Multiple Attribute Group Decision-making Method Research Articles

QUALIFLEX method for MAGDM with probabilistic uncertain linguistic information and its application to green supplier selection

Probabilistic uncertain linguistic sets (PULTSs) have extensively been employed in multiple attribute group decision making (MAGDM)problem. The QUALIFLEX method, which is relatively a novel MAGDM technique, aims to obtain the optimal alternative. This paper proposes the probabilistic uncertain linguistic QUALIFLEX (PUL-QUALIFLEX) method with CRITIC method. To show the effectiveness of the designed method, an application is given for green supplier selection and the derived results are compared with some existing methods. Thus, the advantage of this proposed method is that it is simple to understand and easy to compute. The proposed method can also contribute to the selection of suitable alternative successfully in other selection issues.

TOPSIS Method for Probabilistic Linguistic MAGDM with Entropy Weight and Its Application to Supplier Selection of New Agricultural Machinery Products

In multiple attribute group decision making (MAGDM) problems, uncertain decision information is well-represented by linguistic term sets (LTSs). These LTSs are easily converted into probabilistic linguistic sets (PLTSs). In this paper, a TOPSIS method is proposed for probabilistic linguistic MAGDM in which the attribute weights are completely unknown, and the decision information is in the form of probabilistic linguistic numbers (PLNs). First, the definition of the scoring function is used to solve the probabilistic linguistic entropy, which is then employed to objectively derive the attribute weights. Second, the optimal alternatives are determined by calculating the shortest distance from the probabilistic linguistic positive ideal solution (PLPIS) and on the other side the farthest distance of the probabilistic linguistic negative ideal solution (PLNIS). This proposed method extends the applications range of the traditional entropy-weighted method. Moreover, it doesn’t need the decision-maker to give the attribute weights in advance. Finally, a numerical example for supplier selection of new agricultural machinery products is used to illustrate the use of the proposed method. The result shows the approach is simple, effective and easy to calculate. The proposed method can contribute to the selection of suitable alternative successfully in other selection problems.

A Multiple Attribute Group Decision-making Method Based on the Partitioned Bonferroni Mean of Linguistic Intuitionistic Fuzzy Numbers

As a more effective linguistic information representation model, the linguistic intuitionistic fuzzy number (LIFN), made up of the linguistic membership degree (LMD) and the linguistic non-membership degree (LNMD), plays an important role in describing uncertain-decision information in cognitive activity. The partitioned Bonferroni mean (PBM) operator is constructed based on real conditions, considering that some factors considered by decision-makers are interrelated and some are independent. The PBM operator can aggregate evaluation information under various attributes, which are divided into several independent groups; the factors interact with each other within the same group, but the factors are independent of each other when located in different groups. The classical PBM operators and their extensions can handle many decision-making problems but are unable to handle decision-making problems under a linguistic intuitionistic environment. To take full advantage of the PBM operator and LIFNs, this paper combines the PBM operator with LIFNs to propose several PBM operators for aggregating LIFNs. First, the relative theories about LIFNs are reviewed in brief. Then, linguistic intuitionistic fuzzy partitioned BM aggregation operators and partitioned geometric BM aggregation operators are discussed, including the linguistic intuitionistic fuzzy partitioned Bonferroni mean (LIFPBM) operator, the linguistic intuitionistic fuzzy weighted partitioned Bonferroni mean (LIFWPBM) operator, the linguistic intuitionistic fuzzy partitioned geometric Bonferroni mean (LIFPGBM) operator, and the linguistic intuitionistic fuzzy weighted partitioned geometric Bonferroni mean (LIFWPGBM) operator. Moreover, a novel method constructed on the developed operators is presented to address multiple attribute group decision-making (MAGDM) problems with the LIFNs. The feasibility of the proposed method is given by a numeric example, and the comparative analysis of our proposed method and other methods shows some advantages of these new methods. The developed method is constructed based on LIFNs and the PBM operator, and it is more practical and general than other existing methods and easily describes qualitative information that stems from a decision maker’s cognition. In addition, it can more effectively handle the complex relationship among multiple attributes in MAGDM problems.

Neutrosophic cubic Heronian mean operators with applications in multiple attribute group decision-making using cosine similarity functions

This article introduces the concept of Heronian mean operators, geometric Heronian mean operators, neutrosophic cubic number–improved generalized weighted Heronian mean operators, neutrosophic cubic number–improved generalized weighted geometric Heronian mean operators. These operators actually generalize the operators of fuzzy sets, cubic sets, and neutrosophic sets. We investigate the average weighted operator on neutrosophic cubic sets and weighted geometric operator on neutrosophic cubic sets to aggregate the neutrosophic cubic information. After this, based on average weighted and geometric weighted and cosine similarity function in neutrosophic cubic sets, we developed a multiple attribute group decision-making method. Finally, we give a mathematical example to illustrate the usefulness and application of the proposed method.

A New Method for MAGDM Based on Improved TOPSIS and a Novel Pythagorean Fuzzy Soft Entropy

A decision-making environment is full of uncertainty and complexity. Existing tools include fuzzy sets, soft sets, intuitionistic fuzzy sets, Pythagorean fuzzy sets (PFSs) and so on. Compared with intuitionistic fuzzy sets (IFSs), PFSs proposed by Yager have advantages in handling vagueness in the real world and possess good symmetry. The entropy measure is the most widespread form of uncertainty measure. In this paper, we improve the technique for order preference by similarity to an ideal solution (TOPSIS) method to better deal with multiple-attribute group decision making (MAGDM) problems based on Pythagorean fuzzy soft sets (PFSSs). To better determine the weights of attributes, we firstly define a novel Pythagorean fuzzy soft entropy which is more reasonable and valid. Meanwhile the entropy has good symmetry. Entropy for PFSSs which is used to determine the subjective weights of attributes is also defined. Then we introduce a measure to calculate integrated weights by combining objective weights and subjective weights. Based on the integrated weights, the TOPSIS method is generalized and improved to solve the MAGDM problem. A distance measure taking into account the characteristics of Pythagorean fuzzy numbers (PFNs) is used to calculate distance between alternatives and ideal solutions. Finally, the proposed MAGDM method is applied in the case of selecting a missile position. Compared with other methods, it is shown that the proposed method can rank alternatives more reasonably and have higher distinguishability.

A novel fuzzy stochastic MAGDM method based on credibility theory and fuzzy stochastic dominance with incomplete weight information

PurposeWith respect to multiple attribute group decision-making (MAGDM) in which the assessment values of alternatives are denoted by normal discrete fuzzy variables (NDFVs) and the weight information of attributes is incompletely known, this paper aims to develop a novel fuzzy stochastic MAGDM method based on credibility theory and fuzzy stochastic dominance, and then applies the proposed method for selecting the most desirable investment alternative under uncertain environment.Design/methodology/approachFirst, by aggregating the membership degrees of an alternative to a scale provided by all decision-makers into a triangular fuzzy number, the credibility degree and expect the value of a triangular fuzzy number are calculated to construct the group fuzzy stochastic decision matrix. Second, based on determining the credibility distribution functions of NDFVs, the fuzzy stochastic dominance relations between alternatives on each attribute are obtained and the fuzzy stochastic dominance degree matrices are constructed by calculating the dominance degrees that one alternative dominates another on each attribute. Subsequently, calculating the overall fuzzy stochastic dominance degrees of an alternative on each attribute, a single objective non-linear optimization model is established to determine the weights of attributes by maximizing the relative closeness coefficients of all alternatives to positive ideal solution. If the information about attribute weights is completely unknown, the idea of maximizing deviation is used to determine the weights of attributes. Finally, the ranking order of alternatives is determined according to the descending order of corresponding relative closeness coefficients and the best alternative is determined.FindingsThis paper proposes a novel fuzzy stochastic MAGDM method based on credibility theory and fuzzy stochastic dominance, and a case study of investment alternative selection problem is provided to illustrate the applicability and sensitivity of the proposed method and its effectiveness is demonstrated by comparison analysis with the proposed method with the existing fuzzy stochastic MAGDM method. The result shows that the proposed method is useful to solve the MAGDM problems in which the assessment values of alternatives are denoted by NDFVs and the weight information of attributes is incompletely known.Originality/valueThe contributions of this paper are that to describe the dominance relations between fuzzy variables reasonably and quantitatively, the fuzzy stochastic dominance relations between any two fuzzy variables are redefined and the concept of fuzzy stochastic dominance degree is proposed to measure the dominance degree that one fuzzy variable dominate another; Based on credibility theory and fuzzy stochastic dominance, a novel fuzzy stochastic MAGDM method is proposed to solve MAGDM problems in which the assessment values of alternatives are denoted by NDFVs and the weight information of attributes is incompletely known. The proposed method has a clear logic, which not only can enrich and develop the theories and methods of MAGDM but also provides decision-makers a novel method for solving fuzzy stochastic MAGDM problems.

Generalized Hamacher Aggregation Operators for Intuitionistic Uncertain Linguistic Sets: Multiple Attribute Group Decision Making Methods

In this paper, we consider multiple attribute group decision making (MAGDM) problems in which the attribute values take the form of intuitionistic uncertain linguistic variables. Based on Hamacher operations, we developed several Hamacher aggregation operators, which generalize the arithmetic aggregation operators and geometric aggregation operators, and extend the algebraic aggregation operators and Einstein aggregation operators. A number of special cases for the two operators with respect to the parameters are discussed in detail. Also, we developed an intuitionistic uncertain linguistic generalized Hamacher hybrid weighted average operator to reflect the importance degrees of both the given intuitionistic uncertain linguistic variables and their ordered positions. Based on the generalized Hamacher aggregation operator, we propose a method for MAGDM for intuitionistic uncertain linguistic sets. Finally, a numerical example and comparative analysis with related decision making methods are provided to illustrate the practicality and feasibility of the proposed method.

Multiple‐attribute group decision‐making method of linguisticq‐rung orthopair fuzzy power Muirhead mean operators based on entropy weight

Linguistic q-rung orthopair fuzzy numbers (Lq-ROFNs) are a qualitative form of q-rung orthopair fuzzy numbers (q-ROFNs) where the membership and nonmembership degrees are represented by linguistic variables. The Lq-ROFNs can describe a broader range of linguistic assessment information flexibly by adjusting the parameter q based on different situations, so they are more superior to the linguistic intuitionistic fuzzy numbers and linguistic Pythagorean fuzzy numbers in real application. Based on the Lq-ROFNs, we introduce the entropy measure which can be used to determine the indefiniteness of the assessment information. Then, based on the linguistic entropy measure, we further propose a method to obtain the attribute weights when the weight information is incomplete known. For aggregating the assessment information, the power average (PA) operator can reduce the influence of extreme data caused by the biased decision-makers by considering the support degree of different evaluation individuals, and the Muirhead mean (MM) operator can take the interrelationship of different numbers of attributes into account by adjusting the parameter vector based on the real situations. In this paper, based on these two operators, we firstly propose the linguistic q-rung orthopair fuzzy PA operator and linguistic q-rung orthopair fuzzy weighted PA operator. Further, for combing the advantages of the MM operator and PA operator, we propose the linguistic q-rung orthopair fuzzy power MM (PMM) operator and linguistic q-rung orthopair fuzzy weighted PMM operator, and then investigate some properties of them. Finally, a new multiple-attribute group decision-making (MAGDM) method is proposed to process the Lq-ROFNs, and some practical examples are given to illustrate the effectiveness and superiority of this new method in comparison with other existing MAGDM methods.

Similarity Measures of Linguistic Cubic Hesitant Variables for Multiple Attribute Group Decision-Making

A linguistic cubic hesitant variable (LCHV) is a hybrid form of linguistic values in group decision-making environments. It is composed of an interval language variable and multiple single-valued language variables given by different decision-makers (DMs). Due to the uncertainty and hesitation of DMs, the numbers of language variables in different LCHVs are unequal. Thus, the least common multiple number (LCMN) extension method was adopted. Based on the included angle and distance of two LCHVs, we presented two cosine similarity measures and developed a multiple attribute group decision-making (MAGDM) approach. An example of engineer selection was used to implement the proposed LCHV MAGDM method and demonstrate the simplicity and feasibility of the proposed method. The sensitivity analysis of weight changes for the two measures showed that the similarity measure based on distance was more stable than the similarity measure based on included angle in this application.

Multiple attribute group decision making using J-divergence and evidential reasoning theory under intuitionistic fuzzy environment

The theory of intuitionistic fuzzy sets has been proved to be an effective and convenient tool in the construction of fuzzy multiple attribute group decision-making models to deal with the uncertainty in developing complex decision support systems. Concerning this topic, the current studies mainly focus on their attention on two aspects including aggregation operators on intuitionistic fuzzy sets and determining the weights of both decision makers and attributes. However, some challenges have not been fully considered including existing aggregation operators which may induce unreasonable results in some situations and how to objectively determine the weights of both attributes and decision makers to meet different decision-making demands. To overcome the challenges of existing decision-making models and to satisfy much more decision-making situations, a novel intuitionistic fuzzy multiple attribute group decision-making method via J-divergence and evidential reasoning theory is proposed in this paper as a supplement of conventional models. On the one hand, a weighted J-divergence of intuitionistic fuzzy sets and a J-divergence between two intuitionistic fuzzy matrices are introduced. Following the two concepts, two consensus-based approaches are proposed to determine the weights of both decision makers and attributes. The weights obtained from the proposed method can more accurately reflect the importance levels of both attributes and decision makers from the perspective of consensus by comparison with existing models. On the other hand, an evidential reasoning theory-based operator is established to replace conventional operators for aggregating intuitionistic fuzzy information. The fusion result via this operator is consistent with most of intuitionistic fuzzy numbers. With these works, the proposed method can provide more accurate and reasonable decision results than existing algorithms.

Linguistic neutrosophic uncertain numbers and their multiple attribute group decision-making method

Linguistic neutrosophic uncertain numbers and their multiple attribute group decision-making method

Methods for Multiple-Attribute Group Decision Making with q-Rung Interval-Valued Orthopair Fuzzy Information and Their Applications to the Selection of Green Suppliers

In the practical world, there commonly exist different types of multiple-attribute group decision making (MAGDM) problems with uncertain information. Symmetry among some attributes’ information that is already known and unknown, and symmetry between the pure attribute sets and fuzzy attribute membership sets, can be an effective way to solve this type of MAGDM problem. In this paper, we investigate four forms of information aggregation operators, including the Hamy mean (HM) operator, weighted HM (WHM) operator, dual HM (DHM) operator, and the dual-weighted HM (WDHM) operator with the q-rung interval-valued orthopair fuzzy numbers (q-RIVOFNs). Then, some extended aggregation operators, such as the q-rung interval-valued orthopair fuzzy Hamy mean (q-RIVOFHM) operator; q-rung interval-valued orthopairfuzzy weighted Hamy mean (q-RIVOFWHM) operator; q-rung interval-valued orthopair fuzzy dual Hamy mean (q-RIVOFDHM) operator; and q-rung interval-valued orthopair fuzzy weighted dual Hamy mean (q-RIVOFWDHM) operator are presented, and some of their precious properties are studied in detail. Finally, a real example for green supplier selection in green supply chain management is provided, to demonstrate the proposed approach and to verify its rationality and scientific nature.

Multiple-Attribute Group Decision-Making Based on q-Rung Orthopair Fuzzy Power Maclaurin Symmetric Mean Operators

To be able to describe more complex fuzzy uncertainty information effectively, the concept of q-rung orthopair fuzzy sets (q-ROFSs) was first proposed by Yager. The q-ROFSs can dynamically adjust the range of indication of decision information by changing a parameter q based on the different hesitation degree from the decision-makers, where q ≥ 1, so they outperform the traditional intuitionistic fuzzy sets and Pythagorean fuzzy sets. In real decision-making problems, there is often an interaction phenomenon between attributes. For aggregating these complex fuzzy information, the Maclaurin symmetric mean (MSM) operator is more superior by considering interrelationships among attributes. In addition, the power average (PA) operator can reduce the effects of extreme evaluating data from some experts with prejudice. In this paper, we introduce the PA operator and the MSM operator based on q-rung orthopair fuzzy numbers (q-ROFNs). Then, we put forward the q-rung orthopair fuzzy power MSM (q-ROFPMSM) operator and the q-rung orthopair fuzzy power weighed MSM (q-ROFPWMSM) operator of q-ROFNs and present some of their properties. Finally, we present a novel multiple-attribute group decision-making (MAGDM) method based on the q-ROFPWA and the q-ROFPWMSM operators. The experimental results show that the novel MAGDM method outperforms the existing MAGDM methods for dealing with MAGDM problems.

Multiple-attribute group decision-making based on power Bonferroni operators of linguisticq-rung orthopair fuzzy numbers

In this paper, a new conception of linguistic q-rung orthopair fuzzy number (Lq-ROFN) is proposed where the membership and nonmembership of the q-rung orthopair fuzzy numbers ( q-ROFNs) are represented as linguistic variables. Compared with linguistic intuitionistic fuzzy numbers and linguistic Pythagorean fuzzy numbers, the Lq-ROFNs can more fully describe the linguistic assessment information by considering the parameter q to adjust the range of fuzzy information. To deal with the multiple-attribute group decision-making (MAGDM) problems with Lq-ROFNs, we proposed the linguistic score and accuracy functions of the Lq-ROFNs. Further, we introduce and prove the operational rules and the related properties characters of Lq-ROFNs. For aggregating the Lq-ROFN assessment information, some aggregation operators are developed, involving the linguistic q-rung orthopair fuzzy power Bonferroni mean (BM) operator, linguistic q-rung orthopair fuzzy weighted power BM operator, linguistic q-rung orthopair fuzzy power geometric BM (GBM) operator, and linguistic q-rung orthopair fuzzy weighted power GBM operator, and then presents their rational properties and particular cases, which cannot only reduce the influences of some unreasonable data caused by the biased decision-makers, but also can take the interrelationship between any two different attributes into account. Finally, we propose a method to handle the MAGDM under the environment of Lq-ROFNs by using the new proposed operators. Further, several examples are given to show the validity and superiority of the proposed method by comparing with other existing MAGDM methods.

Multiple attribute group decision-making method with single-valued neutrosophic interval number information

ABSTRACTTo describe decision makers’ judgments for an evaluated object more comprehensively in the decision-making process, this paper firstly defines the concept of a single-valued neutrosophic interval number (SVNIN), which is composed of both its interval number (interval judgment) and its single-valued neutrosophic number (SVNN) (confident degree). Then we present the basic operational laws of SVNINs and the score function of SVNIN based on the attitude index and confident level of decision makers to compare SVNINs. Next, we propose a single-valued neutrosophic interval number weighted arithmetic averaging (SVNINWAA) operator and a single-valued neutrosophic interval number weighted geometric averaging (SVNINWGA) operator to aggregate SVNIN information. Further, a multiple attribute group decision-making (MDGDM) method using the proposed SVNINWAA or SVNINWGA operator is established under an SVNIN environment. Finally, an illustrative example regarding the selection problem of global suppliers is presented to show the application and effectiveness of the developed method.

New form of single valued neutrosophic uncertain linguistic variables aggregation operators for decision-making

A neutrosophic uncertain linguistic variable is composed of an uncertain linguistic variable and a neutrosophic number, which has more advantages than both of uncertain linguistic variable and neutrosophic number in expression. Therefore, the decision-making theory and its related methods based on neutrosophic uncertain linguistic variables have received wide attention of scholars. This paper mainly studies the new expression and operations of single value neutrosophic uncertain linguistic variables and its application in multiple attribute group decision-making (MAGDM). First, a new form of single value neutrosophic uncertain linguistic set (NFSVNULS) and its operational rules are defined. Then, a new form of single value neutrosophic uncertain linguistic variable weighted arithmetic average (NFSVNULVWAA) operator and a new form of single value neutrosophic uncertain linguistic variable weighted geometric average (NFSVNULVWGA) operator are proposed. Furthermore, a MAGDM method based on the proposed aggregation operators is put forward. Finally, an example of investment is used to demonstrate the feasibility and effectiveness of the proposed method.

MAGDM Method with Pythagorean 2-Tuple Linguistic Information and Applications in the HSE Performance Assessment of Laboratory

There is a significant gap between the safety management in the Chinese colleges and many renowned colleges in other countries. The subject of this study is how to assess the performance of health, safety, and environment (HSE) in Chinese college laboratories. The assessment system is established by three parts. First of all, HSE performance assessment indicators for laboratories in Chinese colleges are identified based on the previous studies. Then set valued iteration is used to calculate the weights of the various indicators. Following that, multiple attribute group decision-making (MAGDM) method with Pythagorean 2-tuple linguistic operators is used to assess the laboratory HSE performance in colleges. Finally, taking a college in Sichuan Province as an example, the proposed method is used to assess the laboratory HSE performance. The assessment result shows that the proposed method used in this study is practical and feasible.

Some q-Rung Dual Hesitant Fuzzy Heronian Mean Operators with Their Application to Multiple Attribute Group Decision-Making

The q-rung orthopair fuzzy sets (q-ROFSs), originated by Yager, are good tools to describe fuzziness in human cognitive processes. The basic elements of q-ROFSs are q-rung orthopair fuzzy numbers (q-ROFNs), which are constructed by membership and nonmembership degrees. As realistic decision-making is very complicated, decision makers (DMs) may be hesitant among several values when determining membership and nonmembership degrees. By incorporating dual hesitant fuzzy sets (DHFSs) into q-ROFSs, we propose a new technique to deal with uncertainty, called q-rung dual hesitant fuzzy sets (q-RDHFSs). Subsequently, we propose a family of q-rung dual hesitant fuzzy Heronian mean operators for q-RDHFSs. Further, the newly developed aggregation operators are utilized in multiple attribute group decision-making (MAGDM). We used the proposed method to solve a most suitable supplier selection problem to demonstrate its effectiveness and usefulness. The merits and advantages of the proposed method are highlighted via comparison with existing MAGDM methods. The main contribution of this paper is that a new method for MAGDM is proposed.

Evaluation criterion for different methods of multiple-attribute group decision making with interval-valued intuitionistic fuzzy information

A number of effective methods for multiple-attribute group decision making (MAGDM) with interval-valued intuitionistic fuzzy numbers (IVIFNs) have been proposed in recent years. However, the different methods frequently yield different, even sometimes contradictory, results for the same problem. In this paper a novel criterion to determine the advantages and disadvantages of different methods is proposed. First, the decision-making process is divided into three parts: translation of experts’ preferences, aggregation of experts’ opinions, and comparison of the alternatives. Experts’ preferences aggregation is considered the core step, and the quality of the collective matrix is considered the most important evaluation index for the aggregation methods. Then, methods to calculate the similarity measure, correlation, correlation coefficient, and energy of the intuitionistic fuzzy matrices are proposed, which are employed to evaluate the collective matrix. Thus, the optimal method can be selected by comparing the collective matrices when all the methods yield different results. Finally, a novel approach for aggregating experts’ preferences with IVIFN is presented. In this approach, experts’ preferences are mapped as points into two-dimensional planes, with the plant growth simulation algorithm (PGSA) being employed to calculate the optimal rally points, which are inversely mapped to IVIFNs to establish the collective matrix. In the study, four different methods are used to address one example problem to illustrate the feasibility and effectiveness of the proposed approach.

Multiple attribute group decision-making method using correlation coefficients between linguistic neutrosophic numbers

Multiple attribute group decision-making method using correlation coefficients between linguistic neutrosophic numbers