To address the challenge of facilitating overall problem solving and improving the overall efficiency of intelligent systems efforts through group decision making (GDM) by experts at all stages of the systems, this paper proposes an approach that focuses on improving consistency and enhancing local consensus. The proposed approach specifically considers the probabilistic linguistic preference relations (PLPRs) and incorporates personalized individual semantics (PISs) of decision makers (DMs). For the consistency procedure, we construct an expectation -additive consistency -driven semantic model to acquire PISs of different DMs. Secondly, the preference relation (PR) which does not satisfy the consistency is improved based on a minimum adjustment model. In particular, according to the expected value with PISs this paper, DMs offer PLPRs can be transformed into fuzzy preference relations (FPRs) correspondently for making decisions. For the FPRs, a virtue consensus measure is explored for the consensus reaching process (CRP) from two levels to combine the average value and variance of pair similarities, which effectively improves the accuracy of the consensus measurement. Next, a collective consensus level is calculated to replace the consensus threshold objectively, and then the DMs and alternative pairs that do not reach consensus are identified locally from two levels. Subsequently, an optimisation model that combines the two objectives is developed to improve the consensus level while ensuring consistency. Finally, our method is applied to a publicly available air quality dataset, and the consensus and ranking results are discussed in comparison with other advanced methods to confirm the superiority of the established method.

For multi-attribute group decision-making (MAGDM) problems, this paper proposes a three-way consensus model based on regret theory (RT) under the framework of probabilistic linguistic term sets (PLTSs), i.e., the PL-RT-GTWD model. Specifically, the PL-RT-GTWD model mainly consists of the following two components: (1) The consensus measurement considering the relativity among decision-makers (DMs); (2) A three-way consensus feedback mechanism with the minimum adjustment. First, the relative relationship between DMs is supplemented, and the consensus degree of the DM evaluation matrix is measured by a newly developed distance measure. Second, an optimization model with the minimum adjustment for all DMs to modify and reach the final desired goal (group consensus opinions) is constructed, so that DMs can achieve a balance between reaching consensus and maintaining individual independence. Then, taking the minimum adjustment before and after the adjustment as the objective function, the increase of consensus degrees and the initial range of adjustment parameters as constraints, the goal programming on adjustment parameters is constructed. It is noteworthy that the initial range of adjustment parameters is divided via three-way decision (TWD) tools that consider the regret generated during the adjustment, so as to avoid the subjectivity of the adjustment and reduce adjustment costs. Finally, comparative and sensitivity analyses are carried out to verify the feasibility and superiority of the constructed model.

Aiming at multiattribute decision-making (MADM) problems with probabilistic linguistic term sets (PLTSs), and considering the effective rationality of a decision-maker (DM) in complex decision environments, this article proposes a probabilistic linguistic three-way decision (TWD) method based on the regret theory (RT), namely, PL-TWDR. First, a probabilistic linguistic attribute weight determination method is developed that considers probabilistic linguistic information entropies and the weighted total deviation of all objects from the negative ideal solution (NIS). Then, a new group satisfaction index is designed to replace the utility function in RT, which overcomes the limitation of the RT calculation in PLTSs. Second, the fuzzy c-means (FCM) algorithm is extended to PLTSs for obtaining equivalent objects under different clusters and calculate conditional probabilities in corresponding TWD models, which makes up for the shortage of the PLTS evaluation matrix when dividing equivalence classes. Third, RT is introduced into PLTSs to rank objects according to utility perception values. At the same time, a new TWD model constructed by average utility perception values is used to realize object domains in probabilistic linguistic environments. Finally, the proposed method is applied to realistic cases, and the effectiveness and superiority of the PL-TWDR method are verified via comparative analysis and sensitivity analysis in terms of other nine popular decision-making methods.

Breast cancer is a malignant tumor that seriously threatens women's health. Although classic multi-attribute decision-making (MADM) techniques can handle this kind of medical problem, a decision-maker (DM) can only collect sample data under various indicators for result ranking and analysis. The three-way decision (3WD) theory further supplements a classification scheme. In addition, a DM's own limited rationality and personality traits have a strong impact on decision-making results. By using a dominance-based rough set approach (DRSA), a new 3WD method based on the regret theory (RT) with optimistic, neutral and pessimistic strategies (3WD-RT-OEP) is constructed in a fuzzy environment, so as to prevent diseases in advance and improve the survival rate of patients. First, attribute weights are calculated based on the similarity between the defined attributes of dominance classes, and a new method for calculating conditional probabilities is proposed to enhance the objectivity of the method by the similarity between object dominance classes and decision classes. Second, the score functions of three strategies are proposed by considering regret and rejoicing values in RT, and specific steps and algorithms of the 3WD-RT-OEP method are given as well. Finally, the validity and rationality of the constructed method are proved by experimental analysis with the support of case studies and supplementary data sets.

Cardiovascular disease is a global leading cause of death, and timely monitoring can determine its extent. Clinicians use these diagnostic indicators to make scientific and reasonable decisions. However, when decision-makers (DMs) encounter risks in complex environments, their limited rationality may affect decision behaviors. Therefore, the paper explores a new three-way multi-attribute decision making method based on regret theory (3W-MADM-R), which uses heart disease data to make decisions in fuzzy environments. There are three main steps in developing 3W-MADM-R, i.e., (i) we propose the notion of relative outcome functions and corresponding aggregated regret-based utility functions of each object; (ii) we estimate the conditional probability via an outranked set defined by an outranking relation based on the Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE II); (iii) we construct three-way decision rules to solve the problems of clustering and ranking of objects in data analysis. In order to demonstrate the usefulness of 3W-MADM-R, we apply it to analyze heart disease data. By comparing with results of other methods, we show the feasibility, stability and superiority of the presented 3W-MADM-R method.