Connecting the linguistic hierarchy and the numerical scale for the 2-tuple linguistic model and its use to deal with hesitant unbalanced linguistic information

Consistency Improvement With a Feedback Recommendation in Personalized Linguistic Group Decision Making

Consistency is an important issue in linguistic decision making with various consistency measures and consistency improving methods available in the literature. However, existing linguistic consistency studies omit the fact that words mean different things for different people, that is, decision makers' personalized individual semantics (PISs) over their expressed linguistic preferences are ignored. Therefore, the aim of this article is to propose a novel consistency improving approach based on PISs in linguistic group decision making. The proposed approach combines the characteristics of personalized representation and integrates the PIS-based model in measuring and improving the consistency of linguistic preference relations. A detailed numerical and comparative analysis to support the feasibility of the proposed approach is provided.

Consistency-Driven Methodology to Manage Incomplete Linguistic Preference Relation: A Perspective Based on Personalized Individual Semantics

In linguistic decision-making problems, there may be cases when decision makers will not be able to provide complete linguistic preference relations. However, when estimating unknown linguistic preference values in incomplete preference relations, the existing research approaches ignore the fact that words mean different things for different people, that is, decision makers have personalized individual semantics (PISs) regarding words. To manage incomplete linguistic preference relations with PISs, in this article, we propose a consistency-driven methodology both to estimate the incomplete linguistic preference values and to obtain the personalized numerical meanings of linguistic values of the different decision makers. The proposed incomplete linguistic preference estimation method combines the characteristic of the personalized representation of decision makers and guarantees the optimum consistency of incomplete linguistic preference relations in the implementation process. Numerical examples and a comparative analysis are included to justify the feasibility of the PISs-based incomplete linguistic preference estimation method.

A novel linguistic decision-making method based on the voting model for large-scale linguistic decision making

The notable characteristic of large-scale linguistic decision-making problems is that there are so many decision makers who provide linguistic assessments by using fuzzy linguistic representation models. In real-world applications, fuzzy linguistic terms mean different things for different people, and linguistic assessments based on different linguistic representation models may be simultaneous in the same large-scale linguistic decision-making problems. To this end, a novel linguistic decision-making method based on the voting model is proposed in the paper to deal with multi-linguistic assessments provided by decision makers. In large-scale linguistic decision process, evaluation-based voting is defined and multi-linguistic decision matrix is designed to represent multi-linguistic assessments provided by decision makers by using different linguistic representation models, and properties of the decision matrix are analyzed to show that linguistic assessments based on different linguistic representation models can be simultaneously represented. Based on multi-linguistic decision matrix, a new linguistic decision-making framework is developed to deal with large-scale linguistic decision-making problems with multi-linguistic assessments, in which normalization of multi-linguistic decision matrix and trust degrees of linguistic terms are contained, and more important, based on trust degrees of linguistic terms and 2-tuple fuzzy linguistic aggregation operators, an uniform fusion method of multi-linguistic assessments is proposed to aggregate multi-linguistic assessments of large-scale linguistic decision-making problems. Finally, user experiences of shared bikes, which are a large-scale linguistic decision-making problem in real-world applications, are employed to show the new decision-making framework and the uniform fusion method of multi-linguistic assessments, and furthermore, compared with existing linguistic decision-making methods analyzed in the example, it seems that multi-linguistic decision matrix and the uniform fusion method are useful and effective tools to deal with large-scale linguistic decision-making problems with multi-linguistic assessments.

Evaluation of Online Teaching Quality: An Extended Linguistic MAGDM Framework Based on Risk Preferences and Unknown Weight Information

Evaluation of online teaching quality has become an important issue because many universities are turning to online classes due to the Corona Virus Disease 2019 (COVID-19) pandemic. In this paper, online teaching quality evaluation is considered as a linguistic multi-attribute group decision-making (MAGDM) problem. Generally, the evaluation sematic information can be symmetrically or asymmetrically distributed in linguistic term sets. Thus, an extended linguistic MAGDM framework is proposed for evaluating online teaching quality. As the main contribution, the proposed method takes into account the risk preferences of assessment experts (AEs) and unknown weight information of attributes and sub-attributes. To be specific, the Delphi method is employed to establish a multi-level evaluation indicator system (EIS) of online teaching quality. Then, by introducing the group generalized linguistic term set (GLTS) with two risk preference parameters, a two-stage optimization model is developed to calculate the weights of attributes and sub-attributes objectively. Subsequently, the linguistic MAGDM framework was divided into two stages. The first stage maximizes the group comprehensive rating values of teachers on different attributes to obtain partial ranking results for teachers on each attribute. The latter stage maximizes the group comprehensive rating values of teachers to evaluate the overall quality. Finally, a case study is provided to illustrate how to apply the framework to evaluate online teaching quality.

Probabilistic Hesitant Intuitionistic Fuzzy Linguistic Term Sets and Their Application in Multiple Attribute Group Decision Making

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.

Sigmoid valued fuzzy soft set and its application to haze management

The impetus of this paper is to broaden the structure of linguistic soft set (LSS) to a new domain namely sigmoid valued fuzzy soft set (SVFSS). Some operating laws on SVFSS are also provided. Using the complement concept on SVFSS we define maximum rejection. This maximum rejection paves a way for defining a new similarity measure on SVFSS termed as maximum likely ratio (MLR). A new MCGDM algorithm for SVFSS is proposed using MLR. An illustrative example of haze equipment problem on sigmoid valued fuzzy soft set setting is also given. A comparative analysis of our approach with the existing approaches are also presented to justify our work.

Methods for evaluating the computer network security with fuzzy number intuitionistic fuzzy dual Hamy mean operators

The concept of fuzzy number intuitionistic fuzzy sets (FNIFSs) is designed to effectively depict uncertain information in decision making problems which fundamental characteristic of the FNIFS is that the values of its membership function and non-membership function are depicted with triangular fuzzy numbers (TFNs). The dual Hamy mean (DHM) operator gets good performance in the process of information aggregation due to its ability to capturing the interrelationships among aggregated values. In this paper, we used the dual Hamy mean (DHM) operator and dual weighted Hamy mean (WDHM) operator with fuzzy number intuitionistic fuzzy numbers (FNIFNs) to propose the fuzzy number intuitionistic fuzzy dual Hamy mean (FNIFDHM) operator and fuzzy number intuitionistic fuzzy weighted dual Hamy mean (FNIFWDHM) operator. Then the MADM methods are proposed along with these operators. In the end, we utilize an applicable example for computer network security evaluation to prove the proposed methods.

Group Decision-Making Method Based on Expert Classification Consensus Information Integration

Existing decision-making methods are mostly a simple aggregation of expert decision information when solving large group decision-making problems. In these methods, priority should be given to expert weight information; however, it is difficult to avoid the loss of expert decision information in the decision-making process. Therefore, a new idea to solve the problem of large group decision-making by combining the expert group clustering algorithm and the group consensus model is proposed in this paper in order to avoid the disadvantages of subjectively assigning expert weights. First, expert groups are classified by the clustering algorithm of breadth-first search neighbors. Next, the decision information of the experts in the class is corrected adaptively using the group consensus model; then, expert decision information in the class is integrated using probabilistic linguistic translation methods. This method not only avoids the shortcomings of artificially given expert weights, but also reduces the loss of expert decision information. Finally, the method comprehensively considers the scale of the expert class and the difference between the classes to determine the weight of the expert class, and then it weights and integrates the consensus information of all expert classes to obtain the final decision result. This article verifies the effectiveness of the proposed method through a case analysis of urban water resource sustainability evaluation, and provides a scientific evaluation method for the sustainable development level of urban water resources.

Supplier Selection of Medical Consumption Products with a Probabilistic Linguistic MABAC Method

In order to obtain an optimal medical consumption product supplier, the integration of combined weights and multi-attributive border approximation area comparison (MABAC) under probabilistic linguistic sets (PLTSs) has offered a novel integrated model in which the CRiteria Importance Through Intercriteria Correlation (CRITIC) method is employed for calculating the objective weights of various attributes and the MABAC method with PLTSs is used to acquire the final ranking result of a medical consumption product supplier. Additionally, so as to indicate the applicability of the devised method, this model is confirmed by a numerical case for the supplier selection of medical consumption products. Some comparative studies are made with some existing methods. The proposed method can also successfully select suitable alternatives in other selection problems.

TOPSIS Method for Probabilistic Linguistic MAGDM with Entropy Weight and Its Application to Supplier Selection of New Agricultural Machinery Products

In multiple attribute group decision making (MAGDM) problems, uncertain decision information is well-represented by linguistic term sets (LTSs). These LTSs are easily converted into probabilistic linguistic sets (PLTSs). In this paper, a TOPSIS method is proposed for probabilistic linguistic MAGDM in which the attribute weights are completely unknown, and the decision information is in the form of probabilistic linguistic numbers (PLNs). First, the definition of the scoring function is used to solve the probabilistic linguistic entropy, which is then employed to objectively derive the attribute weights. Second, the optimal alternatives are determined by calculating the shortest distance from the probabilistic linguistic positive ideal solution (PLPIS) and on the other side the farthest distance of the probabilistic linguistic negative ideal solution (PLNIS). This proposed method extends the applications range of the traditional entropy-weighted method. Moreover, it doesn’t need the decision-maker to give the attribute weights in advance. Finally, a numerical example for supplier selection of new agricultural machinery products is used to illustrate the use of the proposed method. The result shows the approach is simple, effective and easy to calculate. The proposed method can contribute to the selection of suitable alternative successfully in other selection problems.

Computing with Words: Revisiting the Qualitative Scale

Computing with Words (CW) is a methodology which takes an essential role in decision making problems, thus the first aim of this paper is to highlight the importance of CW in decision making. There are many proposals of CW models that can be classified in two main fields: approaches based on membership functions and approaches based on qualitative scales. This paper focuses on the qualitative scales since it provides a closer environment to human knowledge and more accurate results avoiding a loss of information. An analysis and discussion of the qualitative scales of linguistic values in CW for decision making is provided. Finally, we highlight the open challenges for the qualitative scales in linguistic decision making.