Multi-attribute group decision-making using double hierarchy hesitant fuzzy linguistic preference information

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

Motivated by the driving force to address global water scarcity, industrial water resources, as the second largest consumption of water resources, its security assessment plays a crucial role in improving the current situation. Hence, this paper proposes a novel methodology to conduct the industrial water resources security (IWRS) assessment. Firstly, a more targeted assessment system based on the framework of the Pressure-State-Response (P-S-R) on IWRS is established. Then, enhanced with a double hierarchy hesitant fuzzy linguistic term set (DHHFLTS), the Best-Worst Method (BWM) now determines subjective weights through DHHFLTS-BWM (DF-BWM). By introducing the Criteria Importance Through Intercriteria Correlation (CRITIC) method, which considers the indicator interactions, objective weights are obtained to modify the subjective weights. Furthermore, the global dominance of all alternatives is calculated by a TODIMSort method and grading them. Moreover, 16 cities in Anhui Province are taken as examples to assess IWRS in the decade from 2011 to 2020. Comparative analysis with original BWM, time series analysis, sensitivity analysis on loss attenuation coefficient, coupling and coordination analysis and obstacle analysis on all indicators are conducted to verify the rationality, effectiveness, and stability of the proposed assessment methodology. Simultaneously, explore the existing issues within IWRS. It can be seen from the results that the performance of Lu'an and Huainan cities is relatively better, while Ma'anshan city shows relatively poorer performance. In addition, per capita water resources and wastewater treatment facilities have a significant impact on the IWRS. Finally, some management suggestions are proposed to enhance the scientific and effective management of industrial water resources and ensure their sustainable utilization.

Double hierarchy hesitant fuzzy linguistic information based framework for personalized ranking of sustainable suppliers

With the growing appetite for reducing carbon footprint, organizations are tirelessly working towards green practices and one such crucial practice is purchasing raw materials from sustainable suppliers (SSs). Inspired by the drift in purchase habits, several sustainable suppliers emerged in the market and a rational selection of a suitable sustainable supplier is a complex decision problem. There are many criteria associated with the evaluation of sustainable suppliers, and double hierarchy hesitant fuzzy linguistic (DHHFL) structure is a popular preference style that accepts complex linguistic expressions in the natural language form. Earlier studies on sustainable supplier selection infer that (i) complex linguistic expressions are not properly modeled, (ii) interrelationship among criteria must be considered during importance assessment, (iii) direct assignment of attitudinal values of experts causes bias and subjectivity, and (iv) nature of criteria play a crucial role in ranking SSs. To overcome these limitations, a novel MCMD framework is proposed in this study in which the attitudinal characteristic values of experts are calculated by using a variance approach. Besides, importance of diverse sustainable criteria is calculated by proposing novel attitude-CRITIC approach that supports proper capturing of interrelationship among criteria along with experts' attitude values. Later, weighted distance approximation algorithm is presented to DHHFL setting for personalized and cumulative ranking of SSs by properly considering nature of criteria. These methods are integrated to form a framework under DHHFL setting, and its usefulness is exemplified by using a case study of SS selection in an automotive firm. A comprehensive sensitivity analysis as well performed to test the validity of the proposed model approves the applicability, validity, and robustness of the model. Lastly, comparison is done with other methods to understand the merits and shortcomings of the proposal.

An integrated decision support taxonmy method using probabilistic double hierarchy linguistic MAGDM for physical health literacy evaluation of college students

Health literacy is an important part of health education and health promotion in my country, and the health literacy level of students majoring in physical education in colleges and universities is an important factor in the development of health education in primary and secondary schools, and also directly affects the implementation of school health education in the future. The physical health literacy evaluation of College students is frequently viewed as the multiple attribute group decision making (MAGDM) issue. In such paper, Taxonmy method is designed for solving the MAGDM under probabilistic double hierarchy linguistic term sets (PDHLTSs). First, the expected function of PDHLTSs and Criteria Importance Though Intercrieria Correlation (CRITIC) method is used to derive the attribute weights. Second, then, the optimal choice is obtained through calculating the smallest probabilistic double hierarchy linguistic development attribute values from the probabilistic double hierarchy linguistic positive ideal solution (PDHLPIS). Finally, a numerical example for physical health literacy evaluation of College students is given to illustrate the built method.

A New Approach to the Viable Ranking of Zero-Carbon Construction Materials with Generalized Fuzzy Information

This paper aims to put forward an integrated decision approach, with generalized fuzzy information for the viable selection of zero- and low-carbon materials for construction. In countries such as India, the construction sector accounts for high pollution levels and high carbon emissions. To restore sustainability and eco-friendliness, the adoption of low-carbon materials for construction is essential and, owing to the multiple attributes associated with the selection, the problem is viewed as a multi-criteria decision-making problem. Earlier studies on material selection have faced certain issues, such as the following: (i) the modeling of uncertainty is an ordeal task; (ii) the flexibility given to experts during preference elicitation is lacking; (iii) the interactions among the criteria are not well captured; and (iv) a consideration of the criteria type is crucial for ranking. To alleviate these issues, the primary objective of this paper was to develop an integrated framework, with decision approaches for material selection in the construction sector that promote sustainability. To this end, generalized fuzzy information (GFI) was adopted as the preference style as it is both flexible and has the ability to model uncertainty from the following three dimensions: membership, non-membership, and hesitancy grades. Furthermore, the CRITIC approach was extended to the GFI context for calculating criteria weights objectively, by effectively capturing criteria interactions. Furthermore, the COPRAS technique was put forward with the GFI rating for ranking zero- and low-carbon construction materials, based on diverse attributes. The usefulness of the framework was demonstrated via a case example from India and the results showed that the design cost, the financial risk, safety, water pollution, and land contamination were the top five criteria, with blended cement, mud bricks, and bamboo as the top three material alternatives for zero- and low-carbon construction. Finally, a sensitivity analysis and a comparison with other methods revealed the theoretical positives of this framework’s robustness and consistency–but it also revealed some limitations of the proposed framework.

A Multiple and Multidimensional Linguistic Truth-Valued Reasoning Method and its Application in Multimedia Teaching Evaluation

With the expansion of the epidemic, online multimedia teaching has become a common trend. The reasoning model of multimedia teaching evaluation is a useful tool to infer the result of teaching effects and predict the tendency. However, the ambiguity in the linguistic-valued evaluation leads to reasoning problems always in the context with uncertainty. To make the reasoning model better deal with multiple and multidimensional reasoning problems in uncertainty environment, while considering both positive evidence and negative evidence at the same time, this paper mainly focuses on a linguistic truth-valued intuitionistic fuzzy layered aggregation (LTV-IFLA) reasoning method. First, based on the layered linguistic truth-valued intuitionistic fuzzy lattice (LTV-IFL), we realize aggregating the linguistic truth-valued information through the layered average aggregation (LAA) operator presented by this paper. Furthermore, a layered weighted average aggregation (LWAA) operator is proposed to consider setting different weights to achieve personalization of the reasoning results. Finally, a multiple multidimensional reasoning model which simulates the reasoning of human language is presented to illustrate the method’s rationality and validity.

An enhanced VIKOR method for multi-criteria group decision-making with complex Fermatean fuzzy sets

This paper aims to propose a new decision-making approach retaining the fascinating traits of the conventional VIKOR method in the context of the enrich multidimensional complex Fermatean fuzzy $ N $-soft set. The VIKOR technique is contemplated as the most reliable decision-making approach among others which employs a strategy to identify the compromise solution with advantageous distance from the positive ideal solution possesses maximum majority utility and minimum individual regret. At the same time, the paramount characteristic of the complex Fermatean fuzzy $ N $-soft set considers the proclivity to capture two-dimensional uncertain and imprecise information along with the multi-valued parameters. This article expands the literature to handle the multi-attribute group decision-making strategy by introducing a technique, namely, the complex Fermatean fuzzy $ N $-soft VIKOR method that amalgamates the unconventional traits of complex Fermatean fuzzy $ N $-soft with the capability of the VIKOR method. The proposed technique permits the assignment of the $ N $-soft grades to the decision-makers, alternatives, and attributes based on their performances. Firstly, we unify these individual opinions of all decision-makers about the alternatives by employing the complex Fermatean fuzzy $ N $-soft weighted average operator. After that, all entities of the aggregated decision matrix are converted into crisp data by utilizing the score function. Furthermore, we calculate the ranking measures of the group utility and the individual regret by assigning the weight of strategy belongs to the interval $ [0, 1]. $ To find the compromise solution, we arrange the ranking measures in ascending order, and the alternative that possesses the conditions of compromise solution is selected. We demonstrate the presented multi-attribute group decision-making technique by selecting the best location for a nuclear power plant. We conduct the comparative analysis of the presented technique with Fermatean fuzzy TOPSIS to endorse the veracity and accuracy of our method. Finally, we explain the merits and limitations of our strategy and give some concluding remarks.

Prioritization of zero-carbon measures for sustainable urban mobility using integrated double hierarchy decision framework and EDAS approach

Zero-carbon is the current buzzword triggering the minds of every people in the world. The current pandemic situation has given the world an alarm to act towards the reduction/eradication of carbon footprint. Developing countries like India are striving hard to strike a balance between sustainability and global growth. To support the nation, certain measures and their prioritization would be helpful. Motivated by this notion, in this study, a new framework is proposed with double hierarchy fuzzy information, which not only gives experts a better style to articulate preferences linguistically but also makes a rational decision with methodical support. Mayor's transport strategy, 2018 is a popular document that provides valuable information towards sustainable transport practices, and the measures considered in this study are adapted from the same. In this framework, (i) a novel attitudinal evidence-based Bayesian approach is proposed for criteria weight estimation; (ii) experts' weights are determined by using variance approach, and (iii) Evaluation based on distance from average solution (EDAS) approach is extended for prioritizing zero-carbon measures. These approaches are integrated into a framework and its practicality is exemplified by considering a case example of prioritizing measures for a smart city in India. Finally, comparison with extant methods reveals the merits and shortcomings of the proposal.

A Novel q-Rung Dual Hesitant Fuzzy Multi-Attribute Decision-Making Method Based on Entropy Weights

In this paper, a new multiple attribute decision-making (MADM) method under q-rung dual hesitant fuzzy environment from the perspective of aggregation operators is proposed. First, some aggregation operators are proposed for fusing q-rung dual hesitant fuzzy sets (q-RDHFSs). Afterwards, we present properties and some desirable special cases of the new operators. Second, a new entropy measure for q-RDHFSs is developed, which defines a method to calculate the weight information of aggregated q-rung dual hesitant fuzzy elements. Third, a novel MADM method is introduced to deal with decision-making problems under q-RDHFSs environment, wherein weight information is completely unknown. Finally, we present numerical example to show the effectiveness and performance of the new method. Additionally, comparative analysis is conducted to prove the superiorities of our new MADM method. This study mainly contributes to a novel method, which can help decision makes select optimal alternatives when dealing with practical MADM problems.

Multi-criteria Optimization Technique with Complex Pythagorean Fuzzy N-soft Information

The main objective of this article is to lay the foundations of a novel multi-criteria optimization technique, namely, the complex Pythagorean fuzzy N-soft VIKOR (CPFNS-VIKOR) method that is highly proficient to express a great deal of linguistic imprecision and vagueness inherent in human assessments. This strategy provides a versatile decision-making tool for the ranking-based fuzzy modeling of two-dimensional parameterized data. The CPFNS-VIKOR method integrates the ground-breaking specialities of the VIKOR method with the outstanding parametric structure of the complex Pythagorean fuzzy N-soft model. It is exclusively designed for the specification of a compromise optimal solution having maximum group utility and minimum individual regret of the opponent by analyzing their weighted proximity from ideal solutions. The developed strategy factually permits specific linguistic terms to demystify the individual perspectives of the decision-making experts regarding the efficacy of the alternatives and the priorities of the applicable criteria. We comprehensively assemble these independent appraisals of all the experts using the complex Pythagorean fuzzy N-soft weighted averaging operator. Moreover, we calibrate the ranking measure by utilizing group utility measure and regret measure in order to specify the hierarchical outranking of the feasible alternatives. We demonstrate the systematic methodology and framework of the proposed method with the assistance of an explicative flow chart. We skilfully investigate an empirical analysis related to selection of constructive industrial robots for the modernization of a manufacturing industry which really justifies the remarkable accountability of the proposed strategy. Furthermore, we validate this technique by a comparative study with the existing complex Pythagorean fuzzy TOPSIS (CPF-TOPSIS) method, complex Pythagorean fuzzy VIKOR (CPF-VIKOR) method and Pythagorean fuzzy TOPSIS (PF-TOPSIS) method. The comparative study is exemplified with an illustrative bar chart that visually endorses the rationality of the proposed methodology by interpreting highly compatible and accurate final outcomes. Finally, we holistically analyze the functionality of the developed strategy to enlighten its merits and prominence over other available competent approaches.

Some self-evaluation models of enterprise’s credit based on some probabilistic double hierarchy linguistic aggregation operators

Probabilistic double hierarchy linguistic term set (PDHLTS) can not only express the complex linguistic information that the probabilistic linguistic term set (PLTS) cannot express, but also reflect the frequency or importance of linguistic term set (LTS)that cannot be reflected by the double hierarchy linguistic term set (DHLTS). It is an effective tool to deal with multiple attribute group decision making (MAGDM) problems. Therefore, in this paper, we propose several aggregation operators which can aggregate PDHLTS information and apply them to MAGDM problems. Firstly, the basic notion of PDHLTS is reviewed, and the distance formula and algorithm of PDHLTS are defined; then, extant weighted averaging (WA) operator, weighted geometric(WG) operator and power weighted averaging (PWA) operator, power weighted geometric(PWG) operator to PDHLTS, and establish probability double hierarchy linguistic weighted averaging (PDHLWA) operator, probability double hierarchy linguistic weighted geometric (PDHLWG) operator, probability double hierarchy linguistic power weighted averaging (PDHLPWA) operator, probability double hierarchy linguistic power weighted geometric (PDHLPWG) operator; in addition, The idempotency, boundedness and monotonicity of these aggregation operators are studied; what’s more, those aggregation operators are proposed to establish the enterprise credit self-evaluation model; Finally, compared with the available probabilistic double hierarchy linguistic MAGDM methods, the defined model is proved to be scientific and effective.

An evidence theory based approach for group decision making under uncertainty

With the changing business environment and the active participation of various stakeholders in the decision making process, it plays an increasingly important role to the weight of decision makers and the preference information given by decision makers. This paper presents a novel approach for group decision making under uncertainty with the involvement of the third-party evaluator in the decision making process. Recognizing the challenge in adequately determining the weight of decision makers in group decision making, the evidence theory is appropriately used with the involvement of the third-party evaluator. To effectively model the uncertainty and imprecision in the decision making process, fuzzy preference relations are used for better representing the subjective assessment of individual decision makers. To adequately determine the ranking of available alternatives, the logarithmic least square method is applied for appropriately aggregating the fuzzy preference relation of individual decision makers. A group consensus index is developed for facilitating consensus building in group decision making. This leads to better group decisions being made. A real-world application is presented that shows the proposed approach is effective in solving group decision making problems under uncertainty.

An integrated decision-making COPRAS approach to probabilistic hesitant fuzzy set information

The paper aims to present an integrated approach to solve the decision-making problem under the probabilistic hesitant fuzzy information (PHFI) features, which is an extension of the hesitant fuzzy set. The considered PHFI not only allows multiple opinions, but also associates occurrence probability to each opinion, which increases the reliability of the information. Motivated by these features of PHFI, an approach is presented to solve the decision problem with partial known information about the attribute and expert weights. In addition, an algorithm for finding some missing values in the preference information is presented and stated their properties. Afterward, the Hamy mean operator has been used to aggregate the different collective information into a single one. Also, we presented a COPRAS method to the PHFI for ranking the given alternatives. The presented algorithm has been demonstrated through a case study of cloud vendor selection and its validity has been revealed by comparing the approach results with the several existing algorithm results.

Hesitant Fuzzy SWARA-Complex Proportional Assessment Approach for Sustainable Supplier Selection (HF-SWARA-COPRAS)

The selection of sustainable supplier is an extremely important for sustainable supply chain management (SSCM). The assessment process of sustainable supplier selection is a complicated task for decision experts due to involvement of several qualitative and quantitative criteria. As the uncertainty is commonly occurred in sustainable supplier selection problem and hesitant fuzzy set (HFS), an improvement of Fuzzy Set (FS), has been proved as one of the efficient and superior ways to express the uncertain information arisen in practical problems. The present study proposes a novel framework based on COPRAS (Complex Proportional Assessment) method and SWARA (Step-wise Weight Assessment Ratio Analysis) approach to evaluate and select the desirable sustainable supplier within the HFSs context. In the proposed method, an extended SWARA method is employed for determining the criteria weights based on experts’ preferences. Next, to illustrate the efficiency and practicability of the proposed methodology, an empirical case study of sustainable supplier selection problem is taken under Hesitant Fuzzy (HF) environment. Further, sensitivity analysis is performed to check the stability of the presented methodology. At last, a comparison with existing methods is conducted to verify the strength of the obtained result. The final outcomes confirm that the developed framework is more consistent and powerful than other existing approaches.

Power Aggregation Operators and VIKOR Methods for Complex q-Rung Orthopair Fuzzy Sets and Their Applications

The aim of this paper is to present the novel concept of Complex q-rung orthopair fuzzy set (Cq-ROFS) which is a useful tool to cope with unresolved and complicated information. It is characterized by a complex-valued membership grade and a complex-valued non-membership grade, the distinction of which is that the sum of q-powers of the real parts (imaginary parts) of the membership and non-membership grades is less than or equal to one. To explore the study, we present some basic operational laws, score and accuracy functions and investigate their properties. Further, to aggregate the given information of Cq-ROFS, we present several weighted averaging and geometric power aggregation operators named as complex q-rung orthopair fuzzy (Cq-ROF) power averaging operator, Cq-ROF power geometric operator, Cq-ROF power weighted averaging operator, Cq-ROF power weighted geometric operator, Cq-ROF hybrid averaging operator and Cq-ROF power hybrid geometric operator. Properties and special cases of the proposed approaches are discussed in detail. Moreover, the VIKOR (“VIseKriterijumska Optimizacija I Kompromisno Resenje”) method for Cq-ROFSs is introduced and its aspects discussed. Furthermore, the above mentioned approaches apply to multi-attribute decision-making problems and VIKOR methods, in which experts state their preferences in the Cq-ROF environment to demonstrate the feasibility, reliability and effectiveness of the proposed approaches. Finally, the proposed approach is compared with existing methods through numerical examples.