Multiple Attribute Group Decision-making Model Research Articles

The generalized dice similarity measures for comprehensive evaluation of graphic design effects based on color psychology with t-spherical fuzzy sets

Traditional Chinese art is vast and profound, with various colors having rich meanings. The combination of colors can vividly and intuitively represent various characteristics of things. Fully reflecting the characteristics of traditional Chinese folk art in graphic design can achieve extremely strong expressive effects. In current graphic design, the artistic colors of traditional Chinese folk art have not yet been fully displayed, and there is a lack of understanding of the profound connotation of traditional Chinese art. The graphic design industry has a very broad development space. The comprehensive evaluation of graphic design effects based on color psychology is a classical multiple attribute group decision making (MAGDM) problems. In this work, we shall present some novel Dice similarity measures (DSM) of T-spherical fuzzy sets(T-SFSs) and the generalized Dice similarity measures (GDSM) of and indicates that the DSM and asymmetric measures (projection measures) are the special cases of the GDSM in some parameter values. Then, we propose the GDSM-based MAGDM models with T-SFSs. Then, we apply the GDSMs between T-SFSs to MAGDM. Finally, an illustrative example for comprehensive evaluation of graphic design effects based on color psychology is given to demonstrate the efficiency of the GDSMs. The main contributions of this paper are summarized: (1) some novel Dice similarity measures (DSM) and the generalized Dice similarity measures (GDSMs) of T-spherical fuzzy sets(T-SFSs) are proposed; (2) The weighted Dice similarity measures (WDSM) and the weighted generalized Dice similarity measures (WGDSMs) of T-spherical fuzzy sets(T-SFSs) are proposed to solve the MAGDM; (3) an illustrative example for comprehensive evaluation of graphic design effects based on color psychology is given to demonstrate the efficiency of the WGDSM; (4) Some comparative analysis are used to show the effectiveness of the proposed Dice similarity measures.

A Novel MAGDM Approach Based on Cubic q -Rung Orthopair Fuzzy Power Generalized Maclaurin Symmetric Mean Operator

The cubic q -rung orthopair fuzzy set (Cq-ROFS) is a basic simplification of several fuzzy notions, including fuzzy set (FS), interval valued FS (INVFS), intuitionistic FS (INTFS), q -rung orthopair FS (q-ROFS), and INV q -rung orthopair FS (INVq-ROFS). By the degrees of INVq-ROFS and q-ROFS, Cq-ROFS exposes fuzzy judgement, and this is one of the advanced mathematical tools to handle more complicated assessment information in multiple attribute group decision-making (MAGDM) problems. In this article, firstly, encouraged from power average (PA) operator, generalized MSM operator, and generalized dual MSM operator, two novel aggregation operators (AOs) such as cubic q -rung orthopair fuzzy power generalized Maclaurin symmetric mean (Cq-ROFPWGMSM) operator and cubic q -rung orthopair fuzzy power generalized dual Maclaurin symmetric mean (Cq-ROFPWGDMSM) operator are initiated by merging PA operator with GMSM and GDMSM operators and some core characteristics of these AOs are investigated. Furthermore, some core cases with respect to different general parameters values are also investigated and found that some aggregation operators are special cases of the initiated AOs. Secondly, the weighted form of these newly initiated aggregation operators is also offered. Thirdly, two MAGDM models are offered based on Cq-OFPGWMSM and Cq-ROFPGWDMSM operators. Lastly, a numerical example about the selection of the best assistant professor of the year is taken as an application to show the effectiveness and capability of the initiated approaches. There is also a comparison with existing decision-making models.

Complex Pythagorean uncertain linguistic group decision-making model based on Heronian mean aggregation operator considering uncertainty, interaction and interrelationship

To effectively solve the mixed problem of considering the uncertainty of individuals and groups, the interaction between membership degree (MD) and non-membership (ND), and the interrelationship between attribute variables in complicated multiple attribute group decision-making (MAGDM) problems, in this paper, a concept of complex Pythagorean uncertain linguistic (CPUL) set (CPULS) is introduced, the interaction operational laws (IOLs) of CPUL variables (CPULVs) are defined. The CPUL interaction weighted averaging and geometric operators are presented. A new concept of CPUL rough number (CPULRN) is further constructed. The CPUL rough interaction weighted averaging and geometric aggregation operators (AOs) are extended. The ordering rules of any two CPULRNs are defined. The CPUL rough interaction Heronian mean (HM) (CPULRIHM) operator and its weighted form are advanced, related properties and special cases are explored. An MAGDM model based on CPUL rough interaction weighted HM (CPULRIWHM) operator is built. Lastly, we conduct a case study of location selection problem for logistics town project to show the applicability of the proposed methodology. The sensitivity and methods comparison are analyzed to verify the effectively and superiority.

A New Order Function for Interval-Valued Intuitionistic Fuzzy Numbers and Its Application in Group Decision Making

Purpose: We introduce a multiple attribute group decision making (MAGDM) method under interval-valued intuitionistic fuzzy (IVIF) domain. In these MAGDM problems, attribute values and attribute weights are represented in terms of IVIF sets (IVIFSs). Methodology: The present methodology is divided into two parts. Firstly, an appropriate order function has been developed for IVIFSs. Secondly, an algorithm has been proposed for solving the MAGDM problems with IVIF decision information. Findings: To show the effectiveness of the proposed method, a theoretical comparative study with respect to some existing literature is provided. A real-life based numerical example is given to demonstrate the proposed solution procedure. The advantage of this method is also described. Values: Using proposed order function, interval-valued intuitionistic fuzzy hybrid geometric and ordered weighted averaging operators, the present method provides a most preferred alternative in six steps. On the basis of a comparative study, it can be observed that the present method simple and easy to implement for solving the IVIF MAGDM model occurrence in real-life decision making problems.

Integrated Weighted Distance Measure for Single-Valued Neutrosophic Linguistic Sets and Its Application in Supplier Selection

The purpose of this study is to propose an integrated distance-based methodology for multiple attribute group decision making (MAGDM) within single-valued neutrosophic linguistic (SVNL) environments. A new SVNL distance measure, namely the SVNL integrated weighted distance (SVNLIWD) measure, is first developed for achieving the aim. The remarkable feature of the SVNLIWD is that it integrates both merits of ordered weighting and average weighting into aggregating SVNL distances; therefore, it can account for both the importance of aggregated deviations as well as ordered positions. Thus, it can highlight the decision makers’ subjective risk attitudes and combine the importance of objective decision information. Some distinctive characteristics and special forms of the presented distance framework are then specifically studied. Moreover, a MAGDM model on the basis of the proposed SVNLIWD form is formulated. Finally, an illustrative numerical case regarding selecting low-carbon supplier is used to test the performance of the designed method.

Entropy-Based GLDS Method for Social Capital Selection of a PPP Project with q-Rung Orthopair Fuzzy Information.

The social capital selection of a public–private-partnership (PPP) project could be regarded as a classical multiple attribute group decision-making (MAGDM) issue. In this paper, based on the traditional gained and lost dominance score (GLDS) method, the q-rung orthopair fuzzy entropy-based GLDS method was used to solve MAGDM problems. First, some basic theories related to the q-rung orthopair fuzzy sets (q-ROFSs) are briefly reviewed. Then, to fuse the q-rung orthopair fuzzy information effectively, the q-rung orthopair fuzzy Hamacher weighting average (q-ROFHWA) operator and q-rung orthopair fuzzy Hamacher weighting geometric (q-ROFHWG) operator based on the Hamacher operation laws are proposed. Moreover, to determine the attribute weights, the q-rung orthopair fuzzy entropy (q-ROFE) is proposed and some significant merits of it are discussed. Next, based on the q-ROFHWA operator, q-ROFE, and the traditional GLDS method, a MAGDM model with q-rung orthopair fuzzy information is built. In the end, a numerical example for social capital selection of PPP projects is provided to testify the proposed method and deliver a comparative analysis.

Single-Valued Neutrosophic Linguistic Logarithmic Weighted Distance Measures and Their Application to Supplier Selection of Fresh Aquatic Products

A single-valued neutrosophic linguistic set (SVNLS) is a popular fuzzy tool for describing deviation information in uncertain complex situations. The aim of this paper is to study some logarithmic distance measures and study their usefulness in multiple attribute group decision making (MAGDM) problems within single-valued neutrosophic linguistic (SVNL) environments. For achieving the purpose, SVNL weighted logarithmic averaging distance (SVNLWLAD) and SVNL ordered weighted logarithmic averaging distance (SVNLOWLAD) measures are firstly developed based on the logarithmic aggregation method. Then, the SVNL combined weighted logarithmic averaging distance (SVNLCWLAD) measure is presented by unifying the advantages of the previous SVNLWLAD and SVNLOWLAD measures. Moreover, a new MAGDM model by utilizing the SVNLCWLAD measure is presented under SVNL environments. Finally, a supplier selection for fresh aquatic products is taken as a case to illustrate the performance of the proposed framework.

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.

The 2-Rank Consensus Reaching Model in the Multigranular Linguistic Multiple-Attribute Group Decision-Making

In the multiple-attribute group decision-making (MAGDM), the decision objective is to obtain a complete ranking of the alternatives from best to worst. In the real world, however, obtaining such a complete ranking of alternatives is very time-consuming, and it is sometimes not necessary. There are many MAGDM problems that we need to assign two rank levels only, so as to create a ranking of one subset of alternatives above another subset. This type of MAGDM problem is called a 2-rank MAGDM problem. This paper investigates the 2-rank MAGDM problem under the multigranular linguistic context, and proposes a 2-rank consensus reaching framework with the minimum adjustments. In the consensus reaching framework, a 2-rank selection process is proposed to find the individual and collective 2-rank preference vectors, and a 2-rank consensus reaching process with the minimum adjustments is put forwarded to help decision makers achieve a consensus. To demonstrate the consensus efficiency of the 2-rank consensus reaching model, a comparison analysis between our proposal and the classical MAGDM models is presented. The main improvement of this paper is to provide a flexible framework to constitute a better approximate decision model to real-world MAGDM problems.

Two MAGDM models based on hesitant fuzzy linguistic term sets with possibility distributions: VIKOR and TOPSIS

Hesitant fuzzy linguistic term sets (HFLTSs) with additional possibility distributions can represent a much broader range of linguistic data. This paper develops compromise solutions for multiple attribute group decision making (MAGDM) using HFLTS. Geodesic distance and possibility distribution based distance measures are introduced to calculate the consensus degrees and determine the participant importance weights for the aggregation. Two models are then proposed to derive a compromise solution for the MAGDM problems. The first model is based on the VIKOR method and is used to determine the compromise between group utility maximization and individual regret minimization. The second model is based on the TOPSIS method and seeks to identify the compromise between the distances from the ideal and anti-ideal solutions. For both models, several ideal solutions and separation measures are presented and some of the properties in the two models are proven. An example based on an assessment of a health-care waste disposal management system illustrates the feasibility and practicability of the two proposed models. A further comparative study highlights the distinct features and potential use of the presented models.

Evaluation and selection of suppliers in the supply chain using the extended group PROMETHEE I procedures

The aim of this paper is to extend the preference ranking organisation method for enrichment evaluations (PROMETHEE I) method for decision-making problems when there is a group of decision makers. One of the advantages of the proposed method is capability of taking the incomparability's into account. Although there are some studies considering this aspect as an advantage, in the current literature, conflicting viewpoints and disagreements are being discussed. In this paper, this phenomenon is thought to be acceptable and should be considered. In this study, a supplier selection problem is treated as multiple attribute group decision making (MAGDM) problems. In order to have a solution in group decision making, first we used PROMETHEE I method to find the individual preference ordering, then by using the weights of decision makers (DMs), all individual partial-orders are aggregated into a collective pre-order. In addition, a new TOPSIS-based approach introduced to determine the importance of DMs. Furthermore, a numerical example in supplier selection context presented to illustrate the feasibility and practability of the proposed MAGDM model. Finally, a comparative analysis is performed and the proposed method seems to be more satisfactory than the group PROMETHEE II (and implicitly, GDSS-PROMETHEE) method for solving the decision problems. While, two best-ranked alternatives are incomparable and there is no clear evidence in favour of either of alternatives, conventional method (PROMETHEE II and implicitly GDSS-PROMETHEE) introduced only one of them as the best (optimal) alternative.

Evaluation and selection of suppliers in the supply chain using the extended group PROMETHEE I procedures

The aim of this paper is to extend the preference ranking organisation method for enrichment evaluations (PROMETHEE I) method for decision-making problems when there is a group of decision makers. One of the advantages of the proposed method is capability of taking the incomparability's into account. Although there are some studies considering this aspect as an advantage, in the current literature, conflicting viewpoints and disagreements are being discussed. In this paper, this phenomenon is thought to be acceptable and should be considered. In this study, a supplier selection problem is treated as multiple attribute group decision making (MAGDM) problems. In order to have a solution in group decision making, first we used PROMETHEE I method to find the individual preference ordering, then by using the weights of decision makers (DMs), all individual partial-orders are aggregated into a collective pre-order. In addition, a new TOPSIS-based approach introduced to determine the importance of DMs. Furthermore, a numerical example in supplier selection context presented to illustrate the feasibility and practability of the proposed MAGDM model. Finally, a comparative analysis is performed and the proposed method seems to be more satisfactory than the group PROMETHEE II (and implicitly, GDSS-PROMETHEE) method for solving the decision problems. While, two best-ranked alternatives are incomparable and there is no clear evidence in favour of either of alternatives, conventional method (PROMETHEE II and implicitly GDSS-PROMETHEE) introduced only one of them as the best (optimal) alternative.

Multiple Attribute Group Decision Analysis for Intuitionistic Triangular and Trapezoidal Fuzzy Numbers

Solving Multiple Attribute Group Decision Making (MAGDM) problems has become one of the most important researches in recent days. In situations where the information or the data is of the form of an Intuitionistic Triangular Fuzzy Number (ITrFN) or Intuitionistic Trapezoidal Fuzzy Number (ITzFN), a new distance function is defined for ranking the alternatives in the decision making process. After processing the decision information through a sequence of arithmetic aggregation operators, namely, the Intuitionistic Triangular Fuzzy Weighted Arithmetic Averaging (ITrFWAA), Intuitionistic Triangular Fuzzy Ordered Weighted Averaging (ITrFOWA) operator and the Intuitionistic Triangular Fuzzy Hybrid Aggregation (ITrFHA) operator, the proposed distance function is utilized to rank the best alternative. A model is proposed to solve MAGDM problems using the developed distance formula defined for ITrFNs. Numerical illustration is provided and comparisons are made with some of the existing MAGDM models and ranking procedures.

Consensus reaching model in the complex and dynamic MAGDM problem

In classical multiple attribute group decision making (MAGDM), decision makers evaluate predefined alternatives based on predefined attributes. In other words, the set of alternatives and the set of attributes are fixed throughout the decision process. However, real-world MAGDM problems (e.g., the decision processes of the United Nations Security Council) frequently have the following features. (1) Decision makers have different interests, and they thus use individual sets of attributes to evaluate the individual alternatives. In some situations, the individual sets of attributes may be heterogeneous. (2) In the decision process, decision makers do not have to reach a consensus regarding the use of the set of attributes. Instead, decision makers hope to find an alternative that is approved by all or most of them. (3) Finally, both the individual sets of attributes and the individual sets of alternatives can change dynamically in the decision process. By incorporating the above practical features into MAGDM, this study defines a complex and dynamic MAGDM problem, and proposes its resolution framework. In the resolution framework, a selection process in the context of heterogeneous attributes is proposed that obtains the ranking of individual alternatives and a collective solution. In addition, a consensus process is developed that generates adjustment suggestions for individual sets of attributes, individual sets of alternatives and individual preferences, thus helping decision makers reach consensus. Compared with existing MAGDM models, this study provides a flexible framework to form an approximate decision model to real-world MAGDM problems.

2-tuple linguistic Muirhead mean operators for multiple attribute group decision making and its application to supplier selection

Purpose– The purpose of this paper is to develop some 2-tuple linguistic aggregation operators based on Muirhead mean (MM), which is combined with multiple attribute group decision making (MAGDM) and applied the proposed MAGDM model for supplier selection under 2-tuple linguistic environment.Design/methodology/approach– The supplier selection problem can be regarded as a typical MAGDM problem, in which the decision information should be aggregated. In this paper, the authors investigate the MAGDM problems with 2-tuple linguistic information based on traditional MM operator. The MM operator is a well-known mean type aggregation operator, which has some particular advantages for aggregating multi-dimension arguments. The prominent characteristic of the MM operator is that it can capture the whole interrelationship among the multi-input arguments. Motivated by this idea, in this paper, the authors develop the 2-tuple linguistic Muirhead mean (2TLMM) operator and the 2-tuple linguistic dual Muirhead mean (2TLDMM) operator for aggregating the 2-tuple linguistic information, respectively. Some desirable properties and special cases are discussed in detail. Based on which, two approaches to deal with MAGDM problems under 2-tuple linguistic information environment are developed. Finally, a numerical example concerns the supplier selection problem is provided to illustrate the effectiveness and feasibility of the proposed methods.Findings– The results show that the proposed can solve the MAGDM problems within the context of 2-tuple linguistic information, in which the attributes are existing interaction phenomenon. Some 2-tuple aggregation operators based on MM have been developed. A case study of supplier selection is provided to illustrate the effectiveness and feasibility of the proposed methods. The results show that the proposed methods are useful to aggregate the linguistic decision information in which the attributes are not independent so as to select the most suitable supplier.Practical implications– The proposed methods can solve the 2-tuple linguistic MAGDM problem, in which the interactions exist among the attributes. Therefore, it can be used to supplier selection problems and other similar management decision problems.Originality/value– The paper develop some 2-tuple aggregation operators based on MM, and further present two methods based on the proposed operators for solving MAGDM problems. It is useful to deal with multiple attribute interaction decision-making problems and suitable to solve a variety of management decision-making applications.

A Multiple Attribute Group Decision-making Model for Selecting the Best Supplier

In the current literature, supplier selection is an important Multi Attribute Group Decision Making (MAGDM) problem which heavily contributes to the overall supply chain performance. Several solutions for the above problem are proposed. In this paper, TOPSIS and Bordas function approach, which is one of these methods, is discussed. So that, in the present model, first TOPSIS is used to find the individual preference ordering. Then, Bordas function is used to find the collective preference orderings. Finally, a simple example is provided in order to demonstrate its applicability and effectiveness of the proposed method.

Efficient Multiple Attribute Group Decision Making Models with Correlation Coefficient of Vague Sets

A new approach for multiple attribute group decision making (MAGDM) problems where the attribute weights and the expert weights are real numbers and the attribute values take the form of vague values, is presented in this paper. Since families of ordered weighted averaging (OWA) operators are available in the literature, and only a few available for vague sets, the vague ordered weighted averaging (VOWA) operator and the induced vague ordered weighted averaging (IVOWA) operator are introduced in this paper and utilized for aggregating the vague information. The correlation coefficient for vague sets is used for ranking the alternatives and a new MAGDM model is developed based on the IVOWA operator and the vague weighted averaging (VWA) operator. In addition to the proposed model, two different models are proposed based on Linguistic Quantifiers for the situation when the expert weights are completely unknown. An illustrative example is given and a comparison is made between the models to demonstrate the applicability of the proposed approach of MAGDM.