Entropy-Based Weights on Decision Makers in Group Decision-Makingsetting with Hybrid Preference Representations
01 Mar 2018-
TL;DR: In this article, a new normalized projection as a separation measure, along with TOPSIS (technique for order preference by similarity to ideal solution) technique, is used for current decision model.
Abstract: Abstract The weights of decision makers play an important role in group decision-making problems. Entropy is a very important measure in information science. This work models an approach to determine the weights of decision makers by using an entropy measure. A new normalized projection as a separation measure, along with TOPSIS (technique for order preference by similarity to ideal solution) technique, is used for current decision model. The attribute values in current model are characterized by exact values and intervals. A comparison and experimental analysis show the applicability, feasibility, effectiveness and advantages of the proposed method.
TL;DR: The literature on deriving decision makers’ weights is reviewed to present the state-of-the-art in the group decision making environment and a new classification system is proposed.
Abstract: 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.
TL;DR: An entropy weight assignment method is proposed to dealing with the situation where the assessment of attributes can contain uncertainties or contain both uncertainties and incompleteness, e.g., interval values or belief distributions, and the advantages and the potential in supporting MADM with uncertain and incomplete information are illustrated.
Abstract: Multiple attribute decision making (MADM) problems often consist of various types of quantitative and qualitative attributes. Quantitative attributes can be assessed by accurate numerical values, interval values or fuzzy numbers, while qualitative attributes can be evaluated by belief distributions, linguistic variables or intuitionistic fuzzy sets. However, the determination of attribute weights is still an open issue in MADM problems until now. In the traditional objective weight assignment method, attributes are usually assessed by accurate values. In this paper, an entropy weight assignment method is proposed to dealing with the situation where the assessment of attributes can contain uncertainties, e.g., interval values, or contain both uncertainties and incompleteness, e.g., belief distributions. The advantage of the proposed method lies in that uncertainties and incompleteness contained in the interval numerical values or belief distributions can be preserved in the generated weights. Specifically, several pairs of programming models to generate the weights of attributes are constructed in three different circumstances: (1) quantitative attribute expressed by interval values; (2) incomplete belief distribution with accurate belief degrees; and (3) belief distribution constituted by interval belief degrees. The evidential reasoning approach is then utilized to aggregate the distributions of attributes based on the generated attribute weights. The normalized interval weight vector is defined, and the characteristics of the weight assignment method are discussed. The proposed method has been experimented with real data to illustrate its advantages and the potential in supporting MADM with uncertain and incomplete information.
TL;DR: A three-phase method for addressing multi-attribute group decision making (MAGDM) with Pythagorean fuzzy numbers (PFNs) with a multi-objective parametric comprehensive deviation programming model to derive attribute weights and a haze management example is elaborated to illustrate the feasibility of the proposed method.
Abstract: Pythagorean fuzzy set (PFS), as a new extension of intuitionistic fuzzy set (IFS), has recently been utilized to describe uncertain information in decision making. This paper aims to develop a three-phase method for addressing multi-attribute group decision making (MAGDM) with Pythagorean fuzzy numbers (PFNs) and apply to haze management. Firstly, the normalized projection of PFNs is defined. Then the entropy and Riemann closeness degree of PFNs are proposed. Based on the normalized projection of PFNs, an extended TOPSIS method is presented to determine the DMs’ weights. A collective decision matrix is obtained by aggregating individual matrices with the DMs’ weights. Subsequently, the deviation of score from entropy and the deviation of accuracy from entropy are defined, respectively. Then a multi-objective parametric comprehensive deviation programming model is constructed to derive the attribute weights. A weighted collective matrix is obtained by the derived attribute weights. The positive ideal solution (PIS) and negative ideal solution (NIS) are determined according to the weighted collective matrix. By calculating the Riemann closeness degrees of alternatives to PIS and NIS, the ranking values of alternatives are computed to generate the ranking order of alternatives. Finally, a haze management example is elaborated to illustrate the feasibility of the proposed method. To illustrate the stability and practicality of the proposed method, the sensitivity analysis, validity test and comparative analysis are conducted.
TL;DR: A novel hybrid multi-criteria method based on IDOCRIW and TOPSIS is proposed for optimal selection of the appropriate waste-to-energy technologies for distributed generation and revealed that the integration of anaerobic digestion and gasification could be more promising in terms of waste management.
Abstract: Waste-to-energy has evolved as a promising solution for sustainable power generation as well and waste management. To effectively harness the potential of the waste-to-energy technologies in a sustainable manner, an optimal choice among the diverse technologies is highly essential. The multi-dimensional nature of waste management makes selection of appropriate waste-to-energy option a complex problem. Therefore, a simple and computationally efficient decision tool is required to aid decision making. In this paper, a novel hybrid multi-criteria method based on IDOCRIW and TOPSIS are proposed for optimal selection of the appropriate waste-to-energy technologies for distributed generation. Fourteen criteria were considered spanning through technical, economic, environmental and social factors. Five technologies such as anaerobic digestion, landfill gas recovery, incineration, pyrolysis and gasification were selected due to their level of maturity and availability. The proposed model was tested using the City of Johannesburg, South Africa as a case study. The overall results indicated that anaerobic digestion is the most attractive technology with a relative closeness of 0.9724 to the ideal solution while incineration is ranked worst with a closeness of 0.6474 to the ideal solution. The result also revealed that the integration of anaerobic digestion and gasification could be more promising in terms of waste management. It could also be a good candidate for distributed generation in a microgrid application by serving as a local power generator when integrated to waste management systems of the City of Johannesburg.
TL;DR: A data-driven GDM method that combines expert weights and criterion weights is proposed and is applied to aid radiologists in diagnosing thyroid nodules in a tertiary hospital located in Hefei, Anhui Province, China.
Abstract: Emerging information technologies integration into various fields has enhanced the development of these fields. Large volumes of data have been accumulated in this process. The accumulated data offer opportunities and challenges for people facing practical problems. On the one hand, it is essential to depend on a groups capabilities rather than an individuals capabilities to handle practical problems because the individual may lack sufficient expertise and experience to use data. In this situation, the practical problems can be considered as group decision making (GDM) problems. On the other hand, the accumulated data can help generate quality solutions to GDM problems. To obtain such solutions under the assumption that the accumulated data regarding a specific decision problem are available, this paper proposes a data-driven GDM method. In the method, decision makers weights are learned from historical overall assessments and the corresponding gold standards, while criterion weights are learned from historical overall assessments and the corresponding decision matrices. The learned expert weights and criterion weights are used to produce the aggregated assessments, from which alternatives are compared or the overall conclusion is made. In a tertiary hospital located in Hefei, Anhui Province, China, the proposed method is applied to aid radiologists in diagnosing thyroid nodules.
TL;DR: The Mathematical Theory of Communication (MTOC) as discussed by the authors was originally published as a paper on communication theory more than fifty years ago and has since gone through four hardcover and sixteen paperback printings.
Abstract: Scientific knowledge grows at a phenomenal pace--but few books have had as lasting an impact or played as important a role in our modern world as The Mathematical Theory of Communication, published originally as a paper on communication theory more than fifty years ago. Republished in book form shortly thereafter, it has since gone through four hardcover and sixteen paperback printings. It is a revolutionary work, astounding in its foresight and contemporaneity. The University of Illinois Press is pleased and honored to issue this commemorative reprinting of a classic.
TL;DR: Given a set of utility functions defined on a decision space for a group of individuals, the concept of utopia point for the group as well as the group regret of a feasible decision is introduced.
Abstract: Given a set of utility functions defined on a decision space for a group of individuals, we introduce the concept of utopia point for the group as well as the group regret of a feasible decision. The group regret of a decision varies with a class of distance functions. The class of solutions under study are those which minimize the group regret according to the class of distance functions. We investigate its properties from!he viewpoint of decision rationale. The bounds and monotonicity of the solutions together with their computation are also explored.
TL;DR: A systematic literature review on articles published from 2008 to 2012 on the application of DM techniques for supplier selection is provided by using a methodological decision analysis in four aspects including decision problems, decision makers, decision environments, and decision approaches.
Abstract: Despite the importance of decision-making (DM) techniques for construction of effective decision models for supplier selection, there is a lack of a systematic literature review for it. This paper provides a systematic literature review on articles published from 2008 to 2012 on the application of DM techniques for supplier selection. By using a methodological decision analysis in four aspects including decision problems, decision makers, decision environments, and decision approaches, we finally selected and reviewed 123 journal articles. To examine the research trend on uncertain supplier selection, these articles are roughly classified into seven categories according to different uncertainties. Under such classification framework, 26 DM techniques are identified from three perspectives: (1) Multicriteria decision making (MCDM) techniques, (2) Mathematical programming (MP) techniques, and (3) Artificial intelligence (AI) techniques. We reviewed each of the 26 techniques and analyzed the means of integrating these techniques for supplier selection. Our survey provides the recommendation for future research and facilitates knowledge accumulation and creation concerning the application of DM techniques in supplier selection.
TL;DR: This paper treats supplier selection as a group multiple criteria decision making (GMCDM) problem and obtain decision makers' opinions in the form of linguistic terms which are converted to trapezoidal fuzzy numbers and extended the VIKOR method with a mechanism to extract and deploy objective weights based on Shannon entropy concept.
Abstract: Recently, resolving the problem of evaluation and ranking the potential suppliers has become as a key strategic factor for business firms. With the development of intelligent and automated information systems in the information era, the need for more efficient decision making methods is growing. The VIKOR method was developed to solve multiple criteria decision making (MCDM) problems with conflicting and non-commensurable criteria assuming that compromising is acceptable to resolve conflicts. On the other side objective weights based on Shannon entropy concept could be used to regulate subjective weights assigned by decision makers or even taking into account the end-users' opinions. In this paper, we treat supplier selection as a group multiple criteria decision making (GMCDM) problem and obtain decision makers' opinions in the form of linguistic terms. Then, these linguistic terms are converted to trapezoidal fuzzy numbers. We extended the VIKOR method with a mechanism to extract and deploy objective weights based on Shannon entropy concept. The final result is obtained through next steps based on factors R, S and Q. A numerical example is proposed to illustrate an application of the proposed method.
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