Multiple Attribute Decision Making Problems Research Articles

Pythagorean fuzzy Muirhead mean operators in multiple attribute decision making for evaluating of emerging technology commercialization

In today’s world, with the advancement of technology, several emerging technologies are coming. Faced with massive emerging technologies which are the component of the technology pool, how to identify the commercial potential of emerging technologies in theory and practice is an important problem. The scientific approach to the selection of these emerging technologies is one of the main objectives of the research. In this paper, we extend Muirhead mean (MM) operator and dual MM (DMM) operator to process the Pythagorean fuzzy numbers (PFNs) and then to solve the multiple attribute decision making (MADM) problems. Firstly, we develop some Pythagorean fuzzy Muirhead mean operators by extending MM and DMM operators to Pythagorean fuzzy information. Then, we prove some properties and discuss some special cases with respect to the parameter vector. Moreover, we present some new methods to deal with MADM problems with the PFNs based on the proposed MM and DMM operators. Finally, we verify the validity and reliability of our methods by using an application example for potential evaluation of emerging technology commercialization, and analyze the advantages of our methods by comparing with other existing methods.

Dual Hesitant Pythagorean Fuzzy Hamy Mean Operators in Multiple Attribute Decision Making

To fuse the information in dual-hesitant Pythagorean fuzzy sets (DHPFSs) more effectively, in this paper, some dual hesitant Pythagorean fuzzy Hamy mean (DHPFHM) operators, which can consider the relationships between being fused arguments, are defined and studied. Afterward, the defined aggregation operators are used to multiple attribute decision-making (MADM) with dual-hesitant Pythagorean fuzzy elements (DHPFEs), and the MADM decision-making model is developed. In accordance with the defined operators and the built model, the dual-hesitant Pythagorean fuzzy weighted Hamy mean (DHPFWHM) operator and the dual-hesitant Pythagorean fuzzy weighted dual Hamy mean (DHPFWDHM) operator are applied to deal with green supplier selection in supply chain management, and the availability and superiority of the proposed operators are analyzed by comparing with some existing approaches. The method presented in this paper can effectually solve the MADM problems, which the decision-making information is expressed by DHPFEs and the attributes are interactive.

Methods for MADM with Picture Fuzzy Muirhead Mean Operators and Their Application for Evaluating the Financial Investment Risk

In this article, we study multiple attribute decision-making (MADM) problems with picture fuzzy numbers (PFNs) information. Afterwards, we adopt a Muirhead mean (MM) operator, a weighted MM (WMM) operator, a dual MM (DMM) operator, and a weighted DMM (WDMM) operator to define some picture fuzzy aggregation operators, including the picture fuzzy MM (PFMM) operator, the picture fuzzy WMM (PFWMM) operator, the picture fuzzy DMM (PFDMM) operator, and the picture fuzzy WDMM (PFWDMM) operator. Of course, the precious merits of these defined operators are investigated. Moreover, we have adopted the PFWMM and PFWDMM operators to build a decision-making model to handle picture fuzzy MADM problems. In the end, we take a concrete instance of appraising a financial investment risk to demonstrate our defined model and to verify its accuracy and scientific merit.

An Entropy-Based Knowledge Measure for Atanassov's Intuitionistic Fuzzy Sets and Its Application to Multiple Attribute Decision Making.

As the complementary concept of intuitionistic fuzzy entropy, the knowledge measure of Atanassov’s intuitionistic fuzzy sets (AIFSs) has attracted more attention and is still an open topic. The amount of knowledge is important to evaluate intuitionistic fuzzy information. An entropy-based knowledge measure for AIFSs is defined in this paper to quantify the knowledge amount conveyed by AIFSs. An intuitive analysis on the properties of the knowledge amount in AIFSs is put forward to facilitate the introduction of axiomatic definition of the knowledge measure. Then we propose a new knowledge measure based on the entropy-based divergence measure with respect for the difference between the membership degree, the non-membership degree, and the hesitancy degree. The properties of the new knowledge measure are investigated in a mathematical viewpoint. Several examples are applied to illustrate the performance of the new knowledge measure. Comparison with several existing entropy and knowledge measures indicates that the proposed knowledge has a greater ability in discriminating different AIFSs and it is robust in quantifying the knowledge amount of different AIFSs. Lastly, the new knowledge measure is applied to the problem of multiple attribute decision making (MADM) in an intuitionistic fuzzy environment. Two models are presented to determine attribute weights in the cases that information on attribute weights is partially known and completely unknown. After obtaining attribute weights, we develop a new method to solve intuitionistic fuzzy MADM problems. An example is employed to show the effectiveness of the new MADM method.

Fuzzy Attribute Expansion Method for Multiple Attribute Decision-Making with Partial Attribute Values and Weights Unknown and Its Applications

In the real world, there commonly exists types of multiple attribute decision-making (MADM) problems with partial attribute values and weights totally unknown. Symmetry among some attribute information that is already known and unknown, and symmetry between the pure attribute set and fuzzy attribute membership set can be a considerable way to solve this type of MADM problem. In this paper, a fuzzy attribute expansion method is proposed to solve this type of problem based on two key techniques: the spline interpolation technique and the attribute weight reconfiguration technique, which are respectively used for the determination of attribute values and the reconfiguration of attribute weights. The spline interpolation technique to expand attribute values can enhance the performance of some regression methods and clustering methods by the comparisons between the results of these methods dealing with practical cases with and without the application of the technique, which further illustrates the effectiveness of this technique. For MADM problems with partial attribute values and weights totally unknown, compared with traditional fuzzy comprehensive evaluation (FCE), FCE with the application of fuzzy attribute expansion method can obtain results more similar with the ones when all attribute values and weights are known, which is proved by the practical power quality evaluation example.

Multiple Attribute Decision-Making with Dual Hesitant Pythagorean Fuzzy Information

Due to the uncertainty and complexity of socioeconomic environments and cognitive diversity of decision makers, the cognitive information over alternatives provided by decision makers is usually uncertain and fuzzy. Dual hesitant Pythagorean fuzzy sets (DHPFSs) provide a useful tool to depict the uncertain and fuzzy cognitions of the decision makers over attributes. To effectively handle such common cases, in this paper, some Bonferroni mean (BM) operators under DHPFS environment are proposed and some methods for multiple attribute decision-making (MADM) problems based on the BM operators with dual Pythagorean hesitant fuzzy numbers (DHPFNs) are investigated. Firstly, some new BM operators to aggregate dual Pythagorean hesitant fuzzy cognitive information are developed, which consider the interrelationship of DHPFNs, and can generate more accurate results than the existing dual Pythagorean hesitant fuzzy aggregation operators. Then, the developed aggregation operator is applied to MADM with DHPFNs and two MADM methods are designed, which can be applied to different decision-making situations. Based on the proposed operators and built models, two methods are developed to solve the MADM problems with DHPFNs and the validity and advantages of the proposed method are analyzed by comparison with some existing approaches. The methods proposed in this paper can effectively handle the MADM problems in which the attribute information is expressed by DHPFNs, the attributes’ weights are completely known, and the attributes are interactive.

Methods for Multiple Attribute Decision Making with Interval-Valued Pythagorean Fuzzy Information

Interval-valued Pythagorean fuzzy numbers (IVPFNs) can easily describe the incomplete and indeterminate information by degrees of membership and non-membership, and the Hamy mean (HM) operator and dual HM (DHM) operators are a good tool for dealing with multiple attribute decision making (MADM) problems because it can capture the interrelationship among the multi-input arguments. Motivated by the studies regarding the HM operator and dual HM operator, we expand the HM operator and dual HM (DMM) operator to process the interval-valued Pythagorean fuzzy numbers (IVPFNs) and then to solve the MADM problems. Firstly, we propose some HM and DHM operators with IVPFNs. Moreover, we present some new methods to solve MADM problems with the IVPFNs. Finally, an applicable example is given.

A Novel Fuzzy Decision-Making Method Using Entropy Weights-Based Correlation Coefficients Under Intuitionistic Fuzzy Environment

In this communication, a new two parametric intuitionistic fuzzy entropy has been introduced and validated. Some of the properties of the proposed measure are also discussed. In addition to this, a new multiple attribute decision-making (MADM) method based on weighted correlation coefficients and the proposed IF entropy is introduced. The necessity of proposed MADM method has been reasonably established. The method is effectively explained with the help of two numerical examples, and the performance is genuinely compared with some existing MADM methods in the literature. Attribute weights play an important role in the solution of MADM problem. In this paper, two methods of obtaining attributes weights are discussed.

Evidential reasoning approach with multiple kinds of attributes and entropy-based weight assignment

Multiple attribute decision making (MADM) problems often consists of quantitative and qualitative attributes which can be assessed by numerical values and subjective judgments. Subjective judgments can be evaluated by linguistic variables, and both numerical values and subjective judgments can be accurate or uncertain. The evidential reasoning (ER) approach provides a process for dealing with MADM problems of both a quantitative and qualitative nature under uncertainty. The existing ER approach considers both benefit and cost attributes in the evidence combination process. In this paper, deviated interval and fixed interval attributes are introduced into ER based MADM approach and the frames of discernment for representing these two kinds of attributes are given. The transformation rules from the assessment values of deviated interval attributes to belief degrees in the ER structure are then studied. An ave-entropy based weight assignment method considering the risk preference of decision maker is also shown to deal with uncertain assessment situation, such as belief distribution with qualitative attribute and uncertain utility function. Some programming models to generate interval weights and utilities are constructed. The rationality and efficiency of the methods in supporting MADM problems are discussed. Two case studies are provided to demonstrate the applicability and validity of the proposed approaches and the potential in supporting MADM under uncertainty.

Finding Missing Links in Complex Networks: A Multiple-Attribute Decision-Making Method

Link prediction, which aims to forecast potential or missing links in a complex network based on currently observed information, has drawn growing attention from researchers. To date, a host of similarity-based methods have been put forward. Usually, one method harbors the idea that one similarity measure is applicable to various networks, and thus has performance fluctuation on different networks. In this paper, we propose a novel method to solve this issue by regarding link prediction as a multiple-attribute decision-making (MADM) problem. In the proposed method, we consider RA, LP, and CAR indices as the multiattribute for node pairs. The technique for order performance by similarity to ideal solution (TOPSIS) is adopted to aggregate the multiattribute and rank node pairs. The proposed method is not limited to only one similarity measure, but takes separate measures into account, since different networks may have different topological structures. Experimental results on 10 real-world networks manifest that the proposed method is superior in comparison to state-of-the-art methods.

Symmetry Measures of Simplified Neutrosophic Sets for Multiple Attribute Decision-Making Problems

A simplified neutrosophic set (containing interval and single-valued neutrosophic sets) can be used for the expression and application in indeterminate decision-making problems because three elements in the simplified neutrosophic set (including interval and single valued neutrosophic sets)are characterized by its truth, falsity, and indeterminacy degrees.

Multiple-attribute decision-making method based on the correlation coefficient between dual hesitant fuzzy linguistic term sets

Hesitant fuzzy linguistic term sets (HFLTS) and dual hesitant fuzzy sets (DHFS) are two important branches of fuzzy mathematics, both of which have been widely applied in multiple-attribute decision-making (MADM) problems under uncertain environments. To humanize the decision-making process, the former deals with hesitant fuzzy linguistic terms in line with people’s common sense, and to reflect the nature of people’s hesitancy, the latter deals with both the membership and nonmembership hesitancy functions of fuzzy sets (FS). However, as the decision-making environment is increasingly complex, the characteristics of these two sets need to be combined to more precisely represent the fuzzy linguistic information. Therefore, this paper proposes a new extension of the HFLTS concept, i.e., dual hesitant fuzzy linguistic term set (DHFLTS), to highlight the importance of the nonmembership degree for HFLTSs. Some properties for the DHFLTS are given. Motivated by information energy, the information energy for DHFLTS and the correlation coefficient between DHFLTSs as well as the weighted correlation coefficient are defined. Finally, a supplier selection problem is given to demonstrate the feasibility and superiority of this method.

An intuitionistic fuzzy information measure of order- $$(\alpha , \beta )$$ ( α , β ) with a new approach in supplier selection problems using an extended VIKOR method

In this communication, a new two parametric fuzzy information measure of order- $$(\alpha , \beta )$$ is proposed in the settings of intuitionistic fuzzy set theory. Besides the validation of proposed measure, some of its major properties are also studied. Attributes weights play an important role in the solution of a MADM problem. Two methods of determining the attributes weights are discussed. Considering the importance of subjective and objective weights, a new multiple attribute decision-making (MADM) method based on the concept of VIsekriterijumska optimizacija i KOmpromisno Resenje (VIKOR) is introduced. The proposed MADM method is suitably explained with the help of two illustrative examples.

A Novel Method for Determining the Attribute Weights in the Multiple Attribute Decision-Making with Neutrosophic Information through Maximizing the Generalized Single-Valued Neutrosophic Deviation

The purpose of this paper is to investigate the weights determination in the multiple attribute decision-making (MADM) with the single valued neutrosophic information. We first introduce a generalized single-valued neutrosophic deviation measure for a group of single valued neutrosophic sets (SVNSs), and then present a novel and simple nonlinear optimization model to determine the attribute weights by maximizing the total deviation of all attribute values, whether the attribute weights are partly known or completely unknown. Compared with the existing method based on the deviation measure, the presented approach does not normalize the optimal solution and is easier to integrate the subjective and objective information about attribute weights in the neutrosophic MADM problems. Moreover, the proposed nonlinear optimization model is solved to obtain an exact and straightforward formula for determining the attribute weights if the attribute weights are completely unknown. After the weights are obtained, the neutrosophic information of each alternative is aggregated by using the single valued neutrosophic weighted average (SVNWA) operator. In what follows, all alternatives are ranked and the most preferred one(s) is easily selected according to the score function and accuracy function. Finally, an example in literature is examined to verify the effectiveness and application of the developed approach. The example is also used to demonstrate the rationality for overcoming some drawbacks of the existing approach according to the maximizing deviation method.

Using Two-layer Minimax Optimization and DEA to Determine Attribute Weights

This study aims to explore a novel method for determining attribute weights, which is a key issue in constructing and analyzing multiple-attribute decision-making (MADM) problems. To this end, a hybrid approach combining the data envelopment analysis (DEA) model without explicit inputs (DEA-WEI) and a two-layer minimax optimization scheme is developed. It is demonstrated that in this approach, the most favorable set of weights is first considered for each alternative or decision-making unit (DMU) and these weight sets are then aggregated to determine the best compromise weights for attributes, with the interests of all DMUs simultaneously considered in a fair manner. This approach is particularly suitable for situations where the preferences of decision-makers (DMs) are either unclear or difficult to acquire. Two case studies are conducted to illustrate the proposed approach and its use for determining weights for attributes in practice. The first case concerns the assessment of research strengths of 24 selected countries using certain measures, and the second concerns the analysis of the performance of 64 selected Chinese universities, where the preferences of DMs are either unknown or ambiguous, but the weights of the attributes should be assigned in a fair and unbiased manner.

Pairwise Comparison Based Ranking Vector Approach to Estimation Performance Ranking

Given multiple statistical estimators, how to rank their performance is a worthwhile problem. We propose an approach to estimation performance ranking based on pairwise comparison. Because ranking is about two or more estimators and is relative, pairwise comparison (e.g., Pitman’s measure of closeness) suits the needs. However, pairwise comparison cannot guarantee transitivity, which is needed for ranking. To get around this problem, we propose a ranking vector (RV) approach based on pairwise comparison. Here, an RV is obtained by using pairwise comparison results without using pairwise ranks directly. An RV provides ordinal information determining the rank and also supplementary cardinal information exhibiting how much one estimator is better than another. Ordinal information is more important and thus is guaranteed by using an order-preserving mapping in obtaining an RV. Our RV approach based on pairwise comparison is also applied to multiple-attribute decision problems. The approach is easily applicable and it does not need data normalization.

Symmetry Measures of Simplified Neutrosophic Sets for Multiple Attribute Decision-Making Problems

A simplified neutrosophic set (containing interval and single-valued neutrosophic sets) can be used for the expression and application in indeterminate decision-making problems because three elements in the simplified neutrosophic set (including interval and single valued neutrosophic sets) are characterized by its truth, falsity, and indeterminacy degrees. Under a simplified neutrosophic environment, therefore, this paper firstly defines simplified neutrosophic asymmetry measures. Then we propose a normalized symmetry measure and a weighted symmetry measure of simplified neutrosophic sets and develop a simplified neutrosophic multiple attribute decision-making method based on the weighted symmetry measure. All alternatives can be ranked through the weighted symmetry measure between the ideal solution/alternative and each alternative, and then the best one can be determined. Finally, an illustrative example on the selection of manufacturing schemes (alternatives) in the flexible manufacturing system demonstrates the applicability of the proposed method in a simplified (interval and single valued) neutrosophic setting, and then the decision-making method based on the proposed symmetry measure is in accord with the ranking order and best choice of existing projection and bidirectional projection-based decision-making methods and strengthens the resolution/discrimination in the decision-making process corresponding to the comparative example.

Some Interval Neutrosophic Linguistic Maclaurin Symmetric Mean Operators and Their Application in Multiple Attribute Decision Making

There are many practical decision-making problems in people’s lives, but the information given by decision makers (DMs) is often unclear and how to describe this information is of critical importance. Therefore, we introduce interval neutrosophic linguistic numbers (INLNs) to represent the less clear and uncertain information and give their operational rules and comparison methods. In addition, since the Maclaurin symmetric mean (MSM) operator has the special characteristic of capturing the interrelationships among multi-input arguments, we further propose an MSM operator for INLNs (INLMSM). Furthermore, considering the weights of attributes are the important parameters and they can influence the decision results, we also propose a weighted INLMSM (WINLMSM) operator. Based on the WINLMSM operator, we develop a multiple attribute decision making (MADM) method with INLNs and some examples are used to show the procedure and effectiveness of the proposed method. Compared with the existing methods, the proposed method is more convenient to express the complex and unclear information. At the same time, it is more scientific and flexible in solving the MADM problems by considering the interrelationships among multi-attributes.

A New Parametric Intuitionistic Fuzzy Entropy and its Applications in Multiple Attribute Decision Making

Role of intuitionistic fuzzy sets (IFSs) in solving multiple attribute decision making (MADM) problem has been established by many researchers. Depending upon the situation, we need different types of entropies based on IFSs. In this paper, we have proposed a new two parametric intuitionistic fuzzy entropy in the settings of IFSs theory. Besides proving some major properties, the proposed entropy is genuinely compared with some other existing entropies in literature. Based on the proposed entropy, a new method for solving MADM problems is introduced. Attribute weights play an eminent role in solving MADM problems. In this communication, two methods of determining the attribute weights are discussed. First is when information about attributes is completely unknown and second is when we have partial information regarding attribute weights. The two methods are effectively explained with the help of three examples. The attribute weights identification based on the proposed intuitionistic fuzzy entropy is offered in context of IFSs.

Some Maclaurin symmetric mean aggregation operators based on two-dimensional uncertain linguistic information and their application to decision making

The Maclaurin symmetric mean (MSM) operator has the characteristic of capturing the interrelationship among the multi-input arguments. The two-dimensional uncertain linguistic variables (2DULVs) add a subjective evaluation on the reliability of the evaluation results given by decision makers, so they can better express fuzzy information, and the improved operational laws of 2DULVs can avoid omitting information and make the operations more accurate. In order to fully take the advantages of the MSM operator and the improved operational laws of the 2DULVs, in this paper, we extend the MSM operator to the environment of 2DULVs, and two new aggregated operators are proposed, including the MSM operator for 2DULVs (2DULMSM) and the weighted MSM operator for 2DULVs (W2DULMSM). Simultaneously, we discuss some desirable properties and special cases with respect to different parameter values in these operators. Further, based on W2DULMSM operator, an approach to multiple-attribute group decision-making problems with 2DULVs is developed. Finally, a numerical example is provided to illustrate the feasibility of the proposed methods.