Probabilistic linguistic term sets in multi-attribute group decision making

In the face of multi-attribute decision problems in complex situations, most traditional multi-attribute group decision methods are based on the assumption that the decision maker is perfectly rational, while in the face of complex decision problems, the decision maker usually has the psychological characteristics of limited rationality and may use more than one linguistic term to describe the decision information when expressing the decision information To this end, this paper selects probabilistic language term sets to describe complex preference information. First, to address the problem that the current probabilistic linguistic term set correlation coefficient cannot appropriately measure the degree of correlation among probabilistic linguistic term sets, this paper proposes a new probabilistic linguistic term set correlation coefficient from three characteristic factors of probabilistic linguistic term sets: mean, variance, and length rate. To integrate the attribute index weights, probabilistic linguistic term set weighted mixed correlation coefficients are proposed. Second, this paper introduces the TODIM method, which can consider the psychological behavior of decision makers, and proposes a TODIM multi-attribute decision making method based on probabilistic linguistic term sets with mixed correlation coefficients. Finally, through an empirical analysis of four Internet listed companies in a new first-tier city in China, this study verifies the rationality and validity of the proposed method. The results show that the mixed correlation coefficient can comprehensively measure the correlation between probabilistic linguistic term sets, which provides an important method for future multi-attribute decision making problems.

Probabilistic linguistic term set solves the problem of probabilistic distribution of linguistic terms. Due to the objective and subjective factors such as the decision makers’experience and preference, the credibility of the linguistic terms is different. However, current studies on PLTSs ignore this difference. In this paper, we first propose a novel concept called Z probabilistic linguistic term set (ZPLTS). As an extension of existing tools, it takes advantage of the fact that Z-number can represent both information and corresponding credibility. At the same time, we discuss the normalization, operational rules, ranking method and distance measure for ZPLTSs. Then, we propose a new weight calculation method, an aggregation-based method and an extended TOPSIS method, and apply them to multi-attribute group decision making in Z probabilistic linguistic environment. Finally, a numerical example and some comparisons with other methods illustrate the necessity and effectiveness of the proposed method.

The sustainable medical supplier selection (SMSS) is an important issue facing the medical industry in the context of sustainable development, which can be regarded as a typical multi-attribute group decision making (MAGDM) problem. In the MAGDM process, linguistic term set (LTS) is particularly natural and convenient for decision makers (DMs) to express evaluation information. Especially, probabilistic linguistic term set (PLTS) is a very critical and effective tool, which can reflect the importance of different linguistic terms. Due to the different preferences and experience of different DMs, they may use multi-granularity probabilistic linguistic term sets (MGPLTSs) to represent different linguistic information. In this article, in order to study the comparison method of MGPLTSs, a new possibility degree formula is firstly proposed and its properties is proved. Then, in order to build a weight model, a possibility degree-based Best-Worst method (BWM) and a probability degree based-maximizing deviation method are established to calculate the subjective weights and objective weights of attributes, respectively. Where after, a MAGDM method is proposed by combining the ELimination Et Choix Traduisant la REalite (ELECTRE) method with Evaluation based on Distance from Average Solution (EDAS) method in the multi-granularity probabilistic linguistic information environment. Finally, the created MAGDM method is applied to the SMSS, and its effectiveness and advantages compared with other existing methods are verified.

Probabilistic linguistic term sets (PLTSs) are an effective tool in keeping with the habits of decision makers (DMs). However, in multi-criteria group decision making (MCGDM) problems, it is necessary to deal with the information reliability problem because of the difference of the DMs’ knowledge backgrounds and knowledge structures. Therefore, this paper proposes a novel concept called probabilistic reliable linguistic term sets. Based on which, some basic operations, comparison laws, distance measures, similarity measures and aggregation operators are defined. After that, we propose the probabilistic reliable linguistic gained and lost dominance score method to cope with MCGDM problems, and we further apply the proposed method to solve an investment project selection problem about lucky bag machine. Finally, we make some comparative analyses to verify the effectiveness and highlight the strength of the proposed method compared with four methods, i.e., the aggregation-based method, the TOPSIS method under probabilistic reliable linguistic environment, the gained and lost dominance score (GLDS) method with probabilistic linguistic information and the GLDS method with hesitant linguistic information.

A Best-Worst multi-attribute decision-making (MADM) method based on a new possibility degree is put forward to deal with MADM problems with probabilistic linguistic evaluation information. Firstly, a new possibility degree for pairwise comparisons with probabilistic linguistic term sets (PLTSs) is defined. Secondly, starting from the new possibility degree, two different ideas of Best-Worst Method (BWM) for getting the optimal attribute weights are put forward. Thirdly, combining the new probabilistic linguistic possibility degree and the two BWM ideas, two optimization models for determining the attribute weights are constructed, respectively. Moreover, consistency ratios for two new BWM models are proposed to check the reliability of the pairwise comparisons. Meanwhile, the state of optimal solutions for the new BWM models is analyzed. Finally, a new Best-Worst MADM method under probabilistic linguistic information is presented, which is applied to a practical example of selecting optimal green enterprises. Some comparative analyses are given to show the rationality and validity of the proposed method.

Probabilistic linguistic multi-attribute group decision making method considering the important degrees of experts and attributes

Probabilistic linguistic term sets (PLTSs), which assign different weights to various linguistic terms, offer an efficient framework for expressing preferences. Meanwhile, the TODIM method, grounded in prospect theory, is adept at incorporating the cognitive behaviors of decision-makers into the decision-making process. In this paper, we extend the TODIM method to solve multi-attribute group decision making (MAGDM) problems with PLTSs. At first, we extend the Frank operators to PLTSs and propose the probabilistic linguistic Frank weighted averaging (PLFWA) operator based on adjusted rules of PLTSs. Further, some desirable properties of them are studied. Meanwhile, we present an innovative distance measure, deeply anchored in linguistic scale functions, designed to overcome the shortcomings of current distance metrics. What’s more, the combined weights for attributes can be obtained by the criteria importance though intercriteria correlation (CRITIC) method and the best-worst method (BWM) and the steps of the extended TODIM method for PLTSs are proposed. Finally, a numerical example for the purchase selection of electric vehicles is given, and some sensitivity and comparative analysis are used to illustrate the effectiveness and rationality of this new method.

Multi-attribute group decision-making (MAGDM) is widely applied to various areas for solving real-life problems, including technology selection, credit assessment, strategic planning evaluation, supplier selection, etc. To describe the complex and imprecise cognition, it is more convenient to provide the decision-making information in linguistic terms rather than concrete numerical values. Thus, several linguistic models, such as the fuzzy linguistic approach (FLA), hesitant fuzzy linguistic term sets (HFLTSs), hesitant intuitionistic fuzzy linguistic term sets (HIFLTSs), and probabilistic linguistic term sets (PLTS) have been proposed successively. Due to the flexibility and comprehensiveness of PLTS, it has aroused growing concern. However, it also has a big limitation of requiring the membership degree to be 1 by default, and it does not consider the degree of non-membership and hesitancy of a linguistic variable. Therefore, the probabilistic hesitant intuitionistic fuzzy linguistic term sets (PHIFLTSs) have been presented to extend the PLTS by combining the membership and non-membership in symmetry to depict the evaluation of the experts. To overcome the existing shortcomings and enrich the methodology framework of PHIFLTSs, some novel operational laws are defined to extend the applicability and methodology of the PHIFLTSs in MAGDM. Furthermore, the distance and correlation measures for the PHIFLTSs are improved to make up the shortage of the current distance measures. In addition, the unbalanced linguistic terms are taken into account to represent the cognitive complex information of experts. At last, a MAGDM model based on the multiplicative multi-objective optimization by ratio analysis (MULTIMOORA) approach with the use of the developed novel operational laws and correlation measures is presented, which results in more accuracy and effectiveness. A real-word application example is presented to demonstrate the working of the proposed methodology. Moreover, a thorough comparison is done with related existing works in order to show the validity of this methodology.

A new method for probabilistic linguistic multi-attribute group decision making: Application to the selection of financial technologies

A linear programming method for multiple criteria decision making with probabilistic linguistic information

The technology of wind power is being widely developed worldwide. Ensuring the reliable operation of wind turbine systems is of significance. A popular tool to identify the potential risk of an engineering system is the failure mode and effect analysis (FMEA) method. However, when conducting a FMEA in a complex and uncertain environment, experts may find it challenging to select an appropriate linguistic term for the evaluation. The probabilistic linguistic term sets (PLTSs) are a useful fuzzy set to help experts in describing their assessment. However, different experts may assign different semantic values to the same linguistic terms, and this aspect has not been extensively examined in the existing studies. Therefore, considering the psychological behaviour of experts and the semantics of linguistic terms in the risk ranking process, an improved FMEA based on the probabilistic linguistic information and TODIM (an acronym in Portuguese of interactive and multicriteria decision making) method was developed to identify the risks in wind turbine systems. Furthermore, to demonstrate the utility of the proposed model, it was applied in a floating offshore wind turbine system. The effectiveness and the validity of the model were verified by comparing with some other methods.

A consensus-based probabilistic linguistic gained and lost dominance score method

The probabilistic linguistic term sets can express not only the decision makers’ several possible linguistic assessment values, but also the weight of each linguistic assessment value, so they can preserve the original decision information and then have become an efficient tool for solving multi-criteria group decision making problems. To promote the wide applicability of probabilistic linguistic term sets in various fields, this chapter focuses on the distance measures for probabilistic linguistic term sets and their applications in multi-criteria group decision making. This chapter first defines the distance between two probabilistic linguistic term elements. Based on this, a variety of distance measures are proposed to calculate the distance between two probabilistic linguistic term sets. Then, these distance measures are further extended to compute the distance between two collections of probabilistic linguistic term sets by considering the weight information of each criterion. After that, the concept of the satisfaction degree of an alternative is given and utilized to rank the alternatives in multi-criteria group decision making. Finally, a real example is given to show the use of these distance measures and then compare the probabilistic linguistic term sets with hesitant fuzzy linguistic term sets.

Mixed fuzzy least absolute regression analysis with quantitative and probabilistic linguistic information

Decision making is the key component of people’s daily life, from choosing a mobile phone to engaging in a war. To model the real world more accurately, probabilistic linguistic term sets (PLTSs) were proposed to manage a situation in which several possible linguistic terms along their corresponding probabilities are considered at the same time. Previously, in linguistic term sets, the probabilities of all linguistic term sets are considered to be equal which is unrealistic. In the process of decision making, due to the vagueness and complexity of real life, an expert usually hesitates and unable to express its opinion in a single term, thus making it difficult to reach a final agreement. To handle real life scenarios of a more complex nature, only membership linguistic decision making is unfruitful; thus, some mechanism is needed to express non-membership linguistic term set to deal with imprecise and uncertain information in more efficient manner. In this article, a novel notion called probabilistic hesitant intuitionistic linguistic term set (PHILTS) is designed, which is composed of membership PLTSs and non-membership PLTSs describing the opinions of decision makers (DMs). In the theme of PHILTS, the probabilities of membership linguistic terms and non-membership linguistic terms are considered to be independent. Then, basic operations, some governing operational laws, the aggregation operators, normalization process and comparison method are studied for PHILTSs. Thereafter, two practical decision making models: aggregation based model and the extended TOPSIS model for PHILTS are designed to classify the alternatives from the best to worst, as an application of PHILTS to multi-attribute group decision making. In the end, a practical problem of real life about the selection of the best alternative is solved to illustrate the applicability and effectiveness of our proposed set and models.