EVALUATE PUBLIC-PRIVATE-PARTNERSHIP’S ADVANCEMENT USING DOUBLE HIERARCHY HESITANT FUZZY LINGUISTIC PROMETHEE WITH SUBJECTIVE AND OBJECTIVE INFORMATION FROM STAKEHOLDER PERSPECTIVE

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

Compared with hesitant fuzzy linguistic term set (HFLTS), double hierarchy hesitant fuzzy linguistic term set (DHHFLTS) has a second hierarchy linguistic term set, which is a detailed supplementary of each linguistic term included in the first hierarchy linguistic term set. Thus, DHHFLTS can express more complex and sufficient evaluation information than HFLTS. To solve multiple attribute group decision making (MAGDM) problems in which the assessment values of alternatives and the preference relations between alternatives are denoted by double hierarchy hesitant fuzzy linguistic elements, this paper extends the traditional LINMAP method under double hierarchy hesitant fuzzy linguistic environment. A practical example is provided to demonstrate the applicability of the proposed method.

Double hierarchy hesitant fuzzy linguistic term set (DHHFLTS) is one of the successful extensions of the hesitant fuzzy linguistic term set used for describing the uncertain information in a more prominent manner for solving the group decision-making problems. In DHHFLTS, the membership functions are represented in terms of linguistic membership degrees which are a flexible structure for preference elicitation and enrich the ability for rational decision-making with complex linguistic expressions. Driven by the flexibility of DHHFLTS, in this paper, a new decision framework is developed for solving decision-making problems, which provides scientific and rational decisions based on the preference information. For it, initially, a new aggregation operator is proposed for aggregating decision-makers’ preferences. Later, the importance of the attribute weights in the problems is determined by formulating a mathematical model and the COPRAS method is extended to the DHHFLTS context for prioritizing alternatives. The applicability of the presented approach is demonstrated through a numeric example related to green supplier selection. A comparative analysis with existing studies is also administered to test the effectiveness and verify the method.

As a generalization to hesitant fuzzy linguistic term set (HFLTS), double hierarchy hesitant fuzzy linguistic term set (DHHFLTS) is presented which circumvents the weakness of HFLTS in representing complex linguistic terms. DHHFLTS has two linguistic hierarchies with the second hierarchy supplementing the primary which enables decision-makers (DMs) to represent complex linguistic terms better. Motivated by the power of DHHFLTS, in this paper, a new decision framework is presented under DHHFLTS context. Initially, a new aggregation operator called double hierarchy hesitant fuzzy hybrid aggregation (DHHFHA) operator is proposed for sensible aggregation of DMs’ preference information. Further, weights of attributes are calculated by extending statistical variance (SV) method under DHHFLTS context. Objects are prioritized by extending the popular WASPAS (weighted aggregated sum product assessment) method to DHHFLTS context. The applicability and usefulness of the proposed framework are realized by demonstrating a risk management technique (RMT) selection problem for a construction project. Finally, the superiority and weakness of the proposed framework are discussed by comparison with other methods.

Multiple criteria decision making based on distance and similarity measures under double hierarchy hesitant fuzzy linguistic environment

Security assessment and diagnosis for industrial water resources using TODIMSort considering Best–Worst Method with double hierarchy hesitant fuzzy linguistic term set

A multi-attribute decision-making framework for Chinese medicine medical diagnosis with correlation measures under double hierarchy hesitant fuzzy linguistic environment

The linguistic terms used in expressing thoughts more naturally are used in many scientific studies, especially decision making. In order to obtain better results than linguistic expressions, studies are carried out to develop the hesitant fuzzy linguistic term sets (HFLTSs), which are used as the main tools for expressing and evaluating linguistic terms. A new example of these studies, the double hierarchy hesitant fuzzy linguistic term set (DHHFLTS) was developed to more accurately describe complex linguistic expressions. In this study, the decision-making problem is dealt with to determine the optimal location for the installation of photovoltaic (PV) solar plants with high installation costs. According to the DHHFLTS, the evaluation statements from the experts are processed by the MULTIMOORA method, which is an important decision-making tool, and the four alternative positions are compared according to four basic criteria.

Double hierarchy hesitant fuzzy linguistic term set (DHHFLTS) can be used to express complex linguistic information by combining two hierarchy linguistic term sets with 2-tuple linguistic structures. In decision-making processes, experts’ assessment information may often be represented by some possible double hierarchy hesitant fuzzy linguistic elements (DHHFLEs) or some DHHFLEs with probability information, and we cannot ignore these probabilities when they are directly provided or aggregated by the experts’ assessments. As we are aware that representing probability information is a new improvement and challenge for DHHFLTSs, this paper defines a novel and more general concept named probabilistic double hierarchy linguistic term set (PDHLTS). Then, to propose some more reasonable operations and a distance measure of PDHLTSs, we develop an adjustment method to ensure that two PDHLTSs have same probability distribution. Additionally, this paper develops an extended probabilistic double hierarchy linguistic VIKOR method by improving the traditional VIKOR method. Moreover, the advantages and practicality of the proposed method are demonstrated by applying it to solve a practical multiple criteria decision-making problem involving smart healthcare. Finally, we make some comparative analyses, as well as discussing possible directions for future studies.

The extent of failure evaluation depends on the complexity and significance of electronic products. However, traditional failure mode and effect analysis (FMEA) has many shortcomings, which brings large difficulty to failure evaluating work. This paper uses the double hierarchy hesitant fuzzy linguistic term set (DHHFLTS) and the K-means clustering algorithm to improve the shortcomings of traditional FMEA. The DHHFLTS is a set of language terms based on the symmetry method and uniform language granularity. Firstly, we determine the product failure mode and set up an evaluation team after formulating an evaluation symmetrical language set. The psychological changes of the evaluators can be truly expressed by using the DHHFLTS. Secondly, the entropy weight method is used to calculate the weight of the evaluation members. The evaluation information of the evaluation personnel on the failure mode is aggregated based on the weight of the evaluation members. Then, the K-means clustering algorithm is used to calculate the distance between failure modes and each cluster center point by using the normalized weight of influencing factors and the evaluation distance of each evaluator. Finally, the evaluation of an electromagnet failure mode is taken as an example to prove the objectivity and practicability of the new method.

Warhead power assessment based on double hierarchy hesitant fuzzy linguistic term sets theory and gained and lost dominance score method

A double hierarchy hesitant fuzzy linguistic term set (DHHFLT) is deemed as an effective and powerful linguistic expression which models complex linguistic decision information more accurately by using two different hierarchy linguistic term sets. The purpose of this paper is to propose a multi-attribute decision making method to tackle complex decision issues in which attribute values are represented as double hierarchy hesitant fuzzy linguistic numbers, and there are some extreme or unreasonable data in the attribute values. To do this, firstly, four double hierarchy hesitant fuzzy linguistic generalized power aggregation operators are introduced, including the double hierarchy hesitant fuzzy linguistic generalized power average (DHHFLGPA) operator, the double hierarchy hesitant fuzzy linguistic generalized power geometric (DHHFLGPG) operator, and their weighted forms. Thereafter, several favorable properties, as well as representative cases of the proposed operators, are investigated in detail. Moreover, by virtue of the proposed operators, a novel approach is developed for coping with multi-attribute decision making cases in the double hierarchy hesitant fuzzy linguistic context. Finally, an illustrated example is given to demonstrate the practical application of the presented approach, an availability verification is given to show its validity, and a comparative analysis is also conducted to highlight the advantages of the proposed approach.

Assessment of traffic congestion with ORESTE method under double hierarchy hesitant fuzzy linguistic environment

Double hierarchy hesitant fuzzy linguistic term set (DHHFLTS) is a newly developed complex linguistic expression model, and has been well applied to multi-criteria decision-making (MCDM) problems. However, the determination of criteria weights and the innovation of decision-making methods are still two issues that worth exploring in this field. At present, conventional weight-determination methods sometimes have the disadvantages of complicated calculation and low consistency of the obtained results. On the other hand, the existing methods for linguistic information sometimes cannot consider the uncertainty of information caused by ignorance. Considering that the best-worst method (BWM) is a weight-determination method, which can not only greatly simplify the calculation process, but also improve the consistency degree of the results. Dempster-Shafer evidence theory (DSET) can better deal with information uncertainty caused by ignorance. Therefore, this paper extends the BWM and DSET to double hierarchy hesitant fuzzy linguistic environment to solve the above two problems respectively, and the DHHFL-BWM-DSET method is proposed. First, the weight of each criterion is derived based on the BWM-based weight-determination method. Then, inspired by DSET, we propose a DSET-based MCDM method which can not only obtain the decision results of a single decision maker, but also integrate the decision information of multiple decision makers to obtain more rational results. Therefore, decision makers can choose the method based on the specific situation. Finally, taking the selection of financial products as an example, it shows that the method proposed in this paper has some breakthroughs and advantages.

Based on the Computing with Words (CW), double hierarchy hesitant fuzzy linguistic term set (DHHFLTS) can be used to express complex linguistic information accurately with two simple linguistic hierarchies. This paper proposes a group decision making (GDM) model based on multiplicative consistency and consensus with double hierarchy hesitant fuzzy linguistic preference relations (DHHFLPRs). Firstly, a correlation coefficient of DHHFLTSs is defined based on the distance measures of double hierarchy hesitant fuzzy linguistic elements (DHHFLEs). Then, a multiplicative consistency property of DHHFLPRs is investigated, and a consistency checking method and a feedback mechanism-based repairing algorithm are developed to ensure all DHHFLPRs with acceptable multiplicative consistency. Furthermore, a correlation measure for DHHFLPRs based on the correlation coefficient of DHHFLTSs is proposed, and a new consensus reaching method on the basis of the correlation measure is developed, which can be used to fully obtain the consensus degree from both positive and negative angles. Finally, we make some comparative analyses with other existing consistency checking and repairing method as well as the consensus reaching approach to illustrate the effectiveness of the proposed method by a case study concerning the assessment of the venture capital project about real estate market in some cities of China.