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

Two Applications Involving the Analytic Hierarchy Process

The analytic hierarchy process (AHP) is a popular tool used in decision making for ranking alternatives based on quantitative and qualitative criteria. In this thesis, we investigate two applications involving the AHP: determining the greatest sports records and generating priority vectors for inconsistent interval judgments. We determine rankings of the greatest active single-season, career, and single-event sports records by applying the ratings mode of the AHP. In addition, we present an extension to a linear programming method used for generating priority vectors for interval pairwise comparison matrices. By introducing multiplicative stretch factors for each interval comparison, our linear programming method with stretching can be used to solve problems when inconsistent interval judgments are present. We describe the linear programming method, apply it to three problems, and compare its performance to other methods for solving inconsistent interval AHP problems

Incomplete interval fuzzy preference relations and their applications

This paper investigates incomplete interval fuzzy preference relations. A characterization, which is proposed by Herrera-Viedma et al. (2004), of the additive consistency property of the fuzzy preference relations is extended to a more general case. This property is further generalized to interval fuzzy preference relations (IFPRs) based on additive transitivity. Subsequently, we examine how to characterize IFPR. Using these new characterizations, we propose a method to construct an additive consistent IFPR from a set of n − 1 preference data and an estimation algorithm for acceptable incomplete IFPRs with more known elements. Numerical examples are provided to illustrate the effectiveness and practicality of the solution process

Incomplete interval fuzzy preference relations for supplier selection in supply chain management

In the analytical hierarchy process (AHP), it needs the decision maker to establish a pairwise comparison matrix requires n(n–1)/2 judgments for a level with n criteria (or alternatives). In some instances, the decision maker may have to deal with the problems in which only partial information and uncertain preference relation is available. Consequently, the decision maker may provide interval fuzzy preference relation with incomplete information. In this paper, we focus our attention on the investigation of incomplete interval fuzzy preference relation. We first extend a characterization to the interval fuzzy preference relation which is based on the additive transitivity property. Using the characterization, we propose a method to construct interval additive consistent fuzzy preference relations from a set of n–1 preference data. The study reveals that the proposed method can not only alleviate the comparisons, but also ensure interval preference relations with the additive consistent property. We also develop a novel procedure to deal with the analytic hierarchy problem for group decision making with incomplete interval fuzzy preference relations. Finally, a numerical example is illustrated and a supplier selection case in supply chain management is investigated using the proposed method. First published online: 05 Feb 201

ANALYTIC HIERARCHY PROCESS APPROACH FOR SELECTION AND EVALUATION OF MAINTENANCE STRATEGY

Selection of suitable maintenance strategy has always been vital for the industries. The selection deals with the large number of tangible and intangible attributes. Estimation of the optimal maintenance strategies for the different failure modes represents the main complexity of the selection process. Equipment, as well as the available maintenance facilities, tools and capabilities delimit the selection of the type of maintenance. In many cases, the selection requires the knowledge of various factors such as safety aspects, environmental problems, costs and budget constraints, manpower utilization and etc. This project presents Analytic Hierarchy Process (AHP) approach to define the best strategies for maintenance of mechanical systems or equipment. The main objective is to develop an application, which would assist in quick selection of maintenance strategy using AHP. User friendly application is developed to assist the user in selection, and weighting the criterions and alternatives. The final output is the scores of each maintenance strategy that will aid in ranking. However, the user is also offered predetermined sets of weightings of criterions and alternatives that are dependent on risk analysis results. Since risk contributes towards decision making by affecting the weighting considerations, the classic definition of risk that accounts both the probability and consequence of accident or failure is also considered, and equipment can be categorized into four risk zones based user’s judgment or assessment results, if any conducted. The developed decision framework is tested for validity of results with help of two case studies. The results obtained prove the validity of developed framework

Optimization for Decision Making II

In the current context of the electronic governance of society, both administrations and citizens are demanding the greater participation of all the actors involved in the decision-making process relative to the governance of society. This book presents collective works published in the recent Special Issue (SI) entitled “Optimization for Decision Making II”. These works give an appropriate response to the new challenges raised, the decision-making process can be done by applying different methods and tools, as well as using different objectives. In real-life problems, the formulation of decision-making problems and the application of optimization techniques to support decisions are particularly complex and a wide range of optimization techniques and methodologies are used to minimize risks, improve quality in making decisions or, in general, to solve problems. In addition, a sensitivity or robustness analysis should be done to validate/analyze the influence of uncertainty regarding decision-making. This book brings together a collection of inter-/multi-disciplinary works applied to the optimization of decision making in a coherent manner

ANALYTIC HIERARCHY PROCESS APPROACH FOR SELECTION AND EVALUATION OF MAINTENANCE STRATEGY

Selection of suitable maintenance strategy has always been vital for the industries. The selection deals with the large number of tangible and intangible attributes. Estimation of the optimal maintenance strategies for the different failure modes represents the main complexity of the selection process. Equipment, as well as the available maintenance facilities, tools and capabilities delimit the selection of the type of maintenance. In many cases, the selection requires the knowledge of various factors such as safety aspects, environmental problems, costs and budget constraints, manpower utilization and etc. This project presents Analytic Hierarchy Process (AHP) approach to define the best strategies for maintenance of mechanical systems or equipment. The main objective is to develop an application, which would assist in quick selection of maintenance strategy using AHP. User friendly application is developed to assist the user in selection, and weighting the criterions and alternatives. The final output is the scores of each maintenance strategy that will aid in ranking. However, the user is also offered predetermined sets of weightings of criterions and alternatives that are dependent on risk analysis results. Since risk contributes towards decision making by affecting the weighting considerations, the classic definition of risk that accounts both the probability and consequence of accident or failure is also considered, and equipment can be categorized into four risk zones based user’s judgment or assessment results, if any conducted. The developed decision framework is tested for validity of results with help of two case studies. The results obtained prove the validity of developed framework