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This study focuses on optimizing offshore drilling operations through Multi-Criteria Decision-Making (MCDM). It recognizes MCDM as a crucial framework for evaluating alternatives in the complex offshore drilling landscape. The objective is to identify the most suitable alternative among four approaches: Advanced Drilling Technologies, Drilling Process Optimization, Human Factors and Safety Enhancement, and Environmental Impact Mitigation. Evaluation criteria include Operational Efficiency, Safety Performance, Environmental Impact, and Cost-effectiveness. The research aims to contribute insights and recommendations for stakeholders in the offshore oil and gas industry. In the field of information aggregation and fusion, there is a growing interest among researchers in the domain of probabilistic linguistic expression sets, which are particularly effective in consolidating uncertain data. This article aims to explore various methodologies for information aggregation using probabilistic linguistic expressions. To achieve this goal, we have introduced procedural principles based on the Dombi (D) framework, specifically designed for managing probabilistic linguistic term elements (PLTEs). These principles are firmly grounded in both the product and sum of Dombi operations. As a result, we have developed a range of techniques for probabilistic linguistic aggregation, including entities such as the Probabilistic Linguistic Dombi Average (PLDA) and the Probabilistic Linguistic Dombi Geometric (PLDG). Additionally, we have created weighted aggregation operators (AOs) such as PLDWA and PLDWG, along with ordered AOs like PLDOWA and PLDOWG. By utilizing the D $\tau $ -norm and $\tau $ -conorm, we have designed versatile aggregation tools that support information reinforcement in both ascending and descending directions. Furthermore, we provide a comparative analysis between our proposed methodologies and the MARCOS approach. Additionally, we offer a detailed explanation of the distinctive attributes associated with these operators. Through the application of PLDA, PLDG, PLDWA, PLDWG, PLDOWA, and PLDOWG, we present strategies for effectively integrating probabilistic linguistic term sets (PLTs) into the realm of MCDM.

When solving group decision-making (GDM) problems, the proper values of consensus thresholds are vital for consensus checking and improving. Decision makers are usually not confident to select a proper threshold. In the linguistic setting, this paper presents a new process to support the determination of consensus thresholds. A new concept, namely random consensus index, is presented to serve as a reference object so that the risk preference of a decision maker could be induced by comparing the quality of the information in hands with the averaging quality of randomly generated information. In this sense, admissible consensus thresholds could be determined automatically, and decision makers are not necessary to focus on the detail of consensus measures. Furthermore, the process is applied to the GDM problems with probabilistic linguistic preference relations, and a new GDM approach is presented. Different from the existing contributions, the consensus is measured by the probability of a set of preference relations being with acceptable consensus, and then the consensus is improved by revising the involved probability distributions. All the involved parameters are intuitive and interpretable. A case study, regarding the departure audit in China, demonstrates that the proposed GDM approach is effective even if the original preferences of experts are with low consistency and consensus. • A process of determining consensus thresholds of LPRs is presented. • Decision maker's risk attitude is induced by comparing with random information. • A novel GDM approach based on probabilistic LPRs is presented. • Consensus of probabilistic LPRs is measured and explained by the probabilities. • Consensus is improved by revising the associated probabilities of terms. [ABSTRACT FROM AUTHOR]