Xunjie Gou

Novel basic operational laws for linguistic terms, hesitant fuzzy linguistic term sets and probabilistic linguistic term sets

In the process of decision making, people sometimes may feel more comfortable to express their preferences by linguistic terms instead of the quantitative form. However, as the basic premise of operations, the existing operational laws of linguistic terms and the extended linguistic term sets are very unreasonable. In order to overcome this issue, in this paper, we redefine some more logical operational laws for linguistic terms, hesitant fuzzy linguistic elements (HFLEs) and probabilistic linguistic term sets (PLTSs) based on two equivalent transformation functions. These novel operational laws can not only avoid the operation values exceeding the bounds of LTSs, but also keep the operation results more reasonable in decision making with linguistic information. Furthermore, the operational laws can keep the probability information complete when computing with PLTSs. Additionally, lots of properties of the operational laws are discussed, and some three-dimensional figures are drawn to show the regions of different operational laws of linguistic terms more vividly.

Multiple criteria decision making based on Bonferroni means with hesitant fuzzy linguistic information

In recent decades, different extensional forms of fuzzy sets have been developed. However, these multitudinous fuzzy sets are unable to deal with quantitative information better. Motivated by fuzzy linguistic approach and hesitant fuzzy sets, the hesitant fuzzy linguistic term set was introduced and it is a more reasonable set to deal with quantitative information. During the process of multiple criteria decision making, it is necessary to propose some aggregation operators to handle hesitant fuzzy linguistic information. In this paper, two aggregation operators for hesitant fuzzy linguistic term sets are introduced, which are the hesitant fuzzy linguistic Bonferroni mean operator and the weighted hesitant fuzzy linguistic Bonferroni mean operator. Correspondingly, several properties of these two aggregation operators are discussed. Finally, a practical case is shown in order to express the application of these two aggregation operators. This case mainly discusses how to choose the best hospital about conducting the whole society resource management research included in a wisdom medical health system.

Hesitant fuzzy linguistic entropy and cross-entropy measures and alternative queuing method for multiple criteria decision making

Hesitant fuzzy linguistic term set (HFLTS) is a useful tool for describing peoples subjective cognitions in the process of decision making. Multiple criteria decision making (MCDM) involves two important steps: (1) determining the criteria weights; (2) obtaining a suitable ranking of alternatives. In this paper, we propose some hesitant fuzzy linguistic entropy and cross-entropy measures, and then establish a model for determining the criteria weights, which considers both the individual effect of each hesitant fuzzy linguistic element (HFLE) and the interactive effect between any two HFLEs with respect to each criterion. Additionally, we give a hesitant fuzzy linguistic alternative queuing method (HFL-AQM) to deal with the MCDM problems. The directed graph and the precedence relationship matrix make the calculation processes and the final results much more intuitive. Finally, a case study concerning the tertiary hospital management is made to verify the weight-determining method and the HFL-AQM.

Double hierarchy hesitant fuzzy linguistic term set and MULTIMOORA method

We define the double hierarchy linguistic term set (DHLTS).We propose the double hierarchy hesitant fuzzy linguistic term set (DHHFLTS).We establish some operational laws and properties of the DHHFLTS.We develop a MULTIMOORA method on the basis of DHHFLTS.We apply this MULTIMOORA method to deal with a practical decision making problem. In recent years, hesitant fuzzy linguistic term sets (HFLTSs) have been studied by many scholars and are becoming gradually mature. However, some shortcomings of HFLTS also emerged. To describe the complex linguistic terms or linguistic term sets more accurately and reasonably, in this paper, we introduce the novel concepts named double hierarchy linguistic term set (DHLTS) and double hierarchy hesitant fuzzy linguistic term set (DHHFLTS). The operational laws and properties of the DHHFLTSs are developed as well.Afterwards, we investigate the multiple criteria decision making model with double hierarchy hesitant fuzzy linguistic information. We develop a double hierarchy hesitant fuzzy linguistic MULTIMOORA (DHHFL-MULTIMOORA) method to solve it. Furthermore, we apply the DHHFL-MULTIMOORA method to deal with a practical case about selecting the optimal city in China by evaluating the implementation status of haze controlling measures. Some comparisons between the DHHFL-MULTIMOORA method and the hesitant fuzzy linguistic TOPSIS method are provided to show the advantages of the proposed method.

Exponential operations of interval-valued intuitionistic fuzzy numbers

The operational laws of intuitionistic fuzzy numbers are useful in dealing with the problems under intuitionistic fuzzy circumstances. As a supplementation, the exponential operational law of intuitionistic fuzzy numbers has been defined. Consider that we may utilize interval-valued intuitionistic fuzzy numbers (IVIFNs) to express uncertain weight information comprehensively in the complex multi-attribute decision making problems, in this paper, we discuss two exponential operational laws of IVIFNs, namely, the exponential operational law of IVIFNs with crisp parameter and the exponential operational law of IVIFNs with interval-valued parameter. Several properties and aggregation methods based on the exponential operational laws are discussed. Furthermore, we propose a new method to compare the novel dual interval-valued intuitionistic fuzzy numbers. Additionally, we give two information aggregation methods over these two exponential operational laws for dealing with some special problems in multi-attribute decision making, and finally, we apply the methods to a practical problem involving the choice of the optimal powered roof support for coal extraction with a high recovery rate.

Alternative queuing method for multiple criteria decision making with hybrid fuzzy and ranking information

Multiple criteria decision making (MCDM), concerning the selection of the most optimal alternative(s), is an essential activity in various fields of management science. In many practical MCDM problems, it is common that there are different types of fuzzy evaluation information as well as ranking information on candidate alternatives with respect to different criteria. In this paper, we propose an alternative queuing method (AQM) to deal with this kind of hybrid fuzzy MCDM problems. Firstly, we develop an algorithm of the AQM to solve the hybrid fuzzy MCDM problems in which the criteria weights are completely known. Secondly, we propose a satisfaction degree based method to derive the criteria weights for the hybrid fuzzy MCDM problems in which the weight information is partly known, and then use the developed algorithm to further solve this kind of problems. Thirdly, we propose a least square method to derive the criteria weights for the hybrid fuzzy MCDM problems in which the weight information is completely unknown. Finally, we apply the AQM to select the optimal treatment technology for disposing the outspent or old medical apparatuses and instruments in West China Hospital.

Consensus reaching process for large-scale group decision making with double hierarchy hesitant fuzzy linguistic preference relations

Abstract Large-scale group decision making (LSGDM) or complex group decision making (GDM) problems are very commonly encountered in actual life, especially in the era of data. At present, double hierarchy hesitant fuzzy linguistic term set is a reasonable linguistic expression when describing some complex linguistic preference information. In this paper, we develop a consensus reaching process for LSGDM with double hierarchy hesitant fuzzy linguistic preference relations. To ensure the implementation of consensus reaching process, we also propose the similarity degree-based clustering method, the double hierarchy information entropy-based weights-determining method and the consensus measures. Finally, we apply our model to deal with a practical problem that is to evaluate Sichuan water resource management and make some comparisons with the existing approaches.

Hesitant Fuzzy Linguistic Possibility Degree-Based Linear Assignment Method for Multiple Criteria Decision-Making

Hesitant fuzzy linguistic term set (HFLTS), as a flexible tool to represent people’s uncertain cognition, has attracted lots of scholars’ research interests, and a series of methodologies have been...

Free Double Hierarchy Hesitant Fuzzy Linguistic Term Sets: An application on ranking alternatives in GDM

Abstract Hesitant fuzzy linguistic term sets have been an active field of research in recent times. Notwithstanding its usefulness to capture the human way of reasoning using linguistic expressions involving different levels of precision, in some situations they do not depict enough details. In this paper, we present a new kind of linguistic term sets, called free double hierarchy linguistic term sets, and their corresponding free double hierarchy hesitant fuzzy linguistic elements, in order to describe the complexity of linguistic expressions used by the decision makers in a more accurate and precise way. Furthermore, an order and a distance between free double hierarchy hesitant fuzzy linguistic elements are introduced to present an approach based on the TOPSIS method to rank alternatives with free double hierarchy hesitant fuzzy linguistic information by taking into consideration the opinions of a group of decision makers. A case study based on tourism management in Barcelona is also provided to illustrate the usefulness of the presented approach.

Exponential operational laws and new aggregation operators of intuitionistic Fuzzy information based on Archimedean T-conorm and T-norm

Atanassov extended the fuzzy set to intuitionistic fuzzy set (IFS) whose basic components are intuitionistic fuzzy numbers (IFNs). IFSs and IFNs can depict the fuzzy characteristics of the objects comprehensively, and lots of operational laws have been introduced to facilitate the use of IFSs and IFNs for solving the practical problems under intuitionistic fuzzy environments. As a supplement of the existing operational laws, we define the exponential operational laws of IFSs and IFNs based on Archimedean t-conorm and t-norm (EOL-IFS-A and EOL-IFN-A), which can be considered as the more general forms of the original exponential operational law. After that, we study the properties of the EOL-IFS-A and EOL-IFN-A. Then, we develop an approach for multiple criteria decision making with intuitionistic fuzzy information. Finally, we give an example to illustrate the application of the developed approach, and make a detailed comparison with the existing method so as to show the advantages of our approach.