Solve Multi-attribute Decision-making Problems Research Articles

CARD: Comprehensive approach based on relative difference for decision-making problems with dual evaluation forms − Application to sustainable renewable energy selection

Numerous multi-attribute decision-making (MADM) methods exist, each aiming to improve decision-making in complex scenarios involving multiple criteria. However, challenges remain, particularly in integrating both quantitative and qualitative evaluations and addressing issues related to attribute weighting and normalization. This study introduces a novel MADM method called the CARD method, designed to address these challenges. The CARD method offers a unified framework that combines direct and pairwise evaluations using logarithmic relative difference measures to compare alternatives in terms of relative superiority. Key innovations of the CARD method include: 1) developing a new utility function; 2) proposing a new closeness coefficient measure; 3) the ability to handle joint quantitative and qualitative inputs; and 4) introducing a new criterion satisfaction coefficient, the so-called strictness degree. These features enable the CARD method to effectively solve MADM problems involving mixed criteria. To demonstrate its applicability, we apply the CARD method to a case study on renewable energy source selection in Spain. The results confirm that wind energy is the optimal renewable energy source for Spain, highlighting its economic, engineering, and sustainable advantages. This study underscores the potential of the CARD method to enhance decision-making processes and provide valuable insights for policymakers and practitioners.

GHF-COPRAS Multiple Attribute Decision-Making Method Based on Cumulative Prospect Theory and Its Application to Enterprise Digital Asset Valuation

With the rapid development of the economy, data have become a new production factor and strategic asset, enhancing efficiency and energy for technological innovation and industrial upgrading in enterprises. The evaluation of enterprise digital asset value (EDAV) is a typical multi-attribute decision-making (MADM) problem. Generalized hesitant fuzzy numbers (GHFNs) can better express the uncertainty and fuzziness of evaluation indexes, thus finding wide applications in MADM problems. In this paper, we first propose the Kullback–Leibler (K-L) divergence distance of GHFNs and prove its mathematical properties. Second, recognizing that decision-makers often have finite rationality in practical problems, we combine the cumulative prospect theory (CPT) with the Complex Proportional Assessment (COPRAS) method to propose the GHF-CPT-COPRAS model for solving MADM problems. Simultaneously, we extend the distance correlation-based Criteria Importance Through Intercriteria Correlation (D-CRITIC) method to the GHF environment to rationally calculate the weights of attributes in the EDAV evaluation problem. Finally, we apply the proposed GHF-CPT-COPRAS model to the EDAV evaluation problem and compare it with existing GHF decision-making methods to verify its effectiveness and feasibility. This study provides an important reference for addressing the EDAV assessment problem within an uncertain fuzzy environment and extends its application methods in the decision-making field.

Multi-attribute decision-making based on dual probabilistic interval-valued intuitionistic hesitant fuzzy weighted heronian mean aggregation operator

Probabilistic interval-valued intuitionistic hesitant fuzzy sets (PIVIHFSs) can well describe the evaluation information of decision-makers (DMs) in multi-attribute decision-making (MADM) problems. However, PIVIHFSs only depict the situation where both membership and non-membership information occur with equal probability while ignoring the situations of non-equal possibility due to DMs’ subjective preferences. In this paper, we develop dual probabilistic interval-valued intuitionistic hesitant fuzzy sets (DPIVIHFSs) concept based on the truncated normal distribution. The DPIVIHFSs overcome the shortcomings of PIVIHFSs and are more interpretable. Then, the operations and ranking method of DPIVIHFSs are introduced. Furthermore, we study MADM methods in dual probabilistic interval-valued intuitionistic hesitant fuzzy environments by aggregation operators (AOs). We propose a series of AOs including the DPIVIHF heronian mean (DPIVIHFHM) operator and the DPIVIHF weighted heronian mean (DPIVIHFWHM) operator. The basic properties of the presented are discussed and proved. Finally, a novel method for solving the MADM problem is proposed based on the DPIVIHFWHM operator and a numerical example of express company selection strategy is used to illustrate the effectiveness of the method. The proposed method in this article can capture more fuzzy and uncertain information when solving MADM problems and have a wider application range.

Multi-Attribute Decision-Making Methods in Additive Manufacturing: The State of the Art

Multi-attribute decision-making (MADM) refers to making preference decisions via assessing a finite number of pre-specified alternatives under multiple and usually conflicting attributes. Many problems in the field of additive manufacturing (AM) are essentially MADM problems or can be converted into MADM problems. Recently, a variety of MADM methods have been applied to solve MADM problems in AM. This generates a series of interesting questions: What is the general trend of this research topic from the perspective of published articles every year? Which journals published the most articles on the research topic? Which articles on the research topic are the most cited? What MADM methods have been applied to the field of AM? What are the main strengths and weaknesses of each MADM method used? Which MADM method is the most used one in this field? What specific problems in AM have been tackled via using MADM methods? What are the main issues in existing MADM methods for AM that need to be addressed in future studies? To approach these questions, a review of MADM methods in AM is presented in this paper. Firstly, an overview of existing MADM methods in AM was carried out based on the perspective of specific MADM methods. A statistical analysis of these methods is then made from the aspects of published journal articles, applied specific methods, and solved AM problems. After that, the main issues in the application of MADM methods to AM are discussed. Finally, the research findings of this review are summarised.

Three-way multi-attribute decision making under incomplete mixed environments using probabilistic similarity

In recent years, many scholars have explored a variety of methods integrating three-way decision (3WD) and multi-attribute decision making (MADM), which enables the classification and priority ranking of alternatives possible and fully reflects the effectiveness and advantages of 3WD in solving MADM problems. However, few of these methods can effectively deal with the MADM problems with incomplete mixed information that are frequently encountered in real-world situations. This study proposes a three-way MADM method for an incomplete mixed information system (IMIS), where the objective determination of conditional probabilities and utility functions in IMIS without decision label is the pivotal issue. To overcome this issue, we define a probabilistic similarity measure for incomplete mixed information. The probabilistic similarity measure is used to replace the distance measure of classical TOPSIS for estimating the conditional probabilities objectively. The probabilistic similarity class is introduced with arithmetic average method to design a conversion mechanism and obtain the objective relative utility functions of incomplete evaluation values. We then construct a novel 3WD model in IMIS and combine it with two customized ranking principles, to solve the incomplete mixed MADM problems from the perspective of classification and ranking in a more thoughtful and interpretable manner. Our study provides a new perspective for the research on MADM in incomplete mixed information environment. Several examples and experimental comparisons verify the effectiveness and stability of the proposed method. The experiments demonstrate that our method can meet more decision-making requirements and is more accurate and rational in some decision-making scenarios than several prior similar methods.

Aczel-Alsina Aggregation Operators on T-Spherical Fuzzy (TSF) Information With Application to TSF Multi-Attribute Decision Making

Aczel-Alsina t-norm (TN) and t-conorm (TCN) were proposed by Aczel and Alsina in 1982 are more flexible than the other TN and TCN. Since Aczel-Alsina TN and TCN have a great impact due to the variableness of involved parameters, they have good applications in multi-attribute decision making (MADM) under fuzzy sets (FSs) construction. Recently, Senapati <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> (2022) developed Aczel-Alsina aggregation operators (AOs) under intuitionistic FSs (IFSs) and interval-valued IFSs (IVIFSs) with their applications in solving IFS and IVIFS MADM problems. We know that T-spherical FSs (TSFSs) are a recently developed approach to uncertain information with less information loss and more reliability than IFSs and IVIFSs. In this paper, we develop these AOs on TSFSs as a new approach to solve MADM problems by using Aczel-Alsina TN and Aczel-Alsina TCN under T-spherical fuzzy (TSF) information. Furthermore, the basic operations of TSF numbers (TSFNs) are developed and exemplified. Based on these operations, two types of AOs, i.e., TSF Aczel-Alsina weighted average (TSFAAWA), and TSF Aczel-Alsina weighted geometric (TSFAAWG) operators, are introduced and investigated. The reliability and accuracy of the newly developed AOs are tested numerically and theoretically by the induction methods. To further give applications and also study the sensitivity of these TSF Aczel-Alsina operators, the problem of project evaluation using these proposed operators is comprehensively observed. The results obtained by using these TSF Aczel-Alsina operators are compared with some previously existing AOs of TSFSs. According to comparison results, we observe the reliability and efficiency of the proposed methods.

Generalized ordered weighted harmonic averaging operator with trapezoidal neutrosophic numbers for solving MADM problems.

Harmonic mean is suitable for algebraic calculation and other mathematical treatments and also suitable for directly aggregated negative indicators. In many different situations, harmonic mean improves the flexibility. In this paper, we develop some new aggregation operators under neutrosophic environment and apply with multi attribute decision making (MADM) problems. First, we provide a Single valued trapezoidal neutrosophic Generalized ordered weighted harmonic averaging(SVTNGOWHA) operator which is the extension of single valued trapezoidal neutrosophic ordered weighted harmonic averaging (SVTNOWHA) operator. To fix the operators on the mount, we have tested these methods in few illustrative examples, and the results have been presented.

The voting linear assignment method for determining priority and weights in solving MADM problems

Linear Assignment (LAM) is one of the Multi-Attribute Decision Making (MADM) methods that uses integer programming models in the solution process. In this method, only the final priority of the alternatives is determined and the distance between the alternatives is not clear. The purpose of this paper is to modify this method so that instead of the final priority of the alternatives, the final weight of the alternatives is presented. This is done using a linear programming model of Data Envelopment Analysis (DEA). In this paper, we propose a hybrid MADM-DEA method called Linear Assignment Voting (VLAM). The new method is explained with a numerical example. The method will then be implemented on a problem in the real world to demonstrate the application of the method. In this case study, VLAM demonstrates the prioritization of models proposed by experts for the purchase of excavators in a road construction company. Also, based on the results of this method, the weight of the first, second and third priorities are 0.39, 0.35 and 0.26, respectively. These results increase the decision maker's power in making the final decision and choice.

An overview of ARAS method: Theory development, application extension, and future challenge

Multi-attribute decision-making (MADM) is one of the most important parts in decision-making theory, and related research is becoming more and more popular over the past few years. Investigating that the information could be qualitative and quantitative, and the different measurement units cause difficulties in some MADM problems, the additive ratio assessment system (ARAS) method was proposed. The method tries to solve MADM problems through a simple way efficiently, and at the same time eliminates the influence of different measurement units. Till now, the method has received extensive attention and has been extended to different information environments and application fields. To know about the development of the method and improve the method efficiently, this paper reviews the studies on the ARAS method from the perspectives of basic information (including the bibliometrics analyses and the outline of ARAS method), the development on theory (including the development on MADM mechanism, different information environments, and combination with different methods), the development on the application and the future challenge. From the overview, the basic situations and the development of the ARAS method are presented clearly, and the analyses of the challenges can also provide useful and sufficient instructions for the future application and improvement of the method.

An Extended VIKOR Method Based on q-Rung Orthopair Shadowed Set and Its Application to Multi-Attribute Decision Making

In the multi-attribute decision making (MADM) process, the attribute values are sometimes provided by experts or the public in the form of words. To model the linguistic evaluation more accurately, this paper proposes the q-rung orthopair shadowed set (q-ROSS) to represent attribute values and extends the VIKOR (VIsekriterijumska optimizacija i KOmpromisno Resenje) method to solve MADM problems in the q-ROSS context. First, we propose the q-ROSS to express evaluation information. Some basic operation rules and distance measures are investigated accordingly. When the amount of data is large, the left and right endpoints of the collected interval numbers will obey symmetric normal distribution. Secondly, based on the normal distribution assumption, the collected data intervals are mapped to shadowed sets through a data processing approach. Furthermore, we extend the VIKOR model to tackle the MADM problem where the evaluation values are expressed by q-rung orthopair shadowed numbers. A location selection problem verifies the practicability of our method, and the effectiveness and superiority of the presented approach are reflected through comparative analysis.

The Extension of TOPSIS Method for Multi-Attribute Decision-Making With q-Rung Orthopair Hesitant Fuzzy Sets

As a combination of q-rung orthopair fuzzy sets (q-ROFSs) and hesitant fuzzy sets (HFSs), q-rung orthopair hesitant fuzzy sets (q-ROHFSs) are more effective, powerful, and meaningful in solving the complexity, ambiguity, and expert hesitancy of membership and non-membership in multi-attribute decision-making (MADM) problems. And so, based on the advantages of q-ROHFSs, we herein propose an improved TOPSIS model in the q-rung orthopair hesitant fuzzy environment. This model can provide more accuracy in expressing fuzzy and ambiguous information. At first, we propose the distance and similarity measures of q-ROHFSs and the properties related to the distance and similarity measures of q-ROHFSs, and secondly, the axiomatized definition and formula for the entropy of q-ROHFSs. Then, for the case where the attribute weights are totally unknown, a combination of subjective and objective attribute weighting model is proposed. This model not only considers the expert's decision preference, but also the objective situation of the attributes. In addition to the above-mentioned outcomes, this paper also improves the relative closeness formula, increases the preference coefficient, and considers the risk-preference of decision makers. Finally, the proposed model is compared with other methods and used to evaluate the effectiveness of military aircraft overhaul. The method is verified to be scientific, reliable and effective for solving MADM problems.

A Normal Wiggly Pythagorean Hesitant Fuzzy Bidirectional Projection Method and Its Application in EV Power Battery Recycling Mode Selection

As a useful mathematical tool to solve the multi-attribute decision-making (MADM) problems, Pythagorean hesitant fuzzy set (PHFS) permits decision makers (DMs) to give several evaluation values in membership and non-membership degrees. Given that much cognitive preferences of DMs may be hidden in the original evaluation information and cannot be fully expressed, we propose the normal wiggly Pythagorean hesitant fuzzy set (NWPHFS) to comprehensively mine the uncertain preferences from original Pythagorean hesitant fuzzy information. NWPHFS can help DMs more accurately express their potential valuable preferences for objects while giving the original evaluation information. We put forward some operational laws and comparison rules of NWPHFS, then present the formulas of projection and bidirectional projection measures between normal wiggly Pythagorean hesitant fuzzy elements (NWPHFEs). Furthermore, we propose the normal wiggly Pythagorean hesitant fuzzy bidirectional projection (NWPHFBP) method and its specific application steps to solve MADM problems. The proposed approach can accurately reflect the projection relationship between the alternatives evaluated and ideal solutions by the NWPHF information. Through constructing a reasonable criteria system, we apply the NWPHFBP method to the issue of electric vehicle (EV) power battery recycling mode selection. Finally, we conduct the sensitivity analysis and verify the effectiveness of the proposed method by comparisons with other approaches.

Evaluating Personal Default Risk in P2P Lending Platform: Based on Dual Hesitant Pythagorean Fuzzy TODIM Approach

An extended approach proposed in this paper is to make a more reasonable assessment of personal default risk in peer to peer (P2P) online lending platform, which reduces uncertainty while taking into account the psychological characteristics of lenders to avoid risk. The TODIM (an acronym in Portuguese of interactive and multi-criteria decision making) approach, which can describe the psychological behaviors of decision maker, has been proved to be effective to solve multi-attribute decision making (MADM) problems. The definitions of dual hesitant Pythagorean fuzzy set (DHPFS) and the processes of traditional TODIM approach are firstly introduced in this paper. Then, the TODIM approach is extended to solve the MADM problems with a dual hesitant Pythagorean fuzzy number (DHPFN). Finally, a case study evaluating the personal default risk in P2P online lending is conducted to demonstrate that the proposed approach is applicable to solve MADM problems. In addition, some comparative analyses are performed to compare the dual hesitant Pythagorean fuzzy TODIM method with the other two integrated operators of DHPFS. Through the comparisons, we conclude that the advantage of the proposed method over other methods is that it reduces uncertainty while taking into account the psychological characteristics of lenders to avoid risk. Today’s credit environment is fraught with risks, and the psychological behaviors of decision makers are important factors that cannot be ignored. For these reasons, the dual Pythagorean hesitant fuzzy TODIM method is applicable for evaluating personal default risk.

IMPLEMENTASI METODE SAW DAN WASPAS DENGAN PEMBOBOTAN ROC DALAM SELEKSI PENERIMAAN PESERTA DIDIK BARU (Studi Kasus: Madrasah Tsanawiyah (MTs) Negeri Kisaran Kabupaten Asahan Provinsi Sumatera Utara Tahun Ajaran 2018/2019)

Multi Attribute Decision Making (MADM) is one of the decision-making methods to determine the best alternative from a number of alternatives based on certain criteria. There are several methods that can be used to solve MADM problems including Simple Additive Weighting (SAW) and Weighted Aggregated Sum Product Assesmen (WASPAS). Both methods are applied in the selection of prospective new students. In this study, MTsN Kisaran selected 192 students received from 422 registrans and determined certain criteria to get quality students. The criteria determined are the value of the national exam, the value of the Al-Qur'an test, and the value of the academic potential test. The method applied is SAW and WASPAS with the weighting Rank Order Centroid (ROC). Then a sensitivity analysis is carried out to determine a viable methods selected to obtain optimal results. This research was designed with the help of the Matlab GUI as a computing tool to simplify and accelerate the selection process. Based on the results of the study, the average percentage value of sensitivity for the SAW method was -0.82% while the WASPAS method was -0.87%. With the existence of sensitivity analysis it can be known the most appropriate method for this case is the SAW method. Keywords: Students, SAW, WASPAS, ROC, Sensitivity, GUI Matlab.

A projection-based regret theory method for multi-attribute decision making under interval type-2 fuzzy sets environment

Interval type-2 fuzzy sets (IT2FSs) can provide more flexibility than type-1 fuzzy sets (T1FSs) for depicting uncertain information, and multi-attribute decision making (MADM) problems with interval type-2 fuzzy information have received increasing attention. A new projection-based regret theory method is proposed to solve MADM problems under IT2FSs environments. First, a projection model of IT2FSs is defined that takes both the distance and angle information into consideration. Second, integrating the proposed projection model with regret theory, new utility and regret-rejoice functions are developed, respectively. Finally, a case study is provided to demonstrate the effectiveness of the proposed method. Sensitivity analysis shows the stability of the proposed method, and the ranking order does not change with different parameters. Comparisons are made with existing approaches to illustrate the advantage of the proposed method in reflecting decision makers’ psychological factors.

Comparative analysis using WP and TOPSIS method to find the best mountain for hiking

Mountain activities or outdoor activities located in the mountains is one form of ecotourism that is popular for many people. One type of mountaineering that is often done is mountain climbing (mountain hiking) because of the many mountains scattered almost throughout the Indonesian archipelago. For beginner hikers it is advisable to hiking in groups, as well as adjusting to the experience and ability of climbers in order to anticipate the subjective risks. In this study, the Design of Decision Supporting Approval Approved Mountain Best For Hiking ‘Go-Hiking’ using Web Based Weighted Product method and for Android using TOPSIS method. Weighted Product (WP) and TOPSIS is example of the methods used to solve MADM problems. Multi Attribute Decision Making (MADM) is a method used to find the most optimal alternative of a number of optimal alternatives with certain criteria. The end result of the use of the weighted product and TOPSIS method is to display the best recommendations that can only be made as a consideration in the selection of the mountain.

Novel decision-making approach based on hesitant fuzzy sets and graph theory

Hesitant fuzzy set is a powerful and effective tool to express uncertain information in multi-attribute decision-making (MADM) process, as it permits the membership degree of an element to a set represented by several possible values in [0,1]. In this paper, we develop a new decision-making approach based on graph theory to deal with the MADM problems, in which the decision information is expressed by hesitant fuzzy elements. Meanwhile, we generalize this approach to make it suitable for processing interval-valued hesitant fuzzy and hesitant triangular fuzzy information. Moreover, we utilize the numerical examples concerning the energy project selection and software evaluation to show the detailed implementation procedure and reliability of our method in solving MADM problems under hesitant fuzzy, interval-valued hesitant fuzzy and hesitant triangular fuzzy environment.

Fuzzy [formula omitted]-covering based [formula omitted]-fuzzy rough set models and applications to multi-attribute decision-making

Multi-attribute decision-making (MADM) can be regarded as a process of selecting the optimal one from all alternatives. Traditional MADM problems with fuzzy information are mainly focused on a fundamental tool which is a fuzzy binary relation. However some complicated problems cannot be effectively solved by a fuzzy relation. For this reason, in order to solve these issues, we set forth two decision-making methods that are stated in terms of novel and flexible fuzzy rough set models. For the purpose of defining these models we employ a fuzzy implication operator I and a triangular norm T. With these adaptable tools we design four kinds of fuzzy β-coverings based (I,T)-fuzzy rough set models. The elements that make these models different are the combination of fuzzy β-neighborhoods that intervene in the definitions of the lower (upper) approximations. Then, we discuss the relationships among these given four types of models. Finally, we propose two novel methodologies to solve MADM problems with evaluation of fuzzy information, which rely on these models. Through the analysis of the ranking results of these two methods, we observe that the optimal selected alternative is the same, which means that these two decision-making methods are reasonable. In addition, by comparing the ranking results of these two methods and the existing traditional methods (WA operator and TOPSIS), we observe that our proposed methods can solve the ranking problems that traditional methods cannot solve, which means that our proposed methods are superior to traditional methods.

Covering-based generalized IF rough sets with applications to multi-attribute decision-making

Multi-attribute decision-making (MADM) can be regarded as a process of selecting the optimal one from all objects. Traditional MADM problems with intuitionistic fuzzy (IF) information are mainly focused on an IF binary relation. However, some complicated problems can not be effectively solved by an IF relation. In order to solve these issues, we set forth two novel decision-making methods that are stated in terms of novel and flexible generalized IF rough set models. For defining these models, four types of IF neighborhoods based on an IF implicator I and an IF triangular norm T are firstly proposed. Secondly, by means of four types of IF neighborhoods, four types of coverings-based generalized IF rough set models are proposed. Furthermore, the relationships among the four types of coverings-based generalized IF rough set models and other types of IF rough set models are also discussed. By means of the principle of the IF-TOPSIS methods, MADM with IF information based on covering-based generalized IF rough sets or based on covering-based generalized fuzzy rough sets is put forward. Finally, we solve MADM problems with the evaluation of IF information based on covering-based generalized IF rough set models. By comparative analysis, we find that the results of this method based on covering-based generalized IF rough set models and based on covering-based generalized fuzzy rough set models are highly consistent. In particular, this method based on covering-based generalized IF rough set models is more effective to deal with MADM than that based on covering-based generalized fuzzy rough set models.

Some Interval Neutrosophic Dombi Power Bonferroni Mean Operators and Their Application in Multi–Attribute Decision–Making

The power Bonferroni mean (PBM) operator is a hybrid structure and can take the advantage of a power average (PA) operator, which can reduce the impact of inappropriate data given by the prejudiced decision makers (DMs) and Bonferroni mean (BM) operator, which can take into account the correlation between two attributes. In recent years, many researchers have extended the PBM operator to handle fuzzy information. The Dombi operations of T-conorm (TCN) and T-norm (TN), proposed by Dombi, have the supremacy of outstanding flexibility with general parameters. However, in the existing literature, PBM and the Dombi operations have not been combined for the above advantages for interval-neutrosophic sets (INSs). In this article, we first define some operational laws for interval neutrosophic numbers (INNs) based on Dombi TN and TCN and discuss several desirable properties of these operational rules. Secondly, we extend the PBM operator based on Dombi operations to develop an interval-neutrosophic Dombi PBM (INDPBM) operator, an interval-neutrosophic weighted Dombi PBM (INWDPBM) operator, an interval-neutrosophic Dombi power geometric Bonferroni mean (INDPGBM) operator and an interval-neutrosophic weighted Dombi power geometric Bonferroni mean (INWDPGBM) operator, and discuss several properties of these aggregation operators. Then we develop a multi-attribute decision-making (MADM) method, based on these proposed aggregation operators, to deal with interval neutrosophic (IN) information. Lastly, an illustrative example is provided to show the usefulness and realism of the proposed MADM method. The developed aggregation operators are very practical for solving MADM problems, as it considers the interaction among two input arguments and removes the influence of awkward data in the decision-making process at the same time. The other advantage of the proposed aggregation operators is that they are flexible due to general parameter.