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Three-way decision, an outstanding method to handle decision-making uncertainties, relies on essentially the loss functions derived from the Bayesian risk decision process. Actually, there are plentiful loss functions that depend on the subjective judgment of decision-makers under different decision scenarios, lacking uniform and objective measurement frameworks. This study pays attention to the real clinical diagnosis, and constructs a weighted probability kernel multi-granularity three-way decision method (WKMG-TWD) integrating gray relation analysis (GRA) over a multi-source heterogeneous decision information system (MHDIS). The method establishes a standardized data-driven calculation framework of loss functions. Foremost, the multi-kernel probabilistic similarity is defined and granularity's weights with knowledge consistency are explored. Subsequently, a weighted probability kernel multi-granularity rough set (WKMGRS) is constructed in this paper. Secondly, to introduce the three-way decision, this study proposes the cost-sensitive individual loss functions considering the correlation determined by GRA between decision objects and different decision classes. Ultimately, this study establishes and applies a three-way iterative classification model to hypertension diagnosis. The experimental results confirm the effectiveness and superiority of the model. The main contribution of this paper is twofold. One is to offer a uniform calculation framework for loss functions and granularity's weights. The other is to furnish invaluable guidance for solving complex medical decision-making problems. [ABSTRACT FROM AUTHOR]

Three-way decision (3WD) theory has been widely used in solving multi-attribute decision-making (MADM) problems, however the calculation method for semantic interpretations of loss functions and conditional probabilities has not been reasonably addressed. Thus, by virtue of existing studies on 3WD and MADM, a novel 3WD method to MADM is explored in the current paper, which is titled the 3W-MADM method. First, a pair of novel pre-order relations are designed by virtue of the classic TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) method, and a new scheme for calculating conditional probabilities is further established. Then, the calculation scheme of loss functions and thresholds is put forward via attribute evaluation values and ideal solutions. In particular, several primary steps and the algorithm of the 3W-MADM method are summed up. Finally, the practicality and validity of the proposed method are demonstrated by a realistic case of lymphography from the UCI database. Moreover, the stability and superiority of the presented method are shown by several experimental analyses. [ABSTRACT FROM AUTHOR]

The paper primarily explores the applicability of three-way decision (TWD) to multi-attribute decision-making (MADM), and establishes a new three-way multi-attribute decision-making (TW-MADM) method under an incomplete environment. For the sake of making rational decisions for MADM problems with fuzzy values, fuzzy rough set models are first utilized to investigate a new TWD model. By taking into account the hesitation degree of each evaluation value, a data-driven method to determine the relative loss functions is presented. Moreover, a new conditional probability calculation method is put forth via the information granularity of each object. In light of the above statement, a novel TWD model with three strategies is proposed. Afterwards, the arithmetic mean method is adopted for patching the lost data to effectively address incomplete MADM problems. Given the uncertainty of the patched data and real data, a new TW-MADM method as well as a corresponding MADM algorithm is designed. By several comparative analysis and experimental analysis, the feasibility, effectiveness, superiority and stability of the method are demonstrated. In addition, the results show that the presented method with optimistic strategies is more viable and stable than the method with compromise and pessimistic strategies. [ABSTRACT FROM AUTHOR]

The model of three-way decision on two universes generalizes various two-universe models of rough sets, and it is in fact defined on 0–1 tables, i.e. binary information tables. This paper generalizes the model of three-way decision from 0–1 tables to general information tables. The framework of three-way decision on general information tables is presented and the connection of existing related models is investigated. In our models, every element in the set of objects is assigned to a value and we can construct a tri-partition of the object set according to a pair of thresholds. We present a fundamental result of the models, which induces two concepts: the fundamental sequence and pair. On the one hand, the fundamental result shows that there exist finitely many pairs of thresholds. That is, we need only to consider the case of finitely many tri-partitions. On the other hand, it describes how the positive region varies based on thresholds and induces a concept of positive region tower. Finally, we evaluate these finite tri-partitions by the weighted entropy, which is a new measure defined as a variant of information entropy. An optimal tri-partition can be obtained according to weighted entropies of the finite tri-partitions. [ABSTRACT FROM AUTHOR]

Intelligent decision-making collaborates with big data analytics to navigate the intricate landscape of the digital economy, orchestrating data-driven strategies to achieve the most favorable results. Through the integration of specific objectives and relevant data, intelligent decision-making involves the modeling, analysis, and realization of decisions. This comprehensive process seamlessly incorporates elements such as constraints, strategies, preferences, and uncertainty, ultimately leading to the autonomous achievement of optimal outcomes. In this context, the probabilistic linguistic preference relation (PLPR) serves as a recently introduced form of linguistic evaluations, offering adaptable expression of expert preference assessments. Within the domain of preferences, consistency emerges as a pivotal consideration. Extremes occur when calculating the additive consistency of PLPR using expectation values. To comprehensively address the trouble, this paper introduces an innovative planning model that employs deviation degrees. The establishment of a consistency threshold is approached objectively using the principle of minimum individual regret and maximum group delight. Once consistency is established, the process advances to consensus reaching process (CRP). During the consensus feedback phase, the infusion of the three-way decision (TWD) theory accounts for distinct expert modification attitudes, while ensuring consistency remains upheld throughout the modification procedure. For clarity, the proposed technique is referred to as the TWD-GC-EA method. Notably, the effectiveness of the designed approach is demonstrated through its application to a real-world scenario. Furthermore, a comparative assessment is conducted against several other consensus methods to validate its efficacy and superiority. • In the consistency stage, the additive consistency in PLPR is more comprehensively measured. • The consistency threshold is determined objectively by minimal individual regret and maximizing group delight. • The majority-half rule is adopted in the consensus measurement stage. • A new consensus adjustment model is designed. [ABSTRACT FROM AUTHOR]

The notion of three-way decisions was originally introduced based on the need to explain the three regions of probabilistic rough sets. In a three-way decision model, every object can be evaluated by a function and according to the evaluation value, the object can be arranged in one of the three regions (i.e., positive, negative, and boundary regions). In this study, we generalize Yao's three-way decision models to a case where every subset in the universe can be evaluated by the evaluation function, and we then propose generalized three-way models. The properties and examples of these new models are presented, as well as extensions of these models. We also give some remarks regarding Hu's three-way decision spaces. Three-way matroids are introduced based on Hu's axiomatic approach and our generalized three-way models. Furthermore, three-way matroids are generalized to three fuzzy matroids as an application of our new model. Finally, we suggest future research related to our new models and three-way fuzzy matroids. [ABSTRACT FROM AUTHOR]