DS/AHP method: A mathematical analysis, including an understanding of uncertainty
TL;DR: In this paper, a mathematical analysis of the analytical hierarchy process (AHP) is presented, constructing the functional form of the preference weightings given to groups of decision alternatives in the DS/AHP method.
About: This article is published in European Journal of Operational Research.The article was published on 2002-07-01. It has received 216 citations till now. The article focuses on the topics: Analytic hierarchy process & Dempster–Shafer theory.
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TL;DR: A literature review of the applications of Analytic Hierarchy Process, which aims to provide a ready reference on AHP, and act as an informative summary kit for the researchers and practitioners for their future work.
2,717 citations
11 Sep 2015
TL;DR: The results of this study indicated that in 2013 scholars have published articles more than in other years, and energy, environment and sustainability were ranked as the first areas that have applied MCDM techniques and approaches.
Abstract: Multiple criteria decision-making (MCDM) is considered as a complex decision-making (DM) tool involving both quantitative and qualitative factors. In recent years, several MCDM techniques and approaches have been suggested to choosing the optimal probable options. The purpose of this article is to systematically review the applications and methodologies of the MCDM techniques and approaches. This study reviewed a total of 393 articles published from 2000 to 2014 in more than 120 peer reviewed journals (extracted from Web of Science). According to experts’ opinion, these articles were grouped into 15 fields. Furthermore, these articles were categorised based on authors, publication date, name of journals, methods, tools, and type of research (MCDM utilising research, MCDM developing research, and MCDM proposing research). The results of this study indicated that in 2013 scholars have published articles more than in other years. In addition, the analytic hierarchy process (AHP) method in the individual tool...
704 citations
TL;DR: The ER rule completes and enhances [email protected]?s rule by identifying how to combine pieces of fully reliable evidence that are highly or completely conflicting through a new reliability perturbation analysis.
508 citations
TL;DR: The ER approach will be used to aggregate multiple environmental factors, resulting in an aggregated distributed assessment for each alternative policy, and a new analytical ER algorithm will be investigated which provides a means for using the ER approach in decision situations where an explicit ER aggregation function is needed.
468 citations
TL;DR: A multicriteria decision making approach for selecting sustainability transportation systems under partial or incomplete information (uncertainty) and its practical applicability and the ability to generate good quality solutions under uncertainty are presented.
Abstract: Sustainable transportation systems are the need of modern times There has been an unexpected growth in the number of transportation activities over years and the trend is expected to continue in the coming years This has obviously associated environmental costs like air pollution, noise, etc which is degrading the quality of life in modern cities To cope us this crisis, municipal administrations are investing in sustainable transportation systems that are not only efficient, robust and economical but also friendly towards environment The challenge before the transportation decision makers is how to evaluate and select such sustainable transportation systems In this paper, we present a multicriteria decision making approach for selecting sustainability transportation systems under partial or incomplete information (uncertainty) The proposed approach comprises of three steps In step 1, we identify the criteria for sustainability assessment of transportation In step 2, experts provide linguistic ratings to the potential alternatives against the selected criteria Fuzzy TOPSIS is used to generate aggregate scores for sustainability assessment and selection of best alternative In step 3, sensitivity analysis is performed to determine the influence of criteria weights on the decision making process A numerical illustration is provided to demonstrate the applicability of the approach The strength of the proposed work is its practical applicability and the ability to generate good quality solutions under uncertainty
256 citations
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 Jan 1976
TL;DR: This book develops an alternative to the additive set functions and the rule of conditioning of the Bayesian theory: set functions that need only be what Choquet called "monotone of order of infinity." and Dempster's rule for combining such set functions.
Abstract: Both in science and in practical affairs we reason by combining facts only inconclusively supported by evidence. Building on an abstract understanding of this process of combination, this book constructs a new theory of epistemic probability. The theory draws on the work of A. P. Dempster but diverges from Depster's viewpoint by identifying his "lower probabilities" as epistemic probabilities and taking his rule for combining "upper and lower probabilities" as fundamental. The book opens with a critique of the well-known Bayesian theory of epistemic probability. It then proceeds to develop an alternative to the additive set functions and the rule of conditioning of the Bayesian theory: set functions that need only be what Choquet called "monotone of order of infinity." and Dempster's rule for combining such set functions. This rule, together with the idea of "weights of evidence," leads to both an extensive new theory and a better understanding of the Bayesian theory. The book concludes with a brief treatment of statistical inference and a discussion of the limitations of epistemic probability. Appendices contain mathematical proofs, which are relatively elementary and seldom depend on mathematics more advanced that the binomial theorem.
14,565 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
TL;DR: The transferable belief model is described, a model for representing quantified beliefs based on belief functions that can be held at two levels: a credal level where beliefs are entertained and quantified by belief functions, and a pignisticlevel where beliefs can be used to make decisions and are quantification by probability functions.
2,089 citations
TL;DR: The analytic hierarchy process AHP is flawed as a procedure for ranking alternatives in that the rankings produced by this procedure are arbitrary as discussed by the authors, and the key to correcting this flaw is the synthesis of the AHP with the concepts of multiattribute utility theory.
Abstract: The analytic hierarchy process AHP is flawed as a procedure for ranking alternatives in that the rankings produced by this procedure are arbitrary. This paper provides a brief review of several areas of operational difficulty with the AHP, and then focuses on the arbitrary rankings that occur when the principle of hierarchic composition is assumed. This principle requires that the weights on the higher levels of a hierarchy can be determined independently of the weights on the lower levels. Virtually all of the published examples of the use of the AHP to evaluate alternatives relative to a set of criteria have assumed this principle. The key to correcting this flaw is the synthesis of the AHP with the concepts of multiattribute utility theory.
1,030 citations