Weights Of Decision Makers Research Articles

A novel interval type-2 fuzzy decision model based on two new versions of relative preference relation-based MABAC and WASPAS methods (with an application in aircraft maintenance planning)

In this paper, concerning advantages of relative preference relation (RPR) and interval type-2 fuzzy sets (IT2FSs), a new IT2F-RPR based on multi-attributive border approximation area comparison (MABAC) method is introduced for determining the critical path of production projects under group decision-making process. IT2FSs are more capable than classic fuzzy sets in coping with uncertainty and providing more degree of freedom to model the uncertain conditions. Also, the RPR is better than defuzzification because it does not lose the fuzzy message, and the method avoids pairwise comparisons. In fact, the MABAC method is extended by the RPR for reducing the time complexity. Furthermore, an extended MABAC method is developed under IT2FSs to better address the uncertainty. Weights of decision makers (DMs) are computed by introducing a new IT2F-RPR-based MABAC concept in the proposed new decision model. Also, experts’ opinions are aggregated by using weights of the DMs. Moreover, weights of criteria are determined based on a new extended weighted aggregated sum-product assessment (WASPAS) method by using the DMs or experts’ opinions on the importance of criteria and weights of DMs. As a matter of fact, weights of DMs are determined by a new version of extended MABAC method, and weights of criteria are specified using a new version of WASPAS method for the first time in the literature. Finally, a case study about aircraft maintenance planning is solved to address the calculation process and applicability of the proposed method. Computational results of the presented model are accurate and suitable for real-life situations.

Projection-based approach to group decision-making with hybrid information representations and application to software quality evaluation

Group decision-making (GDM) is regarded as a main part of modern decision science. The weights of decision makers (DMs) are very important in the actual GDM process. How to determine the weights of DMs and to identify the alternatives are the main activities for GDM problems. This work is devoted to develop an entropy-based approach to determine the weights of DMs. Considering that the projection measure is able to provide not only the distance but also the angle between two decision objects, this article intends to identify the alternatives based on the projection measure. This research, however, also finds that the existing projection measures are unreasonable in real vector, interval vector and intuitionistic fuzzy vector settings. To solve this problem, this work provides a new normalized projection measure. Considering the demands of different attributes, this work presents a GDM method with hybrid information representations. An experimental analysis illustrates the practicability, feasibility and validity of method introduced in this paper.

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.

Interval-Valued Intuitionistic Fuzzy Multiple Attribute Group Decision Making with Uncertain Weights

The theory of interval-valued intuitionistic fuzzy sets (IVIFSs) has been an impactful and convenient tool in the construction of advanced multiple attribute group decision making (MAGDM) models to counter the uncertainty in the developing complex decision support system. To satisfy much more demands from fuzzy decision making problems, we propose a method to solve the MAGDM problem in which all the information supplied by the decision makers is expressed as interval-valued intuitionistic fuzzy decision matrices where each of the elements is characterized by an interval-valued intuitionistic fuzzy number, and the information about the weights of both decision makers and attributes may be completely unknown or partially known. Firstly, we introduce a consensus-based method to quantify the weights of all decision makers based on all interval-valued intuitionistic fuzzy decision matrices. Secondly, we utilize the interval-valued intuitionistic fuzzy weighted arithmetic (IVIFWA) operator to aggregate all interval-valued intuitionistic fuzzy decision matrices into the collective one. Thirdly, we establish an optimization model to determine the weights of attributes depending on the collective decision matrix and the given attribute weight information. Fourthly, we adopt the weighted correlation coefficient of IVIFSs to rank all the alternatives from the perspective of TOPSIS via the collective decision matrix and the obtained weights of attributes. Finally, some examples are used to illustrate the validity and feasibility of our proposed approach by comparison with some existing models.

Methods for assigning weights to decision makers in group AHP decision-making

The method known as the analytical hierarchy process (AHP), a theoretical and methodological concept of multi-criteria analysis, is increasingly used in solving various decision-making problems. AHP is an excellent support to both the individual and group decision-making process, however, the involvement of a greater number of decision makers complicates the process and requires a different approach to when an individual decides alone. The synthesis of individual decisions within a group can be done in various ways, but the problem is how to deal with different levels of consistency when there are a number of decision makers. Thus, this paper presents some of the methods for defining the individual weights of decision makers in group AHP decision making.

Variable weights theory and its application to multi-attribute group decision making with intuitionistic fuzzy numbers on determining decision maker's weights.

The determination of the weights of decision makers (DMs) is an important problem in multi-attribute group decision making. Many approaches have been presented to determine DMs’ weights. However, the computed weight vectors of DMs are usually assumed to be constant in existing studies, and this may cause irrationalities in the decision results. Therefore, this article proposes a novel method to determine DMs’ weights based on variable weights theory in which the evaluation information is described as intuitionistic fuzzy sets (IFSs). First, DMs provide their assessment with IFSs, and the intuitionistic fuzzy weighted averaging (IFWA) operator is applied to obtain weighted decision matrix based on the prior given DMs’ and attributes’ weights. Second, the DMs’ weights are obtained based on variable weights theory, and an alternative decision can be computed. Finally, the converted value of the achieved IFS of each alternative is calculated, and the best appropriate alternative is acquired. Two illustrative examples and the comparisons with exsiting approaches are also used to reflect the effectiveness of the proposed approach.

Consensus-Based Multi-Person Decision Making with Incomplete Fuzzy Preference Relations Using Product Transitivity

In this paper, a consensus-based method for multi-person decision making (MPDM) using product transitivity with incomplete fuzzy preference relations (IFPRs) is proposed. Additionally, an average aggregation operator has been used at the first level to estimate the missing preference values and construct the complete fuzzy preference relation (FPR). Then it is confirmed to be product consistent by using the transitive closure formula. Following this, weights of decision makers (DMs) are evaluated by merging consistency weights and predefined priority weights (if any). The consistency weights for the DMs are estimated through product consistency investigation of the information provided by each DM. The consensus process determines whether the selection procedure should be initiated or not. The hybrid comprises of a quitting process and feedback mechanism, and is used to enhance the consensus level amongst DMs in case of an inadequate state. The quitting process arises when some DMs decided to leave the course, and is common in MPDM while dealing with a large number of alternatives. The feedback mechanism is the main novelty of the proposed technique which helps the DMs to improve their given preferences based on this consistency. At the end, a numerical example is deliberated to measure the efficiency and applicability of the proposed method after the comparison with some existing models under the same assumptions. The results show that proposed method can offer useful comprehension into the MPDM process.

Algorithms for possibility linguistic single-valued neutrosophic decision-making based on COPRAS and aggregation operators with new information measures

The objective of this work is to introduce the concept of the possibility linguistic single-valued neutrosophic set (PLSVNS) for better dealing with the imprecise and uncertain information during the decision-making process. The prominent characteristics of this set are that it considers two distinctive sorts of information such as the membership, indeterminacy, non-membership degrees, and their corresponding possibility degree. In it, first, we stated some operational laws, score and accuracy functions, comparison laws between the pairs of the set. Then, we define weighted averaging and geometric aggregation operators (AOs) to collaborate the PLSVNSs into a single one. Further, we present two algorithms based on a complex proportional assessment (COPRAS) method and AOs based method under PLSVNS information to solve the decision-making problems. In these methods, the information related to weights of decision makers and criteria is determined with the help of a distance and entropy measures. Finally, a practical real-life example is provided to expose the materialness and the viability of our work.

A new soft computing model based on linear assignment and linear programming technique for multidimensional analysis of preference with interval type-2 fuzzy sets

Multiple criteria decision making (MCDM) approach plays an important role in life, since it is always necessary to make decisions through various alternatives based on specific criteria. In this paper, interval type-2 fuzzy sets (IT2FSs) are used because in most cases in the real-world the information is incomplete and ambiguous. A new group decision approach with linear assignment method (LAM) is proposed. In addition, weight of each evaluation factor according to subjective and objective data is constructed based on a new developed version of linear programming technique for multidimensional analysis of preference (LINMAP) method. In the proposed method, weights of decision makers (DMs) are computed based on a novel approach that applies a new modified method based on the concept of ideal solutions. Furthermore, a new IT2F-ranking method is introduced. To display the applicability of the presented soft computing method, firstly, a real case study of green supplier selection problem is adopted from the literature and solved. Moreover, the method is applied in a second case study of project evaluation and selection problem. Two applications show that the introduced method presents a proper soft computing framework that can handle real-world uncertain environments. Moreover, the method can consider importance of the DMs and evaluation criteria.

Multi-Attribute Group Decision Making Method Based on EDAS Under Picture Fuzzy Environment

Multi-attribute group decision making (MAGDM) is one of the most important research hotspots in the field of decision sciences. Many practical problems are often characterized by MAGDM. The aim of this paper is to develop a new approach for MAGDM problems, in which the attribute values take the form of picture fuzzy information, and the information about the weights of attributes and decision makers is unknown. Firstly, some picture fuzzy interaction operators are presented, such as the picture fuzzy weighted interaction averaging (PFWIA) operator, picture fuzzy ordered weighted interaction averaging (PFOWIA) operator and picture fuzzy hybrid ordered weighted interaction averaging (PFHOWIA) operator. In the meantime, some desirable properties of these operators are discussed in detail. Secondly, to get reasonable decision result, we propose a method to determine the weights of decision makers under picture fuzzy setting based on the idea of the Dice similarity measure. Thirdly, for the situations where the information about the attribute weights is partly known, we establish an optimization model to determine the attribute weights on the basis of the maximizing deviation method. Fourthly, we propose a new method to solve MAGDM problems by extending the traditional Evaluation based on Distance from Average Solution (EDAS) method. Finally, an illustrative example is given to demonstrate the calculation process of the proposed method, and the method is verified by comparing the evaluation result with that of two existing methods.

Two New Approaches for Multi-Attribute Group Decision-Making With Interval-Valued Neutrosophic Frank Aggregation Operators and Incomplete Weights

This paper investigates some Frank aggregation operators of interval-valued neutrosophic numbers (IVNNs) and applies to multi-attribute group decision-making (MAGDM) problems. First, the Frank t-conorm and t-norm are extended to interval-valued neutrosophic environment. Some new operational laws for IVNNs are defined and their related properties are investigated. Based on these new operational laws, some new aggregation operators for IVNNs are developed including the interval-valued neutrosophic Frank weighted averaging (IVNFWA) operator and the interval-valued neutrosophic Frank weighted geometric (IVNFWG) operator. Then some desirable properties and special cases of these new operators are further discussed. To solve the MAGDM with IVNNs, the weights of decision makers (DMs) are determined by using extended technique for order preference by similarity to ideal solution (TOPSIS) method based on cross-entropy. Additionally, attribute weights are determined based on the similarity degrees between alternatives and the absolute ideal solutions. Further, two new decision-making approaches for MAGDM with IVNNs are put forward by means of the IVNFWA and IVNFWG operators, respectively. Finally, a case study of selecting an agricultural socialization service provider is analyzed to illustrate the practicality and effectiveness of the developed two approaches.

A Novel Approach for Green Supplier Selection under a q-Rung Orthopair Fuzzy Environment

With environmental issues becoming increasingly important worldwide, plenty of enterprises have applied the green supply chain management (GSCM) mode to achieve economic benefits while ensuring environmental sustainable development. As an important part of GSCM, green supplier selection has been researched in many literatures, which is regarded as a multiple criteria group decision making (MCGDM) problem. However, these existing approaches present several shortcomings, including determining the weights of decision makers subjectively, ignoring the consensus level of decision makers, and that the complexity and uncertainty of evaluation information cannot be adequately expressed. To overcome these drawbacks, a new method for green supplier selection based on the q-rung orthopair fuzzy set is proposed, in which the evaluation information of decision makers is represented by the q-rung orthopair fuzzy numbers. Combined with an iteration-based consensus model and the q-rung orthopair fuzzy power weighted average (q-ROFPWA) operator, an evaluation matrix that is accepted by decision makers or an enterprise is obtained. Then, a comprehensive weighting method can be developed to compute the weights of criteria, which is composed of the subjective weighting method and a deviation maximization model. Finally, the TODIM (TOmada de Decisao Interativa e Multicritevio) method, based on the prospect theory, can be extended into the q-rung orthopair fuzzy environment to obtain the ranking result. A numerical example of green supplier selection in an electric automobile company was implemented to illustrate the practicability and advantages of the proposed approach.

Deriving decision makers’ weights in group decision making: An overview of objective methods

In group decision making problems, it is almost impossible to have a homogeneous group of decision makers whose experiences, attitudes, knowledge are the same or similar. Therefore, it is required to determine the weights of decision makers to reflect their relative importance or contribution to the problem. Decision maker weights show the importance or reliability of decision makers in solving the particular problem. The studies on determining the weights of the decision makers are limited. Besides, there is no comprehensive literature review or survey related to the determination of decision makers’ weight among the limited numbers of studies. Therefore, in this study, the literature on deriving decision makers’ weights is reviewed to present the state-of-the-art in the group decision making environment. Subsequently, a new classification system is proposed. Objective methods for deriving decision makers' weights are classified into five categories: Similarity-based approaches, index-based approaches, clustering-based approaches, integrated approaches, and other approaches. The literature review and analysis of the studies are conducted based on these categories; moreover, challenges and potential research directions are identified. According to the analysis of fifty-five papers, the interest in the topic increases dramatically after 2011. The highest percentage of the studies fell into the similarity-based approaches.

A novel outranking based multi criteria group decision making methodology integrating ELECTRE and VIKOR under intuitionistic fuzzy environment

This study proposes a new group decision making (GDM) methodology to solve outranking problems efficiently under uncertainty integrating multi criteria decision making (MCDM) and intuitionistic fuzzy set (IFS) theory. To this aim, ELECTRE I, an outranking based MCDM approach is extended with VIKOR method, an ideal solution based approach, under intuitionistic fuzzy environment. The methodology utilizes pairwise comparison and outranking relation concepts of ELECTRE methods to construct different concordance and discordance sets in order to reflect preferences of decision makers effectively. By the help of similarities between concordance and discordance characteristics of ELECTRE and maximum group utility and minimum individual regret characteristics of VIKOR, the methodology enables the intuitionistic fuzzy ELECTRE to overcome its weakness in ranking process and presents complete ranking. In addition, this study employs entropy method to identify the weights of criteria and decision makers, and weighted distance approach to determine the weights of different concordance sets. Utilizing these methods leads to specifying these weights objectively. The applicability of the proposed approach is explored by an illustrative example on supplier selection problem by explaining the method step by step. Furthermore, four computational experiments are conducted in order to demonstrate its applicability to the other areas and the results are compared.

Multi-Attribute Group Decision Making Method for Preference Conflicting with Heterogeneous Information

The aim of this article is to propose a multi-objective decision-making method for researching and solving multi-attribute heterogeneous group decision-making problems. This is in the case that the characters of the decision information and decision makers' preferences are heterogeneous, and the weight information is incomplete. In this method, the multi-objective decision-making model, which considers the alternatives decision relative closeness and the preference of heterogeneous degree of decision makers in the objective function, is put forward. In addition, this article uses the minimax method to derive the multi-objective decision-making model and obtain the attribute weights and decision makers weights, and then the optimal scheme is established. Finally, an illustrative example shows the effectiveness of the proposed method.

A New Entropy-Based Approach to Determine the Weights of Decision Makers for Each Criterion With Crisp and Interval Data in Group Decision Making Under Multiple Attribute

The aim of this article is to develop a modified version of the original entropy approach to determine weights of decision makers (DMs) in multi-attribute group decision making (MAGDM) contexts with both crisp and interval data, in which the weights of experts (or DMs) are derived from the decision matrices and DMs have different weights for different criteria. In the proposed method, the experts' weight for each criterion depends on the uncertainty measure of DMs comparisons. In other words, the DMs who give less uncertainty judgments (or less entropy measures), will be evaluated as more importance, and vice-versa. Finally, a numerical example is given to demonstrate the feasibility of the developed method.

A doubly extended TOPSIS method for group decision making based on ordered fuzzy numbers

Multiple Attribute Decision Making methods have become very popular in recent years and are frequently applied in many real-life situations. The increasing complexity of the analysed decision problems makes it less feasible to consider all the relevant aspects of the problem by a single decision maker. As a result, many real-life problems are discussed by a group of decision makers. In such a group each decision maker can specialize in a different field and has his/her own unique characteristics, such as knowledge, skills, experience, personality, etc. This implies that each decision maker should have a different degree of influence on the final result, i.e., the ranking of alternatives. This means that the weights of decision makers should differ. The aim of this paper is to extend the TOPSIS method to group decision making, using ordered fuzzy numbers. The proposed approach uses TOPSIS twice. The first time it is used to determine the weights of decision makers which are then used to calculate the aggregated decision matrix for all the group decision matrices provided by the decision makers. Based on this aggregated matrix, the extended TOPSIS is used again, to rank the alternatives and to select the best one. A numerical example illustrates the proposed approach.

The Application of Fuzzy VIKOR for the Design Scheme Selection in Lean Management

Given that using the same evaluation criteria in group decision making (GDM) may cause solution bias, this research proposes the decision making model using improved fuzzy VIKOR and takes the lean management design scheme selection process in a real estate company as an example to study the way of decision making. Research results are as follows: (1) improved fuzzy VIKOR allows different decision makers to evaluate all schemes with respect to different evaluation criteria systems and, based on this, this research proposes a decision making model which can effectively avoid making decision using the same criteria system; (2) this decision making model is very scientific, as it is not sensitive to the coefficient of selection mechanism, the weight of decision maker, and the weight of evaluation criterion, so the decision results are very stable; (3) the decision making model proposed in this research can effectively obtain the optimal result and avoid suboptimal solution.

Group decision making based on the relationships between the information measures for additive and multiplicative linguistic term sets

This paper investigates the systematic transformation of the information measures including the distance, similarity and entropy measures of linguistic term sets (LTSs) into each other. Firstly, we present the bilateral transforming approach of the distance measure into the similarity measure for both additive LTSs (ALTSs) and multiplicative LTSs. Then, the transformation of the distance measure into the entropy measure for ALTSs is investigated. This cycle of transformation is completed by investigating the transformation of the similarity measure into the entropy measure for ALTSs, and vice versa. In the sequel, in analogous to the results of linguistic arguments, the results of linguistic preference relations are achieved. Further, a rational approach is proposed to evaluate the relative weights of decision makers in the form of linguistic preference information.

Decision making with interval-valued intuitionistic fuzzy preference relations based on additive consistency analysis

This paper discusses the theory and application of interval-valued intuitionistic fuzzy preference relations (IVIFPRs). To do this, we first introduce an additive consistency concept for IVIFPRs that can address the issues in previous ones. Then, several additive consistency-based programming models for judging the consistency of IVIFPRs and for determining missing values are constructed. Furthermore, an approach for calculating the interval-valued intuitionistic fuzzy priority weight vector is offered. With respect to group decision making with IVIFPRs, a consensus index is offered, and an interactive algorithm for improving the consensus level is proposed that can ensure the additive consistency. After that, a consensus analysis-based programming model for determining the weights of decision makers is built. Furthermore, a consistency-and-consensus-based group decision-making method that can address inconsistent and incomplete IVIFPRs is developed. Finally, a practical decision-making problem about evaluating talents in universities is offered to show the feasibility and efficiency of the new method.