Multi-attribute Group Decision Research Articles

Sustainable mining method selection by a multi-stakeholder collaborative multi-attribute group decision-making method

How to protect the ecological environment during mineral resource exploitation is a crucial issue for the survival and development of human society. In this context, mining method selection requires simultaneous achieving environmental protection and resource exploitation, while involving the coordination of multi-agent interests. Therefore, this study develops a multi-stakeholder collaborative multi-attribute group decision-making approach for mining method selection. This method enables multiple stakeholders and experts from different fields to make decisions together. First, a conflict resolution model is proposed to resolve cognitive conflict and interest conflict among multi-stakeholders. Then, the 2-tuple linguistic representation model is used to deal with the decision maker’s fuzzy preference. Next, the comprehensive attribute weights are calculated and the alternatives are prioritized. A case study for mining method selection in a gold mine in Shandong Province, China, is presented to verify the validity of the proposed method. This method considers not only the coordination between mineral resource exploitation and ecological environment protection but also the conflicting views of stakeholders. The proposed method is a useful tool for the assessment and selection of development schemes involving multiple stakeholders.

Consensus adjustment for multi-attribute group decision making based on cross-allocation

Consensus adjustment is crucial in group decision making (GDM), aiming to reduce discrepancies in decision makers’ (DMs’) judgments for final decision results. The consensus adjustments made by DMs are interactive rather than independent. However, few studies investigate the consensus adjustment problem from the perspective of interactions among DMs. This study first constructs a model to determine the total minimum consensus adjustment under the requirements of consensus threshold and individual-collective judgment bias. Then, a consensus adjustment approach based on cross-allocation scheme is proposed to address the inconsistency between individual and collective minimum adjustments, which concerns all DMs’ individual favorable allocation results under the total minimum consensus adjustment. The cross-allocation scheme ensures unanimous support for the same allocation result among all rational DMs, thereby eliminating the discrepancies among them. Subsequently, the optimization model-based minimum consensus judgment penalty is formulated to handle the non-cooperative behaviors of DMs. Furthermore, we show how to determine the unique consensus adjustment result for the non-cooperative DMs using the cross-allocation scheme. Therefore, our study contributes by developing a new GDM method that conducts consensus adjustment allocation by considering interactions among DMs. Finally, a case study is employed to demonstrate the specific application of the new method and discuss its efficiency. Meanwhile, comparison analysis and simulation experiments are provided.

Bonferroni Mean Operator of Interval Linguistic Neutrosophic Uncertain Linguistic Number and its Application in Multi-Attribute Group Decision-Making

This paper proposes the concept of interval linguistic neutrosophic uncertain linguistic number (IL-NULN). As a new and effective way of NS expression, ILNULN combines interval linguistic neutrosophic numbers and uncertain linguistic numbers, which can better handle uncertain and inconsistent information. In the ILNULN, the first part “uncertain linguistic number” reflects the attitude of the decision maker (DM) towards the evaluation object, and the second part “interval linguistic neutrosophic number” reflects the subjective linguistic judgment of the DM on the given uncertain linguistic number. In addition, considering the weighted arithmetic Bonferroni mean (WABM) operator integrates the correlation of aggregation parameters, this paper combines the ILNULN and WABM operator to propose the interval linguistic neutrosophic uncertain linguistic weighted arithmetic Bonferroni mean (ILNUL-WABM) operator. Finally, under the environment of interval linguistic neutrosophic uncertain linguistic number, this paper uses the ILNULWABM operator to make VIKOR decision based on the relative closeness, and gives a practical example to solve multi-attribute group decision making (MAGDM) problems.

A large-scale multi-attribute group decision-making method with R-numbers and its application to hydrogen fuel cell logistics path selection

AbstractThe large-scale multi-attribute group decision-making (LSMAGDM) problem has become a hot research topic in the field of decision science. An R-numbers large-scale multi-attribute group decision-making (R-LSMAGDM) model is proposed to be constructed in this paper based on the advantages of R-numbers in capturing risks. First, the most commonly used clustering method, k-means, is introduced to determine the sub-groups. Then, a new sub-group weighting determination model is constructed by considering sub-group size and sub-group entropy. Next, we also build an optimized consensus-reaching model by improving the calculation method of the mean value. Then, the R-numbers weighted Hamy mean (RNWHM) operator is proposed to aggregate the sub-group information. In addition, the logarithmic percentage change-driven objective weighting (LOPCOW) method and the compromise ranking of alternatives from distance to ideal solution (CRADIS) method are used for attribute weighting calculation and alternative ranking, respectively. Finally, the effectiveness of the model is verified by an application example of hydrogen fuel cell logistics path selection.

Maximum consensus model with individual tolerance and mixed DEA prospect cross-efficiency for multi-attribute group decision-making

Experts are mostly not completely rational, and they generally exhibit different psychological attitudes and behaviors in multi-attribute group decision-making (MAGDM), which may lead to actual decisions deviating from the results obtained by traditional objective methods. Therefore, it is reasonable and necessary to capture individual tolerance and risk attitudes of experts when dealing with MAGDM problems. To achieve this intention, we design a MAGDM method that combines the maximum consensus model with individual tolerance and mixed DEA prospect cross-efficiency. In the consensus reaching process (CRP), we devise a maximum consensus model with individual tolerance, which can achieve a high consensus level with limited expert tolerance. In the selection process, we first define the prospect aggressive and benevolent cross-efficiency functions. Then, a mixed DEA prospect cross-efficiency ranking method is proposed, which reflects the attitudes of DMs (decision-makers) towards losses and gains. Moreover, this method avoids DMs’ hesitation and trouble in choosing between aggressive and benevolent DEA models. Subsequently, the algorithm and framework for the MAGDM method based on individual tolerance and risk attitude are proposed. Finally, the applicability of our method can be validated by an illustrative example. Sensitivity analysis and comparative analysis are supplied to indicate the rationality and superiority of our developed method.

Stochastic multi-attribute group decision-making for long-term comprehensive operation of cascade reservoirs under multiple uncertainties

Study regionThe Three Gorges cascade (TGC) reservoirs, China. Study focusSince uncertainties inherent in inflow forecasting, elevation-storage, discharge capacity, flood routing, and the preferences of decision makers (DMs) persist in the attribute measurements (AMs) and weights (AWs), problems where multiple DMs select the best compromise scheme for the long-term comprehensive operation of cascade reservoirs considering numerous attributes become a stochastic multi-attribute group decision-making (MAGDM) process. To represent uncertain AMs and AWs and consider the bounded rationality of DMs, we propose a stochastic MAGDM with integrated stochastic multicriteria acceptability analysis (SMAA) and gray cumulative prospect theory (GCPT), namely, SMAA-GCPT. After quantifying the uncertainties, SMAA-GCPT is used to model uncertain AMs and imperfect AWs with calculable probability distributions and map the sampled AMs and AWs to utility values to reflect the overall performance assuming bounded rationality. New hydrological insights for the regionExperiments on the TGC indicate that SMAA-GCPT can effectively differentiate alternative schemes and select the best compromise scheme to harmonize the conflicting benefits and risks of the TGC, with higher reliability than SMAA-2 and SMAA-GRA. The influence of uncertain AMs on the reliability of SMAA-GCPT is more obvious than that of uncertain AWs. The decision-making error risk is primarily sensitive to the inflow forecasting uncertainty, followed by the flood routing uncertainty, and is less affected by the uncertainties in elevation-storage and discharge capacity curves.

A new multi-attribute group decision-making method based on probabilistic multi-valued linguistic spherical fuzzy sets for the site selection of charging piles

Motivated by the concepts of low carbon and environmental protection, electric vehicles have received much attention and become more and more popular all around the world. The expanding demand for electric vehicles has driven the rapid development of the charging pile industry. One of the prominent issues in charging pile industry is to determine their sites, which is a complex decision-making problem. As a matter of factor, the process of charging piles sites selection can be regarded as multi-attribute group decision-making (MAGDM), which is the main topic of this paper. The recently proposed linguistic spherical fuzzy sets (LSFSs) composed of the linguistic membership degree, linguistic abstinence degree and linguistic non-membership degree are powerful tools to express the evaluation information of decision makers (DMs). Based on the concept of LSFSs, we introduce probabilistic multi-valued linguistic spherical fuzzy sets (PMVLSFSs), which can describe DMs’ fuzzy evaluation information in a more refined and accurate way. The operation rules of PMVLSFSs are also developed in this article. To effectively aggregate PMVLSFSs, the probabilistic multi-valued linguistic spherical fuzzy power generalized Maclaurin symmetric mean operator and the probabilistic multi-valued linguistic spherical fuzzy power weighted generalized Maclaurin symmetric mean are put forward. Based on the above aggregation operators, a new method for MAGDM problem with PMVLSFSs is established. Further, a practical case of suitable site selection of charging pile is used to verify the practicability of this method. Lastly, comparative analysis with other methods is performed to illustrate the advantages and stability of proposed method.

Combinative distance-based assessment method using linguistic T-spherical fuzzy aggregation operators and its application to multi-attribute group decision-making

Clean energy has become a hot topic worldwide because of the continuous rise in the climate's temperature. Reduced air pollution is only one of the many economic and environmental advantages of clean energy. An effective contractor with experience and knowledge in clean energy projects is always required to handle the complicated process of planning, implementing, and maintaining the new clean energy infrastructure. Contractor selection for renewable energy projects (REPs) is a multi-attribute group decision-making (MAGDM) problem. Linguistic T-spherical fuzzy set (LT-SFS) can be compatible with fuzzier information, and the contractor selection problem also has a lot of fuzzy information, which makes LT-SFS very suitable for contractor selection for REPs. Hence, the present work proposes a MAGDM methodology utilizing a combinative distance-based assessment (CODAS) method within the LT-SF context. For that, the Einstein and Frank t-norm and t-conorm has been used to define new and generalized operational laws for linguistic T-spherical fuzzy numbers. Then, the linguistic T-spherical fuzzy Einstein and linguistic T-spherical fuzzy Frank aggregation operators are proposed to integrate the information data provided by experts. Moreover, the proposed aggregation operators based-CODAS approach is designed to evaluate and rank the available alternatives. A real-life decision problem of selecting the best suitable contractor for a renewable energy project is solved to verify our suggested technique. Moreover, the sensitivity analysis is also carried out by changing the parameter's value to check the consistency of the rank order. Finally, the new model is compared with existing approaches to demonstrate its strength. The comparative analysis shows that the results of the suggested technique are more feasible and beneficial than those of existing approaches.

Reliability Evaluation of Binary Group Decision-Making Mechanism

Decision-making is an important management activity. This study evaluates the reliability of group decision-making (GDM) and multi-attribute GDM (MAGDM) mechanisms for a class of 0–1 binary decision-making problem. We define the reliability of GDM and MAGDM, use the weighted voting system to model the GDM and MAGDM mechanisms, and propose two algorithms to evaluate the reliability of GDM and MAGDM considering the participation of general or professional decision makers. Additionally, the influence of some system parameters, such as the number of decision makers or attributes, cognitive accuracy of decision makers, and threshold of weighted majority voting rule, on the reliability of GDM and MAGDM was analyzed using random simulation experiments. The results of the random experiment show that: increasing the number of decision makers or attributes could improve the decision accuracy; the reduction in the individual subjective accuracy reduces the overall decision accuracy, which was difficult to compensate for by increasing the number of DMs; guiding DMs to reach consensus through group discussion decreased the decision accuracy of GDM and MAGDM.

New distance measure-driven flexible linguistic consensus model with application to urban flooding risk assessment

As a novel linguistic representation tool, flexible linguistic expression (FLE) has substantial flexibility in expressing ambiguous and uncertain information from experts. However, FLEs pose the following challenges to developing information measurement and consensus mechanisms for FLEs-based multi-attribute group decision-making (MAGDM). (1) The current studies primarily use linguistic distribution approximation or triangular fuzzy numbers to measure the difference between FLEs indirectly without proposing an exact distance measure. (2) Few studies have been conducted on direct accurate consensus models incorporating adaptive consensus feedback mechanisms. To deal with these issues, the flexible linguistic ordinal Deng entropy (FLODE) is firstly proposed to measure the uncertainty of FLEs, and by combining it with linguistic scale functions, a new distance measure for FLEs is constructed, which can accurately measure the level of group consensus and the difference in pairwise FLEs. Subsequently, by integrating the defined FLODE with the classical entropy weight method, a new method for determining the experts’ personalized attribute weights is constructed, fully considering the impact of experts’ personalized attribute weights on decision-making results. Also, a new consensus model incorporating a minimum adjustment feedback mechanism and dynamic personalized attribute weights is developed, in which the feedback adjustment coefficients and personalized attribute weights are dynamically updated during the consensus reaching process (CRP). Lastly, an urban flooding risk assessment is applied to confirm the effectiveness of the proposed consensus model.

A novel group decision making method based on CoCoSo and interval-valued Q-rung orthopair fuzzy sets

Interval-valued q-rung orthopair fuzzy set (IVq-ROFS) is a powerful tool for dealing with uncertainty. In this paper, we first propose a new method for aggregating multiple IVq-ROFSs, which is easier to understand and implement in the multi-attribute group decision making process compared to current aggregation operators. Secondly, this paper introduces a new fuzzy entropy with parameters based on IVq-ROFS, which is highly flexible due to its adjustable parameters. Based on this, the IVq-ROFS-based attribute weight calculation method is proposed to obtain the objective weights of the attributes, which is more reasonable and objective than the existing methods. Then, for the dimensional differences between the three compromise scores in the original Combined Compromise Solution (CoCoSo) method, the enhanced compromise scores are proposed. These scores are obtained by normalizing the three dependent compromise scores, ensuring that they fall within the same range. Finally, a novel CoCoSo mothed on IVq-ROFS using the proposed fuzzy entropy and enhanced compromise scores is presented. The proposed method is highly adaptable and scalable, not limited to IVq-ROFS. The excellent performance and robustness of the proposed method are verified in sepsis diagnosis applications.

Multidimensional fuzzy sets: Negations and an algorithm for multi-attribute group decision making

Multidimensional fuzzy sets (MFS) is a new extension of fuzzy sets on which the membership values of an element in the universe of discourse are increasingly ordered vectors on the set of real numbers in the interval [0,1]. This paper aims to investigate fuzzy negations on the set of increasingly ordered vectors on [0,1], i.e. on L∞([0,1]), MFN in short, with respect to some partial order. In this paper we study partial orders, giving special attention to admissible orders on Ln([0,1]) and L∞([0,1]). In addition, we study the possibility of existence of strong multidimensional fuzzy negations and some properties and methods to construct such operators. In particular, we define the ordinal sums of n-dimensional negations and ordinal sums of multidimensional fuzzy negations on a multidimensional product order. A multi-attribute group decision making algorithm is presented.

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The information in the real world often contains many properties such as fuzziness, randomness, and approximation. Although existing linguistic collections attempt to solve these problems, with the emergence of more and more constraints and challenges, this information cannot fully express the problem, leading to an increasing demand for methods that can contain multiple uncertain information. In this paper, we comprehensively consider the various characteristics of information including membership degree, credibility and approximation based on rough sets, and propose the concept of χ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi$$\\end{document}-linguistic sets (χ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi$$\\end{document}LSs), which depend on original data rather than prior knowledge and effectively solve the problem of incomplete information representation. At the same time, the corresponding theories such as the comparison method and operational rules have also been proposed. Subsequently, we construct a new χ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi$$\\end{document}-linguistic VIKOR (χ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi$$\\end{document}LVIKOR) method for multi-attribute group decision making (MAGDM) problem with χ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi$$\\end{document}LSs, and apply it to the risk assessment of COVID-19. Through comparative analysis, we discuss the effectiveness and superiority of χ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi$$\\end{document}LSs.

ExpTODIM-driven framework for 2-tuple linguistic neutrosophic MAGDM with applications to teaching quality evaluation in higher education

Since the new century, the main theme of my country’s higher education is to improve the quality of teaching. To this end, the education administrative department and the vast number of colleges and universities have done a lot of work. Looking back, this teaching quality construction involving thousands of colleges and universities across the country has attracted much attention from all walks of life. The government as the organizer promotes the active participation of colleges and universities in the form of teaching evaluation under the leadership of administrative authority and the “quality engineering” project with resources and reputation, which has played a huge role in improving the teaching quality of colleges and universities. The teaching quality evaluation in higher education is a classical multi-attribute group decision-making (MAGDM) issue. Recently, the Exponential TODIM (ExpTODIM) method has been used to cope with MAGDM issues. The 2-tuple linguistic neutrosophic sets (2TLNSs) are used as a tool for characterizing uncertain information during the teaching quality evaluation in higher education. In this paper, the 2-tuple linguistic neutrosophic number ExpTODIM (2TLNN-ExpTODIM) is built to solve the MAGDM under 2TLNSs. In the end, a numerical case study for teaching quality evaluation in higher education is given to validate the proposed method. The main contribution of this paper is constructed: (1) the Exponential TODIM (ExpTODIM) method is extended to the PLTSs; (2) the 2-tuple linguistic neutrosophic number ExpTODIM (2TLNN-ExpTODIM) is built to solve the MAGDM under 2TLNSs; (3) Finally, a numerical case study for teaching quality evaluation in higher education is given to validate the proposed method.

A MAGDM approach for evaluating the impact of artificial intelligence on education using 2-tuple linguistic q-rung orthopair fuzzy sets and Schweizer-Sklar weighted power average operator.

The impact of artificial intelligence (AI) in education can be viewed as a multi-attribute group decision-making (MAGDM) problem, in which several stakeholders evaluate the advantages and disadvantages of AI applications in educational settings according to distinct preferences and criteria. A MAGDM framework can assist in providing transparent and logical recommendations for implementing AI in education by methodically analyzing the trade-offs and conflicts among many components, including ethical, social, pedagogical, and technical concerns. A novel development in fuzzy set theory is the 2-tuple linguistic q-rung orthopair fuzzy set (2TLq-ROFS), which is not only a generalized form but also can integrate decision-makers quantitative evaluation ideas and qualitative evaluation information. The 2TLq-ROF Schweizer-Sklar weighted power average operator (2TLq-ROFSSWPA) and the 2TLq-ROF Schweizer-Sklar weighted power geometric (2TLq-ROFSSWPG) operator are two of the aggregation operators we create in this article. We also investigate some of the unique instances and features of the proposed operators. Next, a new Entropy model is built based on 2TLq-ROFS, which may exploit the preferences of the decision-makers to obtain the ideal objective weights for attributes. Next, we extend the VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) technique to the 2TLq-ROF version, which provides decision-makers with a greater space to represent their decisions, while also accounting for the uncertainty inherent in human cognition. Finally, a case study of how artificial intelligence has impacted education is given to show the applicability and value of the established methodology. A comparative study is carried out to examine the benefits and improvements of the developed approach.

MABAC-based evaluation of multimedia technology application effect in film and television post-production

Computer multimedia technology first appeared in the late 1980s, which is a functional upgrade based on the development of digital technology. It can achieve functions such as information collection, processing, and storage. Multimedia technology has received widespread attention in the entire computer field and has become a popular technology. Against the backdrop of continuous technological development, various electronic products are presented to people, bringing convenience to their lives. At the same time, they also play a huge role in the work of some industries. The application of multimedia technology, advanced editing software, and digital equipment in the production of video works can present good results and showcase excellent film and television works for people. The application effect evaluation of multimedia technology in the film and television post-production is frequently viewed as a multi-attribute group decision-making (MAGDM) issue. The maximizing deviation method was used to obtain the weight information under intuitionistic fuzzy sets (IFSs). Depending on the MABAC (multi-attributive border approximation area comparison) method and IFSs, this paper design the intuitionistic fuzzy MABAC (IF-MABAC) method to assess the application effect evaluation of multimedia technology in the film and television post-production. Eventually, an example about application effect evaluation of multimedia technology in the film and television post-production and some comparative analysis have been employed to verify the superiority of the designed IF-MABAC method.

Determination of best renewable energy sources in India using SWARA-ARAS in confidence level based interval-valued Fermatean fuzzy environment

The requirement for renewable energy sources arises from the depletion of fossil fuels and the increasing energy demand. A case study in India has been conducted in this context to identify the most promising renewable energy sources. A novel multi-attribute group decision-making (MAGDM) method integrating stepwise weight assessment ratio analysis (SWARA) and additive ratio assessment (ARAS) has been proposed for this purpose. We have used interval-valued Fermatean fuzzy numbers for data representation due to their ability to accommodate a broad range of fuzzy information. By introducing confidence level-based aggregation operators in an interval-valued Fermatean fuzzy environment, we avoid erroneous assessments by decision experts. We have employed objective and subjective weight determination approaches to determine decision experts’ weights. The SWARA method has been used for attribute weight evaluation due to its simplicity and efficiency, and the ARAS method is employed for alternative ranking and optimal choice selection using the utility degree. The findings show the potential to expand solar and wind power, whereas geothermal energy is not yet suitable for widespread deployment because of its early stage of development. We find the technical and environmental aspects to be especially significant during the decision-making process. To demonstrate the proposed method’s applicability, we have compared the results with existing MAGDM methods. To establish its stability, we conducted a sensitivity analysis. The presented MAGDM method can help make informed decisions regarding implementing solar energy as a primary source of energy supply in India, thereby aiding decision-making for policymakers, regulators, energy planners, and stakeholders.

Research on probabilistic language multi-attribute group decision-making method based on correlation coefficient and improved entropy

To address the issue of unknown expert and attribute weights in the comprehensive assessment of hospitals, as well as the potential challenges posed by distance measures, this paper presents a probabilistic language multi-attribute group decision-making (MAGDM) approach that utilizes correlation coefficients and improved entropy. First, the correlation function, called the probabilistic linguistic correlation coefficient, is introduced into the probabilistic linguistic term set(PLTS) to measure the consistency among experts, so as to obtain the weights of experts. Next, based on Shannon entropy, an improved probabilistic linguistic entropy is proposed to measure the uncertainty of PLTS considering the number of alternatives and information quantity. Then, based on the correlation coefficient and improved entropy, the attribute weights are obtained. In addition, in order to overcome the counter-intuitive problem of existing distance measurement, this paper proposes a probabilistic language distance measurement method based on the Bray-Curtis distance to measure the differences between PLTSs. On this basis, by applying the technique for order preference by similarity to ideal solution (TOPSIS) method and using PLTSs to construct the MAGDM method, the ranking of alternative schemes is generated. Finally, the improved MAGDM method is applied to an example of the comprehensive evaluation of the smart medical hospitals. The results show that compared with the existing methods, this method can determine the weight information more reasonably, and the decision-making results are not counter-intuitive, so it can evaluate the hospital more objectively.

Research on Case Reasoning Multi-attribute Group Decision-making Method Based on Hesitant Fuzzy Set

In this study, a hesitant fuzzy set-based case-based reasoning integration method is proposed for the multi-attribute group decision-making problem with unknown attribute weights and mixed forms of attribute values. First, from two perspectives, traditional distance measure and information theory, a multi-objective optimization model is constructed using the distance similarity measure and information entropy of each type of attributes to determine the attribute weights. Secondly, considering the hybrid and nonlinear characteristics of case data, based on the principle of symmetric interaction entropy and TOPSIS method, a global similarity measure based on symmetric interaction entropy is proposed and a case inference algorithm suitable for hesitant fuzzy environment is designed. Finally, by analyzing the arithmetic cases of the target case in the case base, the most similar historical cases to the target case are retrieved to determine the decision-making scheme, and the practicality and feasibility of the decision-making method are verified. The results show that considering hesitant fuzzy theory for case-based reasoning research will help improve the accuracy and reliability of decision-making and provide more effective support for multi-attribute group decision management.

TODIM-PROMETHEE method for tourism landscape planning design scheme evaluation based on the virtual reality technology under spherical fuzzy sets

How to explore the potential value of landscape, realize the organic combination of tourism landscape, enrich landscape elements and enhance tourism experience has become an important topic of tourism landscape planning and design, which is also a practical problem that needs to be solved urgently in the process of tourism landscape development and planning in different regions of China. The tourism landscape planning design scheme evaluation based on the virtual reality technology a typical multi-attribute group decision-making (MAGDM) problem. With the complexity of economic activities, uncertain information has an increasing impact on production activities. However, due to the ambiguity and uncertainty of human cognition, the factors affecting the risk of things cannot be accurately expressed. Therefore, selecting spherical fuzzy sets (SFSs) can make the expression of information more accurate and complete. On basis of the TODIM method and the PROMETHEE method, in this study, spherical fuzzy number TOMIM-PROMETHEE (SFN-TOMIM-PROMETHEE) method is implemented to solve the MAGDM problem under SFSs. Furthermore, CRITIC method under SFSs is implemented to determine relative weights. Then a numerical example for tourism landscape planning design scheme evaluation based on the virtual reality technology is selected to illustrate the effectiveness and practicality of the method. Finally, the comparative analysis shows that the SFN-TOMIM-PROMETHEE method under SFSs is an effective method to deal with MAGDM problems. The main contribution of this paper is managed: (1) the TODIM and PROMETHEE technique was extended to SFSs; (2) CRITIC technique is employed to manage the weight values under SFSs. (3) the SFN-TOMIM-PROMETHEE technique is founded to manage the MAGDM under IVPFSs; (4) a numerical example for tourism landscape planning design scheme evaluation based on the virtual reality technology and comparison analysis are constructed to verify the feasibility and effectiveness of the SFN-TOMIM-PROMETHEE technique.