Search

A group of experts are commonly invited to find an optimal solution to a complex decision making problem. When the bipolarity of decision information should be considered in group decision making (GDM), intuitionistic fuzzy values (IFVs) have the capability to model such opinions of decision makers (DMs). This paper develops a consensus model in GDM under intuitionistic fuzzy environments with flexibility. First, it is assumed that the initial opinions of DMs are expressed as intuitionistic fuzzy preference relations (IFPRs). A novel additive consistency index is constructed to measure the deviation degree of IFPRs from fuzzy preference relations (FPRs) with additive consistency, where the non-determinacy degree of IFPRs is incorporated. The thresholds of the proposed index corresponding to IFPRs with acceptable additive consistency are discussed and computed. Second, the consensus level of DMs is defined using the similarity degree between two IFVs. An optimization problem is established by maximizing the fitness function, which is constructed by linearly combining the proposed additive consistency index and consensus level. Two flexibility degrees are offered to each DM such that the initial opinions with the bipolarity can be adjusted correspondingly. Third, individual IFPRs in GDM are optimized using the particle swarm optimization (PSO) algorithm. Numerical examples are carried out to illustrate the proposed consensus model by comparing with the existing ones. The obtained results reveal that the proposed additive consistency index can reflect the inherent property of IFPRs. Different with the previous studies, two original flexibility degrees are proposed to characterize the multi-granularity of decision information in GDM. • A novel consistency index is constructed to measure the inconsistency degree of IFPRs. • An optimization model is proposed by considering the consistency degree and consensus level. • A novel algorithm of group decision making is established where the PSO algorithm is used. [ABSTRACT FROM AUTHOR]

• Propose a linguistic information granulation model. • Develop a penalty function-based co-evolutionary PSO (PFCPSO) solution approach. • Present the whole algorithm framework for the PFCPSO solution approach. • Discuss how the granulation model and the PFCPSO solution approach work in practice. • Compare PFCPSO and co-evolutionary PSO in terms of the performance of the solution. This study focuses on linguistic information operational realization through information granulation in group decision-making (GDM) scenarios where the preference information offered by decision-makers over alternatives is described using distributed linguistic preference relations (DLPRs). First, an information granulation model is proposed to arrive at the operational realization of linguistic information in the GDM with DLPRs. The information granulation is formulated as a certain optimization problem where a combination of consistency degree of individual DLPRs and consensus degree among individuals is regarded as the underlying performance index. Then, considering that the proposed model is a constrained optimization problem (COP) with an adjustable parameter, which is difficult to be effectively solved using general optimization methods, we develop a novel approach towards achieving the optimal solution, referred to as penalty function-based co-evolutionary particle swarm optimization (PFCPSO). Within the PFCPSO setting, the designed penalty function is used to transform the COPs into unconstrained ones. Besides, the penalty factors and the adjustable parameter, as well as the decision variables of the optimization problems, are simultaneously optimized through the co-evolutionary mechanism of two populations in co-evolutionary particle swarm optimization (CPSO). Finally, a comprehensive evaluation problem about car brands is studied using the proposed model and the newly developed PFCPSO approach, which demonstrates their applicability. Two comparative studies are also conducted to show the effectiveness of the proposals. Overall, this study exhibits two facets of originality: the presentation of the linguistic information granulation model, and the development of the PFCPSO approach for solving the proposed model. [ABSTRACT FROM AUTHOR]

Estimating interest rates is a typical multivariate prediction problem that has garnered considerable attention in the finance industry. However, the rising complexity of the prediction environment has presented significant obstacles to the methodology and application of traditional single-scale rational prediction models. Considering this challenge, the paper presents a new multivariate fusion prediction system that aims to tackle the following issues: (1) How to mine prediction information from multi-scale information systems (MSISs)? (2) How to describe the irrational behavior of decision-makers (DMs) in prediction processes? (3) How to improve the prediction performance and generalization capability of the models? Specifically, the score function of each feature under MSISs is primarily established by applying scale rules, regret theory (RT), and dominance relations to thoroughly explore prediction information across varying scales. Second, an adaptive S3WD model is developed for feature selection, which leverages the feature score distribution and the sequential three-way decision (S3WD) concept to avoid the problem of dimensional disasters, thereby improving the accuracy of selected features and reducing the learning cost. Furthermore, to enhance the effectiveness and rationality of the kernel extreme learning machine (KELM), an improved version known as IKELM is developed, which combines the regret-based comprehensive score of each sample. Finally, a multivariate fusion prediction system is constructed and abbreviated as an S3WD-IKELM-PSO system, where the particle swarm optimization (PSO) algorithm is employed to determine optimal parameters. It is worth noting that actual interest rate estimation datasets are utilized to verify the feasibility and validity of the proposed prediction system. According to the experimental results, the S3WD-IKELM-PSO system exhibits superior prediction performance and generalization ability compared to existing machine learning models. • A regret theory-based multivariate prediction system in MSISs is explored. • A regret-based feature evaluation system in an MSIS is designed. • An adaptive S3WD model for feature selection is proposed. • An improved KELM model is proposed. [ABSTRACT FROM AUTHOR]