Existing Multiattribute Decision Making Methods Research Articles

Evaluation of the Contaminated Area Using an Integrated Multi-Attribute Decision-Making Method

Air pollution affects public health and the environment, creating great concern in developed and developing countries. In India, there are numerous reasons for air pollution, and festivals like Diwali also contribute to air contamination. Determining the polluted region using several air contaminants is significant and should be analyzed carefully. This study aims to analyze the air quality in Tamil Nadu, India, during the Diwali festival from 2019 to 2021, based on multiple air pollutants. The study models the impact of air pollution as a Multi-Attribute Decision-Making (MADM) problem. It introduces a hybrid approach, namely the Analytical Hierarchy Process-Entropy-VlseKriterijumska Optimizacija I Kompromisno Resenje (AHP-Entropy-VIKOR) model, to analyze and rank the areas based on the quality of air. A combined approach of AHP and entropy is employed to determine the weights of multiple air pollutants. The VIKOR approach ranks the areas and identifies the areas with the worst air quality during the festival. The proposed model is validated by performing the Spearman’s rank correlation with two existing MADM methods: Combinative Distance Based Assessment (CODAS) and Weighted Aggregates Sum Product Assessment (WASPAS). Sensitivity analysis is carried out to assess the effects of the priority weights and the dependency of the pollutants in ranking the regions. The highest air pollution level during the festival was seen in Cellisini Colony (2019), Rayapuram (2020), T. Nagar and Triplicane (2021) in their respective year. The results demonstrate the consistency and efficiency of the proposed approach.

A novel multi-attribute decision making method based on interval-valued fermatean fuzzy bonferroni mean operators

When handling complex uncertainty information for multi-attribute decision-making (MADM) problems, interval-valued Fermatean fuzzy sets (IVFFSs) are a novel and powerful tool with a wide range of prospective applications. However, existing MADM methods based on IVFFS ignore associations between attributes and are vulnerable to extreme values. Thus, this research proposes a novel MADM method based on IVFFSs. First, taking into consideration attribute relationships, we propose interval-valued Fermatean fuzzy Bonferroni mean (IVFFBM) operators and interval-valued Fermatean fuzzy weighted Bonferroni mean (IVFFWBM) operators based on IVFFSs. Further, interval-valued Fermatean fuzzy power Bonferroni mean (IVFFPBM) operator and interval-valued Fermatean fuzzy weighted power Bonferroni mean (IVFFWPBM) operator are suggested considering the impact of extreme values. Secondly, Attribute weights are a key component of MADM. A novel method for determining attribute weights based on fuzzy entropy is developed. Finally, a novel MADM approach is proposed based on the proposed operator and weight determination method. Experimental results on one real-life case demonstrate the superiority and effectiveness of our method.

Multiattribute decision making based on nonlinear programming methodology, the Euclidean distance between IVIFVs, and new score function of IVIFVs

In this paper, we propose a new multiattribute decision making (MADM) method based on the proposed nonlinear programming methodology, the Euclidean distance between interval-valued intuitionistic fuzzy values (IVIFVs), and the proposed score function of IVIFVs. Firstly, a new score function of IVIFVs is proposed to overcome the shortcomings of the existing score functions of IVIFVs. Then, we construct the score matrix based on the proposed score function of IVIFVs and the decision matrix given by the decision maker. Then, a nonlinear programming model is proposed based on the Euclidean distance between IVIFVs and the interval-valued intuitionistic fuzzy weights of the attributes provided by the decision maker. Then, we solve the proposed nonlinear programming model to obtain the optimal weights of the attributes. Then, the weighted score of each alternative is calculated based on the obtained score matrix and the obtained optimal weights of the attributes. Finally, the alternatives are ranked according to the obtained weighted scores of the alternatives. The MADM method proposed in this paper can conquer the shortcomings of the existing MADM methods in the environments of IVIFVs.

Multiattribute decision making based on nonlinear programming methodology, novel score function of interval-valued intuitionistic fuzzy values, and the standard deviations of the score values in the score matrix

In this paper, we propose a new multiattribute decision making (MADM) method using the proposed nonlinear programming (NLP) model, the proposed score function (SCF) of interval-valued intuitionistic fuzzy values (IVIFVs), and the standard deviation of the score values appeared in each column of the constructed score matrix (SX). The proposed SCF of IVIFVs can overcome the shortcomings of the existing SCFs of IVIFVs. Firstly, we construct the SX using the decision matrix given by the decision maker and the proposed SCF of IVIFVs. Then, we construct a NLP model using the obtained SX, the standard deviation of the score values appeared in each column of the SX, the interval-valued intuitionistic fuzzy weights of the attributes, the largest ranges of IVIFVs, and the concept of deviation variables. Then, we solve the NLP model to get the optimal weights of the attributes, respectively. Then, based on the constructed SX and the obtained optimal weights of the attributes, we calculate the weighted score of each alternative. Finally, we rank the alternatives according to the obtained weighted scores. The proposed MADM method can overcome the drawbacks of the existing MADM methods.

Multiattribute decision making method based on nonlinear programming model, cosine similarity measure, and novel score function of interval-valued intuitionistic fuzzy values

In this paper, we propose a new multiattribute decision making (MADM) method based on the proposed score function (SF) of interval-valued intuitionistic fuzzy values (IVIFVs), the cosine similarity measure of IVIFVs, and the proposed nonlinear programming (NLP) model. The proposed SF of IVIFVs overcomes some shortcomings of the existing SFs of IVIFVs. The proposed MADM method overcomes some shortcomings of the existing MADM methods based on IVIFVs. Firstly, we propose a novel SF of IVIFVs to overcome the shortcomings of some existing SFs of IVIFVs. Then, we construct a score matrix based on the proposed score function of IVIFVs and the decision matrix given by the decision maker. Then, we build a NLP model based on the cosine similarity measure of IVIFVs and the interval-valued intuitionistic fuzzy weights of the attributes. Then, we solve the NLP model to obtain the optimal weights (OWs) of the attributes, respectively. Based on the obtained OWs of the attributes and the constructed score matrix, we compute the weighted scores (WSs) of the alternatives, respectively. Finally, we rank the alternatives based on the obtained WSs. The proposed MADM method provides us a very useful approach for MADM in the interval-valued intuitionistic fuzzy context.

Multiattribute decision making based on nonlinear programming methodology, score function of interval-valued intuitionistic fuzzy values, and the dispersion degree of score values

In this paper, we propose a new multiattribute decision making (MADM) method based on the proposed nonlinear programming (NLP) model, the proposed score function (SF) of interval-valued intuitionistic fuzzy values (IVIFVs), and the dispersion degree of the score values appeared in each column of the score matrix (SMX). Firstly, we propose a new SF of IVIFVs to construct the SMX. The proposed SF of IVIFVs can overcome the drawbacks of the existing SFs of IVIFVs. Then, we calculate the dispersion degree of the score values appeared at each column of the SMX. Then, we construct a NLP model to get the optimal weight (OW) of each attribute based on the obtained SMX, the dispersion degree of the score values appeared at each column of the SMX, and the interval-valued intuitionistic fuzzy weights of the attributes given by the decision maker. Then, we calculate the weighted score (WS) of each alternative based on the obtained SMX and the obtained OWs of the attributes. Finally, we get the preference order (PFO) of the alternatives based on the obtained WSs of the alternatives. The proposed MADM method can overcome the drawbacks of some existing MADM methods in an interval-valued intuitionistic fuzzy setting.

Multiattribute decision making based on nonlinear programming model, the Gini coefficient, and novel score function of interval-valued intuitionistic fuzzy values

In this paper, we propose a new multiattribute decision making (MADM) method based on the proposed nonlinear programming (NLP) model, the Gini coefficient, and the proposed score function (SF) of interval-valued intuitionistic fuzzy values (IVIFVs). Firstly, we propose a novel SF of IVIFVs to overcome the shortcomings of the existing SFs of IVIFVs. Then, we construct a score matrix (SMX) based on the proposed SF of IVIFVs and the decision matrix given by the decision maker (DMK). Then, we construct a NLP model based on the constructed SMX, the Gini coefficient, and the interval-valued intuitionistic fuzzy (IVIF) weights of the attributes given by the DMK. After solving the constructed NLP model, we obtain the optimal weight (OW) of each attribute. Then, we compute the weighted score (WS) of each alternative based on the constructed SMX and the obtained OWs of the attributes. Finally, we rank the alternatives based on the obtained WSs of the alternatives. The proposed MADM method can overcome the shortcomings of the existing MADM methods in IVIF environments.

A new multi-attribute decision making approach based on new score function and hybrid weighted score measure in interval-valued Fermatean fuzzy environment.

Interval-valued Fermatean fuzzy sets (IVFFSs) were introduced as a more effective mathematical tool for handling uncertain information in 2021. In this paper, firstly, a novel score function (SCF) is proposed based on IVFFNs that can distinguish between any two IVFFNs. And then, the novel SCF and hybrid weighted score measure were used to construct a new multi-attribute decision-making (MADM) method. Besides, three cases are used to demonstrate that our proposed method can overcome the disadvantages that the existing approaches cannot obtain the preference orderings of alternatives in some circumstances and involves the existence of division by zero error in the decision procedure. Compared with the two existing MADM methods, our proposed approach has the highest recognition index and the lowest error rate of division by zero. Our proposed method provides a better approach to dealing with the MADM problem in the interval-valued Fermatean fuzzy environment.

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.

Multiattribute decision making based on Fermatean hesitant fuzzy sets and modified VIKOR method

In this paper, we develop a novel multiattribute decision making (MADM) approach based on Fermatean hesitant fuzzy sets (FHFSs) and the modified VIKOR method. Firstly, we propose the definition of distance measures of FHFSs and present its properties. Further, taking the effectiveness of FHFSs for dealing with ambiguous and imprecise data in MADM problems, this paper proposes the remoteness index-based Fermatean hesitant fuzzy-VIKOR (FHF-VIKOR) MADM method. The generalized distance measure for FHFSs is subsequently employed to establish the notions of remoteness indices with the positive ideal and the negative ideal remoteness indices. The objective weighting procedure is developed using the maximum deviation principle and the generalized distance measure to obtain the attributes’ weights. Some examples are discussed to reveal the performance of the proposed MADM method. Finally, the advantages of the proposed MADM method in terms of the robustness and the flexibility are shown by a comparative study. The proposed MADM method based on FHFSs and the modified VIKOR method can overcome the drawbacks of the existing MADM methods.

Multiattribute decision making based on nonlinear programming methodology and novel score function of interval-valued intuitionistic fuzzy values

In this paper, we propose a novel multiattribute decision making (MADM) method using the nonlinear programming (NLP) methodology and the proposed score function of interval-valued intuitionistic fuzzy values (IVIFVs). Firstly, we propose a new score function of IVIFVs to conquer the drawbacks of the existing score functions of IVIFVs. Then, we construct the converted matrix based on the proposed score function of IVIFVs by calculating the score value of each IVIFV in the decision matrix (DM) offered by the decision maker (DMK). Then, we construct the NLP model via the obtained converted matrix and the interval-valued intuitionistic fuzzy (IVIF) weight of each attribute given by the DMK. Then, we solve the NLP model to obtain the optimal weight for each attribute. Then, based on the obtained converted matrix and the obtained optimal weight of each attribute, we calculate the weighted score of each alternative. Finally, the alternatives are ranked on the basis of the obtained weighted scores of the alternatives. The larger the weighted score of an alternative, the better the preference order of the alternative. The proposed MADM method can overcome the drawbacks of the existing MADM methods. It offers us a very useful approach for MADM in IVIF settings.

Multiattribute decision making based on novel score function and the power operator of interval-valued intuitionistic fuzzy values

In this paper, we propose a novel multiattribute decision making (MADM) method on the basis of the proposed novel score function (SF) of interval-valued intuitionistic fuzzy values (IVIFVs) and the power operator of IVIFVs. The proposed SF of IVIFVs can conquer the shortcomings of the existing SFs of IVIFVs. Based on the proposed SF of IVIFVs and the power operator of IVIFVs, we propose a new MADM method in the interval-valued intuitionistic fuzzy context. The proposed MADM method can conquer the shortcoming of the existing MADM methods. It provides us a very useful approach for MADM in interval-valued intuitionistic fuzzy environments.

An optimization viewpoint on evaluation-based interval-valued multi-attribute three-way decision model

Multi-attribute decision-making (MADM) aims to rank alternatives based on their attributes and evaluation information, which provides decision support for decision-makers. Most existing MADM methods can only obtain ranking results, decision-makers usually need to subjectively choose priority alternatives to make a decision based on the preset evaluation level and ranking results, which does not meet the requirements of complex decision situations and uncertain information processing. A method is urgently needed, which can objectively produce classification results and automatically provide priority objects for decisions. Three-way decisions (3WDs) offer an effective research technique to solve decision-making problems under uncertainty and risk by objectively dividing a universal set into three pairwise disjoint parts: acceptance, non-commitment and rejection, and implementing the corresponding strategy for each part. Considering that it is difficult to accurately determine the exact value of attributes in some cases, interval numbers can be a useful concept to flexibly describe uncertain information and satisfy the decision-maker’s cognition. Therefore, under an interval-valued MADM environment, this paper proposes an evaluation-based interval-valued multi-attribute three-way decision (IVMA3WD) model from an optimization viewpoint. The model achieves an effective fusion of 3WDs and MADM problems, and further expands evaluation-based 3WD models on the totally ordered set. Specifically speaking, in order to depict uncertain information in decision-making, interval numbers are used to describe the evaluation information included in the multi-attribute evaluation matrix. Then, considering a general case that there are no decision attributes in the multi-attribute evaluation matrix, we determine the evaluation function by use of the idea of the interval-valued TOPSIS method. In addition, unlike the fixed-valued loss functions in the majority of 3WD models, the relative loss function in this article is not provided straightly but computed by attribute evaluation values expressed by interval numbers. Furthermore, based on an optimization viewpoint, we construct two optimization models and attempt to find the optimal solution to obtain the threshold pair. A housing market investment decision problem is utilized as an illustrative example to find out the applicability of our built IVMA3WD model. In the end, we adopt a sensitivity analysis and a comparative analysis to demonstrate our proposed model’s characteristics and advantages.

Multiattribute decision making based on new score function of interval-valued intuitionistic fuzzy values and normalized score matrices

In this paper, we propose a novel multiattribute decision making (MADM) method on the basis of the proposed score function of interval-valued intuitionistic fuzzy values (IVIFVs) and normalized score matrices. Firstly, it calculates the score value of each IVIFV in the decision matrix (DM) based on the proposed score function of IVIFVs to construct the score matrix. Then, it constructs the normalized score matrix based on the obtained score matrix. Then, it computes the optimal weight of the interval-valued intuitionistic fuzzy (IVIF) weight of each attribute. Then, based on the obtained normalized score matrix and the obtained optimal weight of the IVIF weight of each attribute, it constructs the weighted normalized DM. Then, based on the obtained weighted normalized DM, it calculates the weighted score value of each alternative. Finally, it ranks the alternatives based on the weighted score values of the alternatives. The larger the weighted score value of an alternative, the better the preference order (PO) of the alternative. The proposed MADM method overcomes the drawbacks of the existing MADM methods. The proposed MADM method provides a very useful way to us for dealing with MADM problems in IVIF environments.

Multiattribute decision making using novel score function of interval-valued intuitionistic fuzzy values and the means and the variances of score matrices

In this paper, we propose a new multiattribute decision making (MADM) method based on the proposed score function of interval-valued intuitionistic fuzzy values (IVIFVs) and the means and the variances of score matrices, where the proposed score function can conquer the shortcomings of the existing score functions. Firstly, it computes the score value of each IVIFV in the decision matrix based on the proposed score function to construct the score matrix. Then, it calculates the mean and the variance of the obtained score matrix. Then, it builds the standard score matrix based on the obtained score matrix. Then, it converts the interval-valued intuitionistic fuzzy (IVIF) weight of each attribute into a crisp weight based on the proposed score function. Finally, based on the obtained standard score matrix and the obtained converted IVIF weights, it calculates the weighted score of each alternative to rank the alternatives. The larger the weighted score of an alternative, the better the preference order (PO) of the alternative. The proposed MADM method can conquer the shortcomings of the existing MADM methods. It offers us a very useful way for MADM in IVIF environments.

Multi-attribute decision making method using advanced Pythagorean fuzzy weighted geometric operator and their applications for real estate company selection

In this paper, a novel multi-attribute decision-making method using Advanced Pythagorean fuzzy weighted geometric operator in a Pythagorean fuzzy environment is developed. Pythagorean fuzzy aggregation operators have drawbacks that they give indeterminate results in some special cases when membership value or non-membership value gets 0 value or 1 value and the weight vector is of type (1,0)T or (0,1)T. The Advanced Pythagorean fuzzy geometric operator, the proposed operator can overcome the drawbacks. In some situations, for example, where the sum of squares of membership degree and non-membership degree gets unit value of a Pythagorean fuzzy number, multi-attribute decision making (MADM) methods using some existing aggregation operators give unreasonable ranking orders (ROs) of alternatives or can't discriminate the ROs of alternatives. But the present MADM method can get over the drawbacks of the existing MADM methods. The present MADM method is devoted to eliminate the drawbacks of the existing MADM methods and to select the best real estate company for investment.

Multiattribute decision making based on the improved intuitionistic fuzzy Einstein weighted averaging operator of intuitionistic fuzzy values

This paper proposes the improved intuitionistic fuzzy Einstein weighted averaging (IIFEWA) operator of intuitionistic fuzzy values (IFVs). The proposed IIFEWA operator can overcome the drawbacks of the intuitionistic fuzzy Einstein improved weighted averaging (IFEIWA) operator, the intuitionistic fuzzy Hamacher improved weighted averaging (IFHIWA) operator, the intuitionistic fuzzy Hamacher weighted averaging (IFHWA) operator, the intuitionistic fuzzy Einstein weighted averaging (IFWAωε) operator, the intuitionistic fuzzy weighted averaging (IFWA) operator and the intuitionistic fuzzy Hamacher interactive ordered weighted averaging (IFHIOWA) operator of IFVs, where they have the drawbacks that (1) the membership grades and the non-membership grades of their obtained aggregating IFVs are indeterminated in some situations and (2) if there is only one IFV whose membership grade is equal to 1, then the membership grade of the aggregated IFV of n IFVs becomes 1; if there is only one IFV whose non-membership grade is equal to 0, then the non-membership grade of the aggregated IFV of n IFVs becomes 0. Based on the proposed IIFEWA operator, we propose a new multiattribute decision making (MADM) method. The proposed MADM method overcomes the drawbacks of the existing MADM methods, where they cannot distinguish the ranking orders of alternatives in some situations.

A picture fuzzy similarity measure based on direct operations and novel multi-attribute decision-making method

Picture fuzzy set (PFS) is a direct generalization of the fuzzy sets (FSs) and intuitionistic fuzzy sets (IFSs) and is quite powerful in modelling the situations that involve more answers of the type yes, no, abstain, and refuse. In this study, we introduce a novel picture fuzzy (PF) similarity measure on the basis of direct operation on the function of membership, the function of non-membership, the function of neutrality, the function of refusal, and the upper bound of the function of membership of two PFSs instead on the basis of distance measure or the association between the functions of membership, non-membership, and neutrality. The comparison of the proposed PF similarity measure with the existing PF similarity measures reveals that it does not give unreasonable results and also overcomes the drawbacks of the existing PF similarity measures. The application of the proposed measure in pattern recognition is also discussed. Moreover, we also introduce a new multi-attribute decision-making (MADM) method using the proposed PF similarity measure that overcomes a major drawback of the technique for order preference by similarity to ideal solution (TOPSIS). Finally, we contrast the performance of the proposed MADM method with several existing MADM methods in the PF environment.

Multiattribute decision making based on interval-valued intuitionistic fuzzy values, score function of connection numbers, and the set pair analysis theory

This paper proposes a new multiattribute decision making (MADM) method based on the proposed score function of connection numbers (CNs) and the set pair analysis (SPA) theory in the interval-valued intuitionist fuzzy (IVIF) context. Firstly, we develop a score function for ranking CNs. The various notable characteristics of the proposed score function of CNs are also presented. Then, we propose a new MADM method based on interval-valued intuitionist fuzzy values (IVIFVs), the proposed score function of CNs and the SPA theory, where we convert IVIFVs into CNs and the optimal weights of attributes are calculated from the IVIF weights of attributes. Finally, the proposed MADM method is applied for MADM in the IVIF context, where the preference orders (POs) of the alternatives obtained by the proposed MADM method are compared with the ones obtained by the existing MADM methods. The proposed MADM method can overcome the drawbacks of the existing MADM methods.

Multiattribute decision making using probability density functions and transformed decision matrices in interval-valued intuitionistic fuzzy environments

In this paper, we propose a new method for multiattribute decision making (MADM) using probability density functions and the transformed decision matrix (TDMx) of the decision matrix (DMx) offered by the decision maker (DM) in interval-valued intuitionistic fuzzy (IVIF) environments. First, it gets the TDMx of the DMx given by the DM. Then, it computes the average value of the interval-valued intuitionistic fuzzy values (IVIFVs) appearing at each column of the TDMx. Then, it calculates the variance of each IVIFV in the TDMx. Then, it computes the standard deviation (SD) of the IVIFVs appearing at each column of the TDMx. Then, based on the obtained TDMx, the obtained average value of the IVIFVs appearing at each column of the TDMx, and the obtained SD of the IVIFVs appearing at each column of the TDMx, it gets the z-score DMx. Then, each attribute’s IVIF weight is transformed into a crisp weight between zero and one. Finally, each alternative’s weighted score is calculated using the z-score DMx and each attribute’s transformed crisp weight. The larger the weighted score of an alternative, the better the preference order (PO) of the alternative. It can overcome the shortcomings of the existing MADM methods.