Publications

Linguistic multiple attribute decision making (LMADM) has been widely used in different decision contexts to achieve a final solution, e.g., obtaining the ranking of alternatives. Evaluation information using linguistic scales in LMADM is usually expressed in simple discrete linguistic terms. In this article, we consider that each simple linguistic term in LMADM actually has a continuous representation (denoted as a linguistic two tuples) whose rounding operation matches the linguistic term. Under such conditions, the ranking of alternatives based on the simple linguistic terms may not be consistent with that based on the linguistic two tuples. Thus, this article studies the linguistic scale ranking consistency issue in LMADM under seven classical and commonly used decision rules: weighted averaging, ordered weighted averaging, weighted geometric averaging, ordered weighted geometric averaging, preference ranking organization method for enrichment evaluation, technique for order preference by similarity to an ideal solution, and elimination et choice translating reality. We first define the concept of the linguistic scale ranking consistency in LMADM. Afterward, several consistency conditions are presented analytically for the selected decision rules to guarantee the linguistic scale ranking consistency. Finally, we present the detailed theoretical and simulation-based comparisons. The theoretical comparisons show the roles of decision rules and granularity in the consistency conditions, and the simulation-based comparisons demonstrate the performance of the selected decision rules in defending against the ranking inconsistency in LMADM.

In this research, as a first step toward applying Bayesian inference to subjective expected utility analysis under judgment uncertainty, a Bayesian analysis framework for decision making with interval pairwise comparison judgments is developed on the basis of the analytic hierarchy process. This framework helps to effectively capture the inherent uncertainties associated with interval judgments and integrate prior information, including partially known preferences with observed judgments, to infer posterior preference. The key novelty of this framework lies in its mechanism for incorporating partially known preferences. Moreover, a consistency index is introduced to assess the inconsistency between partially known preferences and observed judgments. Results of illustrative examples and sensitivity analysis demonstrate that the proposed framework is adaptable to various judgmental data and model assumptions, the preference reversal probability is controlled by the inconsistency level and utility gap, and the impact of prior information can be regulated by manipulating its hyperparameters. Funding: This work was supported by the Top Talent Academic Foundation for University Discipline of Anhui Province [Grant gxbjZD2020056] and the National Natural Science Foundation of China [Grants 72171002, 72201004, 72271002, 72301003, and U22A20366]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/deca.2024.0207 .

Effective constraint handling techniques (CHTs) are of great significance for evolutionary algorithms (EAs) dealing with constrained optimization problems (COPs). To date, many CHTs, such as penalty function, superiority of feasible solutions, and ϵ-constraint (EC), have been designed. However, different CHTs are usually suited to different problems, even the most appropriate technique changes along with the stages of the optimization process. Motivated by this phenomenon, we propose a voting-mechanism-based ensemble framework, named voting mechanism for constraint handling (VMCH), to integrate multiple CHTs for solving various COPs. In this framework, each CHT acts as a voter, all voters vote for each pair of solutions, and the solution in each pair with the highest weighted votes is considered better. In addition, an adaptive strategy is developed to adjust the voter weights according to their historical voting performance. To investigate the performance of VMCH in improving existing algorithms, the proposed VMCH is embedded into the three best algorithms in the competition on constrained single objective real-parameter optimization at CEC 2018, namely, MAgES, iLSHADE ϵ, and IUDE, to form three new algorithm versions, i.e., MAgES-VMCH, iLSHADE ϵ-VMCH, and IUDE-VMCH. They are compared with seven state-of-the-art peer algorithms. Extensive experiments are conducted on 57 real-world COPs. The ranking results show that the new algorithm version MAgES-VMCH takes first place among the ten comparison algorithms. Moreover, all the new VMCH-enhanced versions of the three best algorithms are superior to their original versions. Therefore, the proposed VMCH framework can achieve competitive performance in solving COPs.