A Pairwise Comparison Matrix Framework for Large-Scale Decision Making

abstract: A Pairwise Comparison Matrix (PCM) is used to compute for relative priorities of criteria or alternatives and are integral components of widely applied decision making tools: the Analytic Hierarchy Process (AHP) and its generalized form, the Analytic Network Process (ANP). However, a PCM suffers from several issues limiting its application to large-scale decision problems, specifically: (1) to the curse of dimensionality, that is, a large number of pairwise comparisons need to be elicited from a decision maker (DM), (2) inconsistent and (3) imprecise preferences maybe obtained due to the limited cognitive power of DMs. This dissertation proposes a PCM Framework for Large-Scale Decisions to address these limitations in three phases as follows. The first phase proposes a binary integer program (BIP) to intelligently decompose a PCM into several mutually exclusive subsets using interdependence scores. As a result, the number of pairwise comparisons is reduced and the consistency of the PCM is improved. Since the subsets are disjoint, the most independent pivot element is identified to connect all subsets. This is done to derive the global weights of the elements from the original PCM. The proposed BIP is applied to both AHP and ANP methodologies. However, it is noted that the optimal number of subsets is provided subjectively by the DM and hence is subject to biases and judgement errors. The second phase proposes a trade-off PCM decomposition methodology to decompose a PCM into a number of optimally identified subsets. A BIP is proposed to balance the: (1) time savings by reducing pairwise comparisons, the level of PCM inconsistency, and (2) the accuracy of the weights. The proposed methodology is applied to the AHP to demonstrate its advantages and is compared to established methodologies. In the third phase, a beta distribution is proposed to generalize a wide variety of imprecise pairwise comparison distributions via a method of moments methodology. A Non-Linear Programming model is then developed that calculates PCM element weights which maximizes the preferences of the DM as well as minimizes the inconsistency simultaneously. Comparison experiments are conducted using datasets collected from literature to validate the proposed methodology.Dissertation/ThesisPh.D. Industrial Engineering 201

Multi crteria decision making and its applications : a literature review

This paper presents current techniques used in Multi Criteria Decision Making (MCDM) and their applications. Two basic approaches for MCDM, namely Artificial Intelligence MCDM (AIMCDM) and Classical MCDM (CMCDM) are discussed and investigated. Recent articles from international journals related to MCDM are collected and analyzed to find which approach is more common than the other in MCDM. Also, which area these techniques are applied to. Those articles are appearing in journals for the year 2008 only. This paper provides evidence that currently, both AIMCDM and CMCDM are equally common in MCDM

Stochastic Judgments in the AHP: The Measurement of Rank Reversal Probabilities

Recently, the issue of rank reversal of alternatives in the Analytic Hierarchy Process (AHP) has captured the attention of a number of researchers. Most of the research on rank reversal has addressed the case where the pairwise comparisons of the alternatives are represented by single values, focusing on mathematical properties inherent to the AHP methodology that can lead to rank reversal if a new alternative is added or an existing one is deleted. A second situation, completely unrelated to the mathematical foundations of the AHP, in which rank reversal can occur is the case where the pairwise judgments are stochastic, rather than single values. If the relative preference ratings are uncertain, one has judgment intervals, and as a consequence there is a possibility that the rankings resulting from an AHP analysis are reversed, i.e., incorrect. It is important for modeler and decision maker alike to be aware of the likelihood that this situation of rank reversal will occur. In this paper, we introduce methods for assessing the relative preference of the alternatives in terms of their rankings, if the pairwise comparisons of the alternatives are stochastic. We develop multivariate statistical techniques to obtain point estimates and confidence intervals of the rank reversal probabilities, and show how simulation experiments can be used as an effective and accurate tool for analyzing the stability of the preference rankings under uncertainty. This information about the extent to which the ranking of the alternatives is sensitive to the stochastic nature of the pairwise judgments should be valuable information into the decision making process, much like variability and confidence intervals are crucial tools for statistical inference. Although the focus of our analysis is on stochastic preference judgments, our sampling method for estimating rank reversal probabilities can be extended to the case of non-stochastic imprecise fuzzy judgments. We provide simulation experiments and numerical examples comparing our method with that proposed previously by Saaty and Vargas (1987) for imprecise interval judgments

Organic farming and multicriteria decisions: An economic survey

Organic food production is a sphere where decision making is multi-facetted and complex. This applies to producers, political decision makers and consumers alike. This paper provides an overview of the economic methods that can aid such multi criteria decision making. We first provide an outline of the many different Multi-Criteria Analysis (MCA) techniques available and their relative advantages and disadvantages. In addition, theoretical and practical problems related to the use of Cost-Benefit Analysis (CBA) and MCA respectively are briefly discussed. We then review the MCA literature on case studies on organic farming. Based on this review we provide directional markers for future research where MCA may possibly be applied and adapted in order to provide useful knowledge and support for decision makers in the context of organic farming

Partner selection in agile supply chains: A fuzzy intelligent approach

Partner selection is a fundamental issue in supply chain management as it contributes significantly to overall supply chain performance. However, such decision-making is problematic due to the need to consider both tangible and intangible factors, which cause vagueness, ambiguity and complexity. This paper proposes a new fuzzy intelligent approach for partner selection in agile supply chains by using fuzzy set theory in combination with radial basis function artificial neural network. Using these two approaches in combination enables the model to classify potential partners in the qualification phase of partner selection efficiently and effectively using very large amounts of both qualitative and quantitative data. The paper includes a worked empirical application of the model with data from 84 representative companies within the Chinese electrical components and equipment industry, to demonstrate its suitability for helping organisational decision-makers in partner selection

Decision-making methods in engineering design: a designer-oriented approach

The use of decisional methods for the solution of engineering design problems has to be tackled on a "human" viewpoint. Hence, fundamental is the identification of design issues and needs that become a designer oriented viewpoint. Decision-based methods are systematically classified in MCDM methods, Structured Design methods and Problem Structuring methods. The results are organised in order to provide a first reference for the designer in a preliminary selection of decision-based methods. The paper shows the heterogeneous use of decision-based methods, traditionally expected to solve only some specific design problems, which have been used also in different design contexts. Moreover, several design issues, which emerged from the review process, have been pointed out and discussed accordingly. This review provided useful results for the enlargement of the state of the art on Decision Based Design methods in engineering design contexts

A Maut aprroach for reusing domain ontologies on the basis of the NeOn Methodlogy

Knowledge resource reuse has become a popular approach within the ontology engineering field, mainly because it can speed up the ontology development process, saving time and money and promoting the application of good practices. The NeOn Methodology provides guidelines for reuse. These guidelines include the selection of the most appropriate knowledge resources for reuse in ontology development. This is a complex decision-making problem where different conflicting objectives, like the reuse cost, understandability, integration workload and reliability, have to be taken into account simultaneously. GMAA is a PC-based decision support system based on an additive multi-attribute utility model that is intended to allay the operational difficulties involved in the Decision Analysis methodology. The paper illustrates how it can be applied to select multimedia ontologies for reuse to develop a new ontology in the multimedia domain. It also demonstrates that the sensitivity analyses provided by GMAA are useful tools for making a final recommendation