Proposed Multiattribute Decision Making Method Research Articles

A Multi-attribute Decision-making Method for Interval Rough Number Information System Considering Distribution Types

This paper proposes a novel multi-attribute decision-making (MADM) method for interval rough numbers (IRNs) considering different distribution types, namely uniform, exponential, and normal distributions. Upper and lower approximate interval dominance degrees are defined and aggregated using dynamic weights to obtain pairwise comparisons of IRNs. The properties of dominance are verified, and an attribute weight determination method based on the dominance balance degree is introduced. The proposed MADM method is data-driven and does not rely on the subjective preferences of decision-makers. Case analysis demonstrates the effectiveness and rationality of the proposed method, revealing that the distribution type of IRNs significantly impacts decision results, potentially leading to reversed ranking outcomes. The proposed method offers a comprehensive framework for handling MADM problems with IRNs under different distributions.

Longitudinal vibration control strategy for long-span suspension bridges under operational and extreme excitations using eddy current dampers

A full-floating or a semi-floating system is conventionally employed in long-span suspension bridges (LSSBs) to reduce the excessive internal forces of main girders when subjected to various ambient loads/effects. However, such a system may induce appreciable back-and-forth longitudinal displacements of the main girder and result in the deterioration of auxiliary structural components (e.g., expansion joints). In light of this, this paper presents a vibration control strategy for mitigating the longitudinal girder vibrations of LSSBs under primary operational loads (i.e., wind and traffic) and extreme seismic effects using eddy current dampers (ECDs). A general computational framework of the seismic-wind-traffic-bridge system is first developed, whereby the longitudinal girder vibration characteristics of a prototype LSSB with and without ECD installations under various loading scenarios are investigated. Particularly, a novel multi-attribute decision-making (MADM) method is introduced to address a common challenge in developing optimal vibration control designs, i.e., the optimal vibration control design for one objective might adversely affect the others, which is especially critical from a life-cycle bridge management perspective. By using the MADM, typical bridge performance indices under various loading scenarios can be rationally involved in the associated optimization. The results show that different excitations can induce longitudinal girder vibrations with different dominant frequencies, which can be effectively mitigated by the ECD. However, for different bridge performance indices and different loading scenarios, the optimal ECD parameters may vary significantly. The proposed MADM method can help develop a balanced vibration control design that can ensure excellent bridge safety and serviceability simultaneously.

Fermatean fuzzy Archimedean Heronian Mean-Based Model for estimating sustainable urban transport solutions

Public transportation frameworks assume a critical role in the metropolitan region, especially in huge urban communities, where they offer a feasible answer for easing gridlock, moderating commotion contamination, and diminishing CO2 discharges. This paper presents some novel Fermatean fuzzy Heronian mean operators based on Archimedean t-norms, specifically the generalized Fermatean fuzzy Archimedean Heronian mean (GFFAHM) and the Fermatean fuzzy Archimedean geometric Heronian mean (FFAGHM). The study investigates different unique instances of these operators while exploring their essential properties. Besides, a powerful multiattribute decision-making (MADM) method is developed using the proposed operators. This approach offers a key asset for handling complex decision-making problems. Overcoming the capabilities of conventional BM operators, the GFFAHM and FFAGHM operators effectively minimize the potential redundancy in interrelationships during the decision-making process. The inclusion of the flexible parameters ρ and ϕ, which have a big impact on the decision-making process’ outcomes, increases the adaptability and resilience of the Archimedean t-based operators. To depict the feasibility of the proposed MADM method, a thorough quantitative model is introduced, outlining its useful execution. Through an exhaustive case study, the predominance of the proposed approach over existing strategies is experimentally established. Remarkably, the study uncovers that reducing fares is the most compelling factor in expanding the public transport framework, subsequently advancing sustainable urban transport. This study’s findings provide useful insights into decision-making processes and practical implications for policymakers, allowing them to make informed and impactful changes to the public transportation system. The proposed MADM method can play a vital role in upgrading the public transport framework, making way for remarkable strategy interventions in urban transport sustainability.

Hesitant Fermatean fuzzy Bonferroni mean operators for multi-attribute decision-making

Hesitant Fermatean fuzzy sets (HFFS) can characterize the membership degree (MD) and non-membership degree (NMD) of hesitant fuzzy elements in a broader range, which offers superior fuzzy data processing capabilities for addressing complex uncertainty issues. In this research, first, we present the definition of the hesitant Fermatean fuzzy Bonferroni mean operator (HFFBM). Further, with the basic operations of HFFS in Einstein t-norms, the definition and derivation process of the hesitant Fermatean fuzzy Einstein Bonferroni mean operator (HFFEBM) are given. In addition, considering how weights affect decision-making outcomes, the hesitant Fermatean fuzzy weighted Bonferroni mean (HFFWBM) operator and the hesitant Fermatean fuzzy Einstein weighted Bonferroni mean operator (HFFEWBM) are developed. Then, the properties of the operators are discussed. Based on HFFWBM and HFFEWBM operator, a new multi-attribute decision-making (MADM) approach is provided. Finally, we apply the proposed decision-making approach to the case of a depression diagnostic evaluation for three depressed patients. The three patients' diagnosis results confirmed the proposed method's validity and rationality. Through a series of comparative experiments and analyses, the proposed MADM method is an efficient solution for decision-making issues in the hesitant Fermatean fuzzy environment.

Interval type-2 trapezoidal fuzzy multi-attribute decision-making method and its application to the corporate investment selection

Interval type-2 trapezoidal fuzzy (IT2TrF) number is a powerful tool to depict fuzzy information. Information measures methods have received more and more attention in recent years as they play an important role in decision-making theory. A new multi-attribute decision-making (MADM) method supported by IT2TrF information measures is investigated in this paper under the IT2TrF information environment. Firstly, three axiomatic definitions of IT2TrF information measures are introduced, which include information entropy, similarity measure and cross-entropy. Secondly, with the help of the exponential function, we formulate some information measure formulas, which are followed by the proofs that the exponential entropy, exponential similarity measure and exponential cross-entropy fit the three axiomatic definitions. Subsequently, a novel IT2TrF MADM method is designed, in which the IT2TrF exponential entropy and cross-entropy are utilized to generate the attribute weights, the IT2TrF exponential similarity measure is employed to obtain the closeness degree of the ideal solution and derive the most satisfying solution. Lastly, we provide a numerical example of corporate investment to demonstrate the applicability and feasibility of the proposed MADM method. The robustness and merits of the developed MADM method are highlighted by the comparative analysis.

RETRACTED: 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.

RETRACTED: 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.

RETRACTED: 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.

RETRACTED: 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.

Supplier Evaluation Considering Green Production Based on Probabilistic Linguistic Information

The evaluation of manufacturing component suppliers is focused on economic indicators, with insufficient emphasis on green indicators and no consideration of the correlation between indicators. Firstly, indicators related to green production are incorporated into the supplier evaluation system. Then, for the problem that attributes in decision making can be divided into different categories and there are interrelationships between attributes of the same category, a multi-attribute decision-making (MADM) method based on the partitioned Maclaurin symmetric mean operator (PMSM) is proposed. Finally, the proposed MADM method was applied to the evaluation of component suppliers considering green production. Comparing popular decision methods with the newly proposed method for validation, it was demonstrated that the proposed multi-attribute decision method is highly flexible and versatile. Furthermore, the newly proposed aggregation operator can not only handle the correlation between multiple attributes, but also be converted to other general aggregation operators through parameter adjustment.

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.

Bipolar fuzzy metric spaces with application

The concept of a bipolar metric space is presented in this article. In bipolar fuzzy metric space, the notions of continuous t-norms and bipolar continuous symmetry t_s-conorms employs important role. Requirements in metric space, triangular norms are used to extrapolate with the probability density function of triangle inequality. Dual processes of triangular norms are known as triangular conorms. Continuous t-norms and continuous symmetry t_s-conorms are used to define bipolar metric space in this paper. Besides, a number of topological and functional properties of the bipolar metric space have been studied. Afterwards, Baire Category and Uniform Convergence Theorems for bipolar metric spaces are presented. After that, an application on determining the appropriate type of vaccine in the treatment process of COVID-19 is given using similarity measure between bipolar fuzzy metric spaces. For vaccine selection and supply chain management, an advanced multi-attribute decision-making (MADM) algorithm is being developed. Finally, the validity of the proposed MADM method for selecting the best proper form of vaccine is also established.

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.

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.

A novel dynamic credit risk evaluation method using data envelopment analysis with common weights and combination of multi-attribute decision-making methods

Credit risk evaluation is always the most important factor in determining Customers' credit status in financial institutions. Multi-Attribute Decision-Making (MADM) methods have been widely used in this field. But most of the studies neglect the undeniable impact of time and changes of the credit assessment criteria, their importance and evaluation data over time. On the other hand, developed Dynamic MADM (DMADM) methods often used subjective weighting methods and then applied some aggregation operators to rank alternatives. This paper proposes a new combination of Data Envelopment Analysis (DEA) as a powerful objective weighting method with DMADM as a novel dynamic decision-making method for credit performance evaluation. For this aim, the credit performance criteria were extracted using literature review and experts’ views. Criteria weights were calculated with dynamic DEA common set of weights approach. Then, the applicants are prioritized using five Grey MADM methods (including SAW-G, VIKOR-G, TOPSIS-G, ARAS-G and COPRAS-G). Finally, a new method called Correlation Coefficient and Standard Deviation (CCSD) was used to determine the final aggregated rank. This novel method is applied in order to credit ratings of the clients in the Beekeeping Industry Development Funding Institute IRAN The results indicate that the proposed MADM method, while eliminating the limitations of previous methods, has been able to maintain robustness. Also, the results are highly correlated with the results of previous methods.

An innovative picture fuzzy distance measure 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). The concept of PFS is suitable to model the situations that involve more answers of the type yes, no, abstain, and refuse. In this study, we introduce a novel picture fuzzy (PF) distance measure on the basis of direct operation on the functions of membership, non-membership, neutrality, refusal, and the upper bound of the function of membership of two PFSs. We contrast the proposed PF distance measure with the existing PF distance measures and discuss the advantages in the pattern classification problems. The application of fuzzy and non-standard fuzzy models in the real data is very challenging as real data is always found in crisp form. Here, we also derive some conversion formulae to apply proposed method in the real data set. Moreover, we introduce a new multi-attribute decision-making (MADM) method using the proposed PF distance measure. In addition, we justify necessity of the newly proposed MADM method using appropriate counterintuitive examples. Finally, we contrast the performance of the proposed MADM method with the classical MADM methods in the PF environment.