes. First, the interval type-2 fuzzy linguistic term sets (IT2 FLTSs) are defined to represent and normalize the uncertain preference information in linguistic decision-making. Subsequently, perception computing based on computing with words paradigm is introduced to implement information fusion among different decision-makers in the linguistic information-based fuzzy logic reasoning process. Then, a three-way decision (3WD) theory based on IT2 FLTSs with fuzzy neighborhood covering is proposed, and the corresponded tri-partitioning strategies that satisfy Jaccard similarity of membership distributions are given. Finally, 3WD theory is applied to multi-criteria group decision-making with linguistic terms, and the algorithm steps are illustrated by a promising application under the background of coronavirus disease 2019 to reveal the feasibility and practicability of the proposed approach.

Matrix-based reduction approach for one-sided fuzzy three-way concept lattices

Three-way concept analysis is a mathematical model of the combination of formal concept analysis and three-way decision, and knowledge discovery plays a significant impact on formal fuzzy contexts since such datasets are frequently encountered in real life. In this paper, a novel type of one-sided fuzzy three-way concept lattices is presented in a given formal fuzzy context with its complement, in which a ternary classification is available. In such case, we comprehensively explore the connections between the proposed models and classical fuzzy concept lattices among elements, sets, and orders. Furthermore, approaches to granular matrix-based reductions are investigated, by which granular consistent sets, and granular reducts via discernibility Boolean matrices are tectonically put forward. At last, the demonstrated results are performed by several experiments which enrich the research of three-way concept analysis.

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

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.