A three-way decision method based on prospect theory under probabilistic linguistic term sets

In real-world decisions, we often encounter situations when decision-makers’ (DMs’) preferences can only be expressed as uncertain linguistic terms instead of crisp values. Similarly, when decisions involving several risky prospects with linguistic outcome information, it is a challenge to properly calculate the corresponding prospect values. To address this issue, this paper proposes a decision-making framework based on prospect theory where the outcomes are characterized by probabilistic linguistic term sets (PLTSs). The key contributions of this research are twofold: Firstly, it allows DMs to express their assessment of outcomes in terms of linguistic terms with interval probabilities. Secondly, it furnishes a paradigm to extend prospect theory to accommodate other forms of fuzzy and linguistic input. To begin with, this paper first presents different types of PLTSs. Then, gains and losses are calculated based on the positive and negative reference points and the operation rules of PLTSs. In accordance with the value and probability weight functions, the weighted prospect values are determined. Finally, we apply the decision-making framework to a practical case to illustrate its feasibility under linguistic environment.

Prospect theory based method for heterogeneous group decision making with hybrid truth degrees of alternative comparisons

An integrated method for multi-granular probabilistic linguistic multiple attribute decision-making with prospect theory

In this paper, a probabilistic-linguistic-information-driven decision-making method is proposed to help decision makers make decisions with historical data. Historical individual assessments and collective assessments represented by probabilistic linguistic term sets (PLTSs) are used to extract criterion weights to train a decision model in the proposed method. To support the extraction of criterion weights, a new difference measure between PLTSs is developed, which considers semantics of linguistic terms and all possible difference cases except for intersection between PLTSs. The arithmetic, geometric, and quadratic mean operators are developed to iteratively combine individual assessments to generate the aggregated assessments, in which the problem of combinatorial explosion is effectively avoided. The three operators accomplish the training of the decision model based on the extracted criterion weights. The proposed method is used to help radiologists diagnose thyroid nodules, in which its applicability is verified and the performance of the three aggregation operators is compared.

The highest level of interface design for online games is to achieve invisibility, which means that the interface is very natural and easy to use. Players are proficient in using it and fully immerse themselves in the world of online games. It seems that the interface is transparent and they no longer feel its existence. Excellent online game interface design is the requirement of users that runs through the entire design process. But this is not to say that the usability of online game software can surpass other factors. All great designs seek a balance and harmony between artistic beauty, reliability, security, usability, cost, and performance. The quality evaluation of online games interface design is a multiple-attribute group decision-making (MAGDM) problem. Recently, the Evaluation Based on Distance from Average Solution (EDAS) technique, cosine similarity measure (CSM), Dice similarity measure (DSM), Jaccard similarity measure (JSM) and entropy technique has been separately employed to cope with MAGDM issues. The probabilistic linguistic term sets (PLTSs) are employed as a tool for conveying uncertain information during the quality evaluation of online games interface design. In this paper, the EDAS technique is expanded to the PLTSs and the probabilistic linguistic EDAS (PL-EDAS) technique based on cosine similarity measure (CSM), Dice similarity measure (DSM) and Jaccard similarity measure (JSM) is constructed to manage MAGDM issue. The information entropy technique is employed to implement the weight values based on CSM technique, DSM technique and JSM technique under PLTSs. Finally, the quality evaluation of online games interface design is employed to demonstrate the PL-EDAS technique and some comparative analysis is employed to demonstrate the PL-EDAS technique. Thus, the main research contribution of this work is constructed: (1) the information entropy technique is constructed to implement the attribute weight values based on CSM technique, DSM technique and JSM technique; (2) the PL-EDAS technique is constructed under PLTSs based on CSM technique, DSM technique and JSM technique; (3) an example for quality evaluation of online games interface design is employed to verify PL-EDAS technique and several decision comparative analysis is employed to verify the PL-EDAS technique.

A probabilistic linguistic-based deviation method for multi-expert qualitative decision making with aspirations

In group decision-making problems, decision makers prefer to use several linguistic terms to describe their own perception and knowledge, and give their preference intensity of each possible linguistic terms based on their own understanding and interpretation. Due to the nonlinearity of decision maker’s cognition, the gaps between adjacent linguistic terms are unbalanced. The unbalanced probabilistic linguistic term set (UPLTS) is proposed to present such situation. To this phenomenon, a resolution framework is constructed to analyze multiple attribute group decision-making problems under unbalanced probabilistic linguistic environment. Firstly, the integration model based on evidential reasoning theory is proposed to aggregate UPLTSs from different groups in view of incomplete probabilistic distributions in UPLTS. Secondly, the transformation function based on proportional 2 tuple is developed to transform UPLTS into probabilistic linguistic term set, making it easier for subsequent analysis and processing. Thirdly, Based on the multiple types of partitioned structure relationship among attributes, partitioned fuzzy measure is developed to globally capture these interactions among attributes. Then the probabilistic linguistic Choquet integral operator with partitioned fuzzy measure is proposed to obtain the comprehensive performances of alternatives. Lastly, the effectiveness and practicability of the proposed method is demonstrated using three numerical examples and comparing with other methods.

Multi-attribute group decision making is widely used in the real world, and many scholars have done a lot of research on it. The public’s focus on emergencies can provide an important reference for emergency handling decision making in the social media big data environment. Due to the complexity of emergency handling decision making, the asymmetry of user evaluation information is easy to cause the loss of important information. It is very important to mine valuable information for decision making through online reviews. Then, a generalized extended hybrid distance measure method between the probabilistic linguistic term sets is proposed. Based on this, an extended GDMD-PROMETHEE large-scale multi-attribute group decision-making method is proposed as well, which can be used to decision making under symmetric information and asymmetric information. Firstly, web crawler technology is used to explore the topics of public concern of emergency handling on social media platforms, and use k-means cluster analysis to classify the crawling variables, then the attributes and subjective weights of emergency handling plans are obtained by TF-IDF and Word2vec technology. Secondly, in order to better retain the linguistic evaluation information from decision-makers, a new generalized probabilistic hybrid distance measure method based on Hamming distance is proposed. Considering the difference of decision makers’ evaluation, the objective weight of decision makers is calculated by combining the maximum deviation method with the new extended hybrid Euclidean distance. On this basis, the comprehensive weights of the attributes are calculated by combining subjective and objective factors. Meanwhile, this paper realizes the distance measures and information fusion of probabilistic linguistic term sets under cumulative prospect theory, and the ranking results of the emergency handling plans based on the extended GDMD-PROMETHEE algorithm are given. Finally, the feasibility and effectiveness of the extended GDMD-PROMETHEE algorithm are verified by the case study of the explosion accident handling decision making of Shanghai “6.18” Petrochemical, and the comparative analyses between the several traditional algorithms demonstrate the extended GDMD-PROMETHEE algorithm is more scientific and superior in this paper.

In a recent work (Wang et al. 2020), a partial order ⪯, a join operation ⊔ and a meet operation ⊓ of probabilistic linguistic term sets (PLTSs) were introduced and it was proved that L1 ⊓ L2 ⪯ L1 ⪯ L1 ⊔ L2 and L1 ⊓ L2 ⪯ L2 ⪯ L1 ⊔ L2. In this paper, we demonstrate that its join and meet operations are not satisfy the above requirement. To satisfy this requirement, we modify its join and meet operations. Moreover, we define a negation operation of PLTSs based on the partial order ⪯. The combinations of the proposed negation, the modified join and meet operations yield a bounded, distributive lattice over PLTSs. Meanwhile, we also define a new join operation and a new meet operation which, together with the negation operation, yield a bounded De Morgan over PLTSs.

A decision-support model through online reviews: Consumer preference analysis and product ranking

The edge node selection problem in edge computing is a typical multi-criteria group decision-making problem. In this paper, we put forward an ELECTRE II method with the probabilistic linguistic information to handle the edge node selection problem. First, a novel distance measure is developed for probabilistic linguistic term sets (PLTSs) and an entropy measure is devised to measure the uncertainty degree of PLTSs. Based on the score value and entropy, a novel method is put forward to compare two PLTSs. Next, a weight-determining method for criteria based on multiple correlation coefficient and a weight-determining method for experts based on entropy theory are proposed. After that, a novel probabilistic linguistic ELECTRE II method is put forward to deal with the edge node selection problem. Comparison with previous methods is provided to verify the superiority of our method.

Multi-criteria outranking method based on probability distribution with probabilistic linguistic information

With the rapid advancement of artificial intelligence/generative AI (AI/GenAI), various industries have undergone significant transformations, particularly in the realm of consumer devices and services. AI/GenAI plays a pivotal role in product purchase decisions by analyzing vast amounts of user-generated information, such as reviews. This article aims to provide new solutions for new energy vehicle (NEV) purchase decisions through AI/GenAI to better serve consumers. First, a genetic algorithm-guided long short-term memory and gated recurrent unit are integrated for sentiment analysis to accurately express the sentiment tendencies through AI/GenAI, with the results being converted into probabilistic linguistic term sets. Second, an enhanced K-means++ and an adaptive three-way clustering algorithm are utilized to ensure the accuracy of clustering results. Third, a model based on confidence and conflict levels to identify the non-cooperative behaviors is established to facilitate consensus among decision-makers. Fourth, during the selection phase, the three-way decision is combined with multiattributive border approximation area comparison methods to obtain the optimal alternatives. Finally, using NEV purchase examples, the proposed methods demonstrate robustness and reliability, showcasing their effectiveness in enabling GenAI-driven consumer services.

As an enhanced version of traditional linguistic term sets, Probabilistic Linguistic Term Sets (PLTS) incorporate probabilistic information, thereby offering a more robust approach to Multiple Attribute Group Decision-Making (MAGDM) and significantly improving its efficacy. This paper proposes two novel information aggregation operators for PLTS to address MAGDM problems in the PLTS context. Firstly, we introduce Choquet integral-based generalized arithmetic and geometric operators, which are designed to fuse decision information expressed by different PLTSs, thereby more comprehensively considering the interrelationships among various attributes. Subsequently, we further define measures of group consistency and inconsistency for individual decision information in MAGDM, which are used to determine the information weights of decision-makers. Finally, the group decision information is aggregated using the proposed PLTS aggregation operators. The effectiveness as well as the applicability of the developed method are illustrated through numerical examples and comparative analysis.

In practical decision-making problems, probabilistic linguistic term sets (PLTSs) are a very useful and flexible way to represent the qualitative judgments of experts. The PLTSs also have strong ability to express the information vagueness and uncertainty in the real-world applications. Considering the interrelationship among the input arguments of PLTSs, we extend the geometric Bonferroni mean to the probabilistic linguistic environment and design an approach for the application of multi-criteria group decision-making with PLTSs. First, we develop the probabilistic linguistic geometric Bonferroni mean and the weighted probabilistic linguistic geometric Bonferroni mean (WPLGBM) operators. The properties of these aggregation operators are investigated. Second, we utilize the WPLGBM operators to fuse the information in the probabilistic linguistic multi-criteria group decision-making (PLMCGDM) problem, which can obtain much more information in the process of group decision-making. By introducing the grey relational analysis method, we present its extension and further design a new approach for the PLMCGDM. Finally, an example is given to elaborate our proposed algorithm and successfully validate its performance.