A consensus approach for hesitant fuzzy linguistic decision information

Limited budget-based consensus model for large group decision making with hesitant fuzzy linguistic information

Inspired by the nonlinear weighted average operator, this paper proposes several generalized power average operators to aggregate hesitant fuzzy linguistic decision information. It is worth noting that the new operators take both the location and date weight information and the relative closeness of the decision-making information into consideration, a characteristic that results in objectivity and fairness in a group decision making. Moreover, we demonstrate some useful properties of the operators and discuss their associations. A new approach based on the designed operators is then proposed for hesitant fuzzy linguistic multiple attribute group decision-making problems, in which the attribute weights are known or unknown. Finally, this paper demonstrates the efficiency and feasibility of the proposed method through a numerical example.

Considering that the existing cosine similarity measure between hesitant fuzzy linguistic term sets(HFLTSs) has an impediment as it does not satisfy the axiom of similarity measure, we propose a new similarity measure of HFLTSs in the paper, which is constructed based on the existing cosine similarity measure and Euclidean distance measure of HFLTSs. Then the corresponding distance measure of HFLTSs is obtained according to the relationship between the similarity measure and the distance measure. Furthermore, we develop the TOPSIS method to the proposed distance measure in hesitant fuzzy linguistic decision environment and apply the closeness coefficients to rank the alternatives. The main advantage of the proposed method is that it not only considers the distance measure from the point view of algebra and geometry but also overcomes the disadvantage of the existing cosine similarity measure. Finally, an example is provided to illustrate the feasibility of the proposed method and some comparative analyses are given to show its efficiency.

A group decision-making model based on incomplete comparative expressions with hesitant linguistic terms

We propose a novel method for hesitant fuzzy linguistic decision making by utilizing Dempster–Shafer (D–S) theory of evidence. First, we propose some novel operations of hesitant fuzzy linguistic term sets (HFLTSs) on the basis of closed operations on linguistic 2-tuples and distribution linguistic average aggregation (DLAA) operators. These novel operations not only avoid information loss and operational results exceeding the boundary of linguistic term sets, but also make the aggregation results interpretable. Then, we define the hesitant fuzzy linguistic Archimedean weighted arithmetic mean (HFLAWAM) and hesitant fuzzy linguistic Archimedean weighted geometric mean (HFLAWGM) operators of HFLTSs. These two proposed operators are able to overcome the shortcomings of the existing approaches to multicriteria decision making (MCDM) with HFLTSs. Then, to take into account the novel operations of HFLTSs and the MCDM under uncertainty, we propose the belief structure-HFLAWAM (BS-HFLAWAM) and belief structure-HFLAWGM (BS-HFLAWGM) operators of HFLTSs. After that, we create an approach to handle the hesitant fuzzy linguistic MCDM problems in light of proposed operators. Finally, we apply the created approach to a MCDM problem regarding political management of a country.

Multiple criteria decision-making methods with completely unknown weights in hesitant fuzzy linguistic term setting

The aim of this paper is to develop some novel operational laws for a hesitant fuzzy linguistic term set (HFLTS)-based on the improved supplementary regulation and Archimedean t-norms and s-norms. The improved supplementary regulation for HFLTSs can reserve the fidelity of original information commendably, and it brings a new conception to research on information measures of HFLTS. As a hot and key research topic for information fusion, some Archimedean t-norms and s-norms based hesitant fuzzy linguistic aggregation operators are proposed to aggregate HFLTSs. Some essential properties together with their special cases of such aggregation operators are discussed in detail. The entropy and cross-entropy of HFLTSs are proposed and applied to derive the attribute weights. An approach to multiple attributes group decision making with hesitant fuzzy linguistic information is developed. Finally, a numerical example related to the assessment of health-care waste disposal methods is provided to show the utility and effectiveness of our methods, which are then compared to the existing methods.

Double hierarchy hesitant fuzzy linguistic term set and MULTIMOORA method: A case of study to evaluate the implementation status of haze controlling measures

Hesitant fuzzy linguistic term sets (HFLTSs) provide a linguistic and computational basis to increase the flexibility and richness of linguistic elicitation based on the fuzzy linguistic approach. Based on the traditional Hamming distance, Euclidean distance and generalized distance, some new class of distance measures for hesitant fuzzy linguistic numbers which include the hesitance degree of hesitant fuzzy element are provided and some linguistic scale functions are applied. We also define the continuous distance measure between two collections of HFLTSs. Furthermore, the proposed distance measures based on TOPSIS method for hesitant fuzzy linguistic multiple criteria decision making are developed, which calculate the distances between the alternatives and the positive ideal solution, the negative ideal solution, respectively. Then, the relative closeness degree to the ideal solution is calculated to rank all the alternatives. The main characteristics of the proposed distance measures are that it not only considers the hesitance of the hesitant fuzzy elements but also deals with linguistic transformation problem under different semantic situations, which efficiently avoid information loss and distortion. Finally, an example is provided to illustrate the feasibility and effectiveness of the developed method, which are then compared to the existing methods.

To solve a multi-attribute group decision-making problem, since its attribute weight is completely unknown, based on the prospect theory, a hesitant fuzzy multi-attribute group decision making method is proposed. According to the single-attribute-preference function provided by a decision maker, an improved entropy weight method is proposed to calculate the attribute weight. The hesitant fuzzy decision-making matrix is transformed into the prospect decision-making matrix which utilizes positive and negative ideal solutions as reference points. Then alternative schemes are ranked according to the ratio of profit to loss. Finally, a numerical example is provided to verify the effectiveness and feasibility of the proposed method.

Hesitant fuzzy linguistic term set HFLTS is a very useful technology in dealing with decision-making problems where people have hesitancy in providing their linguistic assessments. Distinct methods have been developed to aid decision making with HFLTSs, yet there is little research involving the issue that how to deal with the multigranularity hesitant fuzzy linguistic information. The aim of this paper is to develop the aggregation method for multigranularity hesitant fuzzy linguistic information and solve the linguistic group decision problem with different linguistic term sets. To do so, we first modify the translation functions and aggregation operators in the existing 2-tuple linguistic representation models so as to aggregate linguistic terms from different linguistic term sets. Then, we introduce the notion of hesitant 2-tuple sets to make computation of HFLTSs without loss of information, and develop some new operators to aggregate HFLTSs from different linguistic term sets. Using these operators, we propose a method to deal with multigranularity linguistic group decision-making problems with different situations where importance weights of either criteria or experts are known or unknown. Finally, the multigranularity linguistic group decision-making model is implemented to the healthcare waste treatment in West China Hospital to validate its effectiveness and efficiency in aiding decision-making process.

Group decision-making and the analytic hierarchy process: Exploring the consensus-relevant information content

After the epidemic, all enterprises are faced with the difficult decision about whether the enterprise should resume work and production immediately, which is related to the safety and development of enterprises. The three-way decisions offer a novel study perspective to solve this problem. Firstly, we describe some relevant attributes of the enterprise with double hierarchy hesitant fuzzy linguistic term sets, and construct double hierarchy hesitant fuzzy linguistic information systems for each enterprise. Secondly, we get the weights of attributes with the entropy weight method, and take the weighted aggregation of attributes information as the conditional probability that the enterprise is in a safe state. Next, we classify each enterprise according to its size. Considering the influence of different sizes of enterprises, we put forward the corresponding loss function matrix. Then we get the decision results about work resumption based on the principle of minimizing the loss, which demonstrates the practicability and effectiveness of our method. Finally, we compare the method proposed by us with the other method and discuss the advantages and limitations of our proposed method.

Group decision-making approaches are very important due to the complexity and uncertainty of many real-world decision-making problems. Some of the decision-making problems are defined in qualitative frameworks. Extended hesitant fuzzy linguistic term set (EHFLTS) is proposed as a new and powerful tool for elicitation of hesitant qualitative information in group decision-making process. In this paper, we first introduced the comparison laws and a family of distance and similarity measures for extended hesitant fuzzy linguistic terms (EHFLTs) and EHFLTSs, respectively. Next, we developed the extended hesitant fuzzy linguistic (EHFL)-VIKOR method as a qualitative multi-attributes group decision-making approach based on the EHFLTS distance measures to deal with the qualitative hesitancy in group decision making. Finally, we presented an application example about selection of suitable telecommunications service provider of small- and medium-sized enterprises to verify applicability and validation of proposed method in the process of qualitative group decision making.

In this paper, motivated by the Einstein operations and Bonferroni mean, we investigate the multiple attribute decision making problems for evaluating the enterprise risk with the hesitant fuzzy linguistic information. Then, we propose the hesitant fuzzy linguistic Einstein Bonferroni mean (HFLEBM) operator. Then, we have utilized the HFLEBM operator to develop an approach for evaluating the enterprise risk with the hesitant fuzzy linguistic information. Finally, a practical example for evaluating the Enterprise risk is given.