A subjective and objective integrated approach to determine attribute weights
TL;DR: This paper proposes an integrated approach to determine attribute weights in the multiple attribute decision making (MADM) problems that makes use of the subjective information provided by a decision maker and the objective information to form a two-objective programming model.
About: This article is published in European Journal of Operational Research.The article was published on 1999-01-16. It has received 446 citations till now. The article focuses on the topics: Decision theory & Programming paradigm.
Citations
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TL;DR: A correlation coefficient (CC) and standard deviation (SD) integrated approach for determining the weights of attributes in multiple attribute decision making (MADM) and a global sensitivity analysis to the weights determined are proposed to ensure the stability of the best decision alternative or alternative ranking.
283 citations
Cites background from "A subjective and objective integrat..."
...’s subjective and objective integrated approach [29] which is formulated as a two-objective mathematical programming...
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TL;DR: A new objective weighting method that employs intuitionistic fuzzy (IF) entropy measures to solve multiple-attribute decision-making problems in the context of intuitionistically fuzzy sets based on the credibility of the input data is proposed.
263 citations
TL;DR: In this article, the authors provide a review on the application and use of decision making approaches in regard to energy management problems, from 1995 to 2015 in 72 important journals, which chosen from the Web of Science database and in this regard, the systematic and meta-analysis method called PRISMA has been proposed.
Abstract: Energy management problems associated with rapid institutional, political, technical, ecological, social and economic development have been of critical concern to both national and local governments worldwide for many decades; thus, addressing such issues is a global priority. The main of objective of this study is to provide a review on the application and use of decision making approaches in regard to energy management problems. This paper selected and reviewed 196 published papers, from 1995 to 2015 in 72 important journals related to energy management, which chosen from the “Web of Science” database and in this regard, the systematic and meta-analysis method which called “PRISMA” has been proposed. All published papers were categorized into 13 different fields: environmental impact assessment, waste management, sustainability assessment, renewable energy, energy sustainability, land management, green management topics, water resources management, climate change, strategic environmental assessment, construction and environmental management and other energy management areas. Furthermore, papers were categorized based on the authors, publication year, nationality of authors, region, technique and application, number of criteria, research purpose, gap and contribution, solution and modeling, results and findings. Hybrid MCDM and fuzzy MCDM in the integrated methods were ranked as the first methods in use. The Journal of Renewable and Sustainable Energy Review was the important journal in this paper, with 32 published papers. Finally, environmental impact assessment was ranked as the first area that applied decision making approaches. Results of this study acknowledge that decision making approaches can help decision makers and stakeholders in solving some problems under uncertainties situations in environmental decision making and these approaches have seen increasing interest among previous researchers to use these approaches in various steps of environmental decision making process.
230 citations
TL;DR: A new approach is presented to make use of both the decision makers' social fuzzy preference relation on alternatives and decision matrix to form an optimization model that can be used to determine the attribute weights and rank the alternatives.
215 citations
Cites background from "A subjective and objective integrat..."
...Although lots of research on MADM problems have been done (Chen and Hwang, 1992; Hwang and Yoon, 1981), the area of MADM problems is still open for new challenges (Cook and Kress, 1994; Ma et al., 1999; Malakooti and Zhou, 1994)....
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...approaches with preference information on attributes (Carrizosa et al., 1995; Li, 1999; Ma et al., 1999; Marmol, 1998) and (2) the approaches with preference information on alternatives (Chiclana et al., 1996, 1998; Hwang and Yoon, 1981; Malakooti and Zhou, 1994; Tanino, 1984, 1990)....
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...1184 approaches with preference information on attributes (Carrizosa et al., 1995; Li, 1999; Ma et al., 1999; Marmol, 1998) and (2) the approaches with preference information on alternatives (Chiclana et al....
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...MADM problems arise in many real-word situations (Chen and Hwang, 1992; Hwang and Yoon, 1981; Cook and Kress, 1994; Ma et al., 1999; Malakooti and Zhou, 1994)....
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01 Jan 2013
TL;DR: In this paper, a grant from the Polish National Sciencce Center (DEC-2011/03/======B/HS4/03857) was used to support the work of the authors.
Abstract: This work was supported by the grant from
Polish National Scien
ce Center (DEC-2011/03/
B/HS4/03857).
183 citations
Cites background or methods from "A subjective and objective integrat..."
...[Wu, Chen, 2007] and ideal point method [Ma et al., 1999]....
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...The subjective and objective integrated approach [Ma et al., 1999] is formulated as a two-objective mathematical programming model, integrated approach [Fan et al....
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...Maggino and Ruviglioni [2011] suggest that: “equal weighting represents the preferred procedure, adopted in most of the applications....
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...The subjective and objective integrated approach [Ma et al., 1999] is formulated as a two-objective mathematical programming model, integrated approach [Fan et al., 2002] integrates decision maker’s fuzzy preference information on decision alternatives and objective decision matrix information into…...
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References
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01 Jan 1985
TL;DR: Analytic Hierarchy Process (AHP) as mentioned in this paper is a systematic procedure for representing the elements of any problem hierarchically, which organizes the basic rationality by breaking down a problem into its smaller constituent parts and then guides decision makers through a series of pairwise comparison judgments to express the relative strength or intensity of impact of the elements in the hierarchy.
Abstract: This chapter provides an overview of Analytic Hierarchy Process (AHP), which is a systematic procedure for representing the elements of any problem hierarchically. It organizes the basic rationality by breaking down a problem into its smaller constituent parts and then guides decision makers through a series of pair-wise comparison judgments to express the relative strength or intensity of impact of the elements in the hierarchy. These judgments are then translated to numbers. The AHP includes procedures and principles used to synthesize the many judgments to derive priorities among criteria and subsequently for alternative solutions. It is useful to note that the numbers thus obtained are ratio scale estimates and correspond to so-called hard numbers. Problem solving is a process of setting priorities in steps. One step decides on the most important elements of a problem, another on how best to repair, replace, test, and evaluate the elements, and another on how to implement the solution and measure performance.
16,547 citations
Book•
01 Mar 1981
TL;DR: In this paper, the authors present a classification of MADM methods by data type and propose a ranking method based on the degree of similarity of the MADM method to the original MADM algorithm.
Abstract: I. Introduction.- II. Multiple Attribute Decision Making - An Overview.- 2.1 Basics and Concepts.- 2.2 Classifications of MADM Methods.- 2.2.1 Classification by Information.- 2.2.2 Classification by Solution Aimed At.- 2.2.3 Classification by Data Type.- 2.3 Description of MADM Methods.- Method (1): DOMINANCE.- Method (2): MAXIMIN.- Method (3): MAXIMAX.- Method (4): CONJUNCTIVE METHOD.- Method (5): DISJUNCTIVE METHOD.- Method (6): LEXICOGRAPHIC METHOD.- Method (7): LEXICOGRAPHIC SEMIORDER METHOD.- Method (8): ELIMINATION BY ASPECTS (EBA).- Method (9): LINEAR ASSIGNMENT METHOD (LAM).- Method (10): SIMPLE ADDITIVE WEIGHTING METHOD (SAW).- Method (11): ELECTRE (Elimination et Choice Translating Reality).- Method (12): TOPSIS (Technique for Order Preference by Similarity to Ideal Solution).- Method (13): WEIGHTED PRODUCT METHOD.- Method (14): DISTANCE FROM TARGET METHOD.- III. Fuzzy Sets and their Operations.- 3.1 Introduction.- 3.2 Basics of Fuzzy Sets.- 3.2.1 Definition of a Fuzzy Set.- 3.2.2 Basic Concepts of Fuzzy Sets.- 3.2.2.1 Complement of a Fuzzy Set.- 3.2.2.2 Support of a Fuzzy Set.- 3.2.2.3 ?-cut of a Fuzzy Set.- 3.2.2.4 Convexity of a Fuzzy Set.- 3.2.2.5 Normality of a Fuzzy Set.- 3.2.2.6 Cardinality of a Fuzzy Set.- 3.2.2.7 The mth Power of a Fuzzy Set.- 3.3 Set-Theoretic Operations with Fuzzy Sets.- 3.3.1 No Compensation Operators.- 3.3.1.1 The Min Operator.- 3.3.2 Compensation-Min Operators.- 3.3.2.1 Algebraic Product.- 3.3.2.2 Bounded Product.- 3.3.2.3 Hamacher's Min Operator.- 3.3.2.4 Yager's Min Operator.- 3.3.2.5 Dubois and Prade's Min Operator.- 3.3.3 Full Compensation Operators.- 3.3.3.1 The Max Operator.- 3.3.4 Compensation-Max Operators.- 3.3.4.1 Algebraic Sum.- 3.3.4.2 Bounded Sum.- 3.3.4.3 Hamacher's Max Operator.- 3.3.4.4 Yager's Max Operator.- 3.3.4.5 Dubois and Prade's Max Operator.- 3.3.5 General Compensation Operators.- 3.3.5.1 Zimmermann and Zysno's ? Operator.- 3.3.6 Selecting Appropriate Operators.- 3.4 The Extension Principle and Fuzzy Arithmetics.- 3.4.1 The Extension Principle.- 3.4.2 Fuzzy Arithmetics.- 3.4.2.1 Fuzzy Number.- 3.4.2.2 Addition of Fuzzy Numbers.- 3.4.2.3 Subtraction of Fuzzy Numbers.- 3.4.2.4 Multiplication of Fuzzy Numbers.- 3.4.2.5 Division of Fuzzy Numbers.- 3.4.2.6 Fuzzy Max and Fuzzy Min.- 3.4.3 Special Fuzzy Numbers.- 3.4.3.1 L-R Fuzzy Number.- 3.4.3.2 Triangular (or Trapezoidal) Fuzzy Number.- 3.4.3.3 Proof of Formulas.- 3.4.3.3.1 The Image of Fuzzy Number N.- 3.4.3.3.2 The Inverse of Fuzzy Number N.- 3.4.3.3.3 Addition and Subtraction.- 3.4.3.3.4 Multiplication and Division.- 3.5 Conclusions.- IV. Fuzzy Ranking Methods.- 4.1 Introduction.- 4.2 Ranking Using Degree of Optimality.- 4.2.1 Baas and Kwakernaak's Approach.- 4.2.2 Watson et al.'s Approach.- 4.2.3 Baldwin and Guild's Approach.- 4.3 Ranking Using Hamming Distance.- 4.3.1 Yager's Approach.- 4.3.2 Kerre's Approach.- 4.3.3 Nakamura's Approach.- 4.3.4 Kolodziejczyk's Approach.- 4.4 Ranking Using ?-Cuts.- 4.4.1 Adamo's Approach.- 4.4.2 Buckley and Chanas' Approach.- 4.4.3 Mabuchi's Approach.- 4.5 Ranking Using Comparison Function.- 4.5.1 Dubois and Prade's Approach.- 4.5.2 Tsukamoto et al.'s Approach.- 4.5.3 Delgado et al.'s Approach.- 4.6 Ranking Using Fuzzy Mean and Spread.- 4.6.1 Lee and Li's Approach.- 4.7 Ranking Using Proportion to The Ideal.- 4.7.1 McCahone's Approach.- 4.8 Ranking Using Left and Right Scores.- 4.8.1 Jain's Approach.- 4.8.2 Chen's Approach.- 4.8.3 Chen and Hwang's Approach.- 4.9 Ranking with Centroid Index.- 4.9.1 Yager's Centroid Index.- 4.9.2 Murakami et al.'s Approach.- 4.10 Ranking Using Area Measurement.- 4.10.1 Yager's Approach.- 4.11 Linguistic Ranking Methods.- 4.11.1 Efstathiou and Tong's Approach.- 4.11.2 Tong and Bonissone's Approach.- V. Fuzzy Multiple Attribute Decision Making Methods.- 5.1 Introduction.- 5.2 Fuzzy Simple Additive Weighting Methods.- 5.2.1 Baas and Kwakernaak's Approach.- 5.2.2 Kwakernaak's Approach.- 5.2.3 Dubois and Prade's Approach.- 5.2.4 Cheng and McInnis's Approach.- 5.2.5 Bonissone's Approach.- 5.3 Analytic Hierarchical Process (AHP) Methods.- 5.3.1 Saaty's AHP Approach.- 5.3.2 Laarhoven and Pedrycz's Approach.- 5.3.3 Buckley's Approach.- 5.4 Fuzzy Conjunctive/Disjunctive Method.- 5.4.1 Dubois, Prade, and Testemale's Approach.- 5.5 Heuristic MAUF Approach.- 5.6 Negi's Approach.- 5.7 Fuzzy Outranking Methods.- 5.7.1 Roy's Approach.- 5.7.2 Siskos et al.'s Approach.- 5.7.3 Brans et al.'s Approach.- 5.7.4 Takeda's Approach.- 5.8 Maximin Methods.- 5.8.1 Gellman and Zadeh's Approach.- 5.8.2 Yager's Approach.- 5.9 A New Approach to Fuzzy MADM Problems.- 5.9.1 Converting Linguistic Terms to Fuzzy Numbers.- 5.9.2 Converting Fuzzy Numbers to Crisp Scores.- 5.9.3 The Algorithm.- VI. Concluding Remarks.- 6.1 MADM Problems and Fuzzy Sets.- 6.2 On Existing MADM Solution Methods.- 6.2.1 Classical Methods for MADM Problems.- 6.2.2 Fuzzy Methods for MADM Problems.- 6.2.2.1 Fuzzy Ranking Methods.- 6.2.2.2 Fuzzy MADM Methods.- 6.3 Critiques of the Existing Fuzzy Methods.- 6.3.1 Size of Problem.- 6.3.2 Fuzzy vs. Crisp Data.- 6.4 A New Approach to Fuzzy MADM Problem Solving.- 6.4.1 Semantic Modeling of Linguistic Terms.- 6.4.2 Fuzzy Scoring System.- 6.4.3 The Solution.- 6.4.4 The Advantages of the New Approach.- 6.5 Other Multiple Criteria Decision Making Methods.- 6.5.1 Multiple Objective Decision Making Methods.- 6.5.2 Methods of Group Decision Making under Multiple Criteria.- 6.5.2.1 Social Choice Theory.- 6.5.2.2 Experts Judgement/Group Participation.- 6.5.2.3 Game Theory.- 6.6 On Future Studies.- 6.6.1 Semantics of Linguistic Terms.- 6.6.2 Fuzzy Ranking Methods.- 6.6.3 Fuzzy MADM Methods.- 6.6.4 MADM Expert Decision Support Systems.- VII. Bibliography.
8,629 citations
TL;DR: A method of scaling ratios using the principal eigenvector of a positive pairwise comparison matrix is investigated, showing that λmax = n is a necessary and sufficient condition for consistency.
8,117 citations
"A subjective and objective integrat..." refers background or methods in this paper
...the Satty’s matrix [16]) on the attribute set P ....
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...Many methods for solving MADM problems require definitions of quantitative weights for the attributes [1-4,6-8,10-19,21]....
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...The subjective approaches select weights based on preference information of attributes given by the DM, they include eigenvector method [16], weighted least square method [3], and Delphi method [10] etc....
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TL;DR: In this paper, a linear programming model is proposed for analyzing individual differences in preference judgments with regard to a set of stimuli prespecified in a multidimensional attribute space, in which the individual is modelled as possessing an ideal point denoting his most preferred stimulus location in this space and weights which reveal the relative saliences of the attributes.
Abstract: This paper offers a new methodology for analyzing individual differences in preference judgments with regard to a set of stimuli prespecified in a multidimensional attribute space. The individual is modelled as possessing an “ideal point” denoting his most preferred stimulus location in this space and a set of weights which reveal the relative saliences of the attributes. He prefers those stimuli which are “closer” to his ideal point (in terms of a weighted Euclidean distance measure). A linear programming model is proposed for “external analysis”i.e., estimation of the coordinates of his ideal point and the weights (involved in the Euclidean distance measure) by analyzing his paired comparison preference judgments on a set of stimuli, prespecified by their coordinate locations in the multidimensional space. A measure of “poorness of fit” is developed and the linear programming model minimizes this measure overall possible solutions. The approach is fully nonmetric, extremely flexible, and uses paired comparison judgments directly. The weights can either be constrained nonnegative or left unconstrained. Generalizations of the model to consider ordinal or interval preference data and to allow an orthogonal transformation of the attribute space are discussed. The methodology is extended to perform “internal analysis,”i.e., to determine the stimuli locations in addition to weights and ideal points by analyzing the preference judgments of all subjects simultaneously. Computational results show that the methodology for external analysis is “unbiased”—i.e., on an average it recovers the “true” ideal point and weights. These studies also indicate that the technique performs satisfactorily even when about 20 percent of the paired comparison judgments are incorrectly specified.
631 citations
"A subjective and objective integrat..." refers methods in this paper
...Many methods for solving MADM problems require definitions of quantitative weights for the attributes [1-4,6-8,10-19,21]....
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