Pairwise comparison matrix in multiple criteria decision making

The measurement scales, consistency index, inconsistency issues, missing judgment estimation and priority derivation methods have been extensively studied in the pairwise comparison matrix (PCM). Various approaches have been proposed to handle these problems, and made great contributions to the decision making. This paper reviews the literature of the main developments of the PCM. There are plenty of literature related to these issues, thus we mainly focus on the literature published in 37 peer reviewed international journals from 2010 to 2015 (searched via ISI Web of science). We attempt to analyze and classify these literatures so as to find the current hot research topics and research techniques in the PCM, and point out the future directions on the PCM. It is hoped that this paper will provide a comprehensive literature review on PCM, and act as informative summary of the main developments of the PCM for the researchers for their future research. First published online: 02 Sep 201

A multi-step goal programming approach for group decision making with incomplete interval additive reciprocal comparison matrices

This article presents a goal programming framework to solve group decision making problems where decision-makers’ judgments are provided as incomplete interval additive reciprocal comparison matrices (IARCMs). New properties of multiplicative consistent IARCMs are put forward and used to define consistent incomplete IARCMs. A two-step goal programming method is developed to estimate missing values for an incomplete IARCM. The first step minimizes the inconsistency of the completed IARCMs and controls uncertainty ratios of the estimated judgments within an acceptable threshold, and the second step finds the most appropriate estimated missing values among the optimal solutions obtained from the previous step. A weighted geometric mean approach is proposed to aggregate individual IARCMs into a group IARCM by employing the lower bounds of the interval additive reciprocal judgments. A two-step procedure consisting of two goal programming models is established to derive interval weights from the group IARCM. The first model is devised to minimize the absolute difference between the logarithm of the group preference and that of the constructed multiplicative consistent judgment. The second model is developed to generate an interval-valued priority vector by maximizing the uncertainty ratio of the constructed consistent IARCM and incorporating the optimal objective value of the first model as a constraint. Two numerical examples are furnished to demonstrate validity and applicability of the proposed approach

Approaches to improving consistency of interval fuzzy preference relations

This article introduces a consistency index for measuring the consistency level of an interval fuzzy preference relation (IFPR). An approach is then proposed to construct an additive consistent IFPR from a given inconsistent IFPR. By using a weighted averaging method combining the original IFPR and the constructed consistent IFPR, a formula is put forward to repair an inconsistent IFPR to generate an IFPR with acceptable consistency. An iterative algorithm is subsequently developed to rectify an inconsistent IFPR and derive one with acceptable consistency and weak transitivity. The proposed approaches can not only improve consistency of IFPRs but also preserve the initial interval uncertainty information as much as possible. Numerical examples are presented to illustrate how to apply the proposed approaches

Introduction to the Analytic Hierarchy Process

The Analytic Hierarchy Process (AHP) has been one of the foremost mathematical methods for decision making with multiple criteria and has been widely studied in the operations research literature as well as applied to solve countless real-world problems. This book is meant to introduce and strengthen the readers’ knowledge of the AHP, no matter how familiar they may be with the topic. This book provides a concise, yet self-contained, introduction to the AHP that uses a novel and more pedagogical approach. It begins with an introduction to the principles of the AHP, covering the critical points of the method, as well as some of its applications. Next, the book explores further aspects of the method, including the derivation of the priority vector, the estimation of inconsistency, and the use of AHP for group decisions. Each of these is introduced by relaxing initial assumptions. Furthermore, this booklet covers extensions of AHP, which are typically neglected in elementary expositions of the methods. Such extensions concern different numerical representations of preferences and the interval and fuzzy representations of preferences to account for uncertainty. During the whole exposition, an eye is kept on the most recent developments of the method.Peer reviewe

Distance-based consensus models for fuzzy and multiplicative 3 preference relations

This paper proposes a distance-based consensus model for fuzzy preference relations where the weights of fuzzy preference relations are automatically determined. Two indices, an individual to group consensus index (ICI) and a group consensus index (GCI), are introduced. An iterative consensus reaching algorithm is presented and the process terminates until both the ICI and GCI are controlled within predefined thresholds. The model and algorithm are then extended to handle multiplicative preference relations. Finally, two examples are illustrated and comparative analyses demonstrate the effectiveness of the proposed methods

Uncertain Multi-Criteria Optimization Problems

Most real-world search and optimization problems naturally involve multiple criteria as objectives. Generally, symmetry, asymmetry, and anti-symmetry are basic characteristics of binary relationships used when modeling optimization problems. Moreover, the notion of symmetry has appeared in many articles about uncertainty theories that are employed in multi-criteria problems. Different solutions may produce trade-offs (conflicting scenarios) among different objectives. A better solution with respect to one objective may compromise other objectives. There are various factors that need to be considered to address the problems in multidisciplinary research, which is critical for the overall sustainability of human development and activity. In this regard, in recent decades, decision-making theory has been the subject of intense research activities due to its wide applications in different areas. The decision-making theory approach has become an important means to provide real-time solutions to uncertainty problems. Theories such as probability theory, fuzzy set theory, type-2 fuzzy set theory, rough set, and uncertainty theory, available in the existing literature, deal with such uncertainties. Nevertheless, the uncertain multi-criteria characteristics in such problems have not yet been explored in depth, and there is much left to be achieved in this direction. Hence, different mathematical models of real-life multi-criteria optimization problems can be developed in various uncertain frameworks with special emphasis on optimization problems

Multi-criteria decision methods to support the maintenance management of complex systems

[ES] Esta tesis doctoral propone el uso de métodos de toma de decisiones multi-criterio (MCDM, por sus iniciales en inglés) como herramienta estratégica para apoyar la gestión del mantenimiento de sistemas complejos. El desarrollo de esta tesis doctoral se enmarca dentro de un acuerdo de cotutela entre la Università degli Studi di Palermo (UNIPA) y la Universitat Politècnica de València (UPV), dentro de sus respectivos programas de doctorado en 'Ingeniería de Innovación Tecnológica' y 'Matemáticas'. Estos programas están estrechamente vinculados a través del tópico MCDM, ya que proporciona herramientas cruciales para gestionar el mantenimiento de sistemas complejos reales utilizando análisis matemáticos serios. El propósito de esta sinergia es tener en cuenta de forma sólida la incertidumbre al atribuir evaluaciones subjetivas, recopilar y sintetizar juicios atribuidos por varios responsables de la toma de decisiones, y tratar con conjuntos grandes de esos elementos. El tema principal del presente trabajo de doctorado es el gestionamiento de las actividades de mantenimiento para aumentar los niveles de innovación tecnológica y el rendimiento de los sistemas complejos. Cualquier sistema puede ser considerado objeto de estudio, incluidos los sistemas de producción y los de prestación de servicios, entre otros, mediante la evaluación de sus contextos reales. Esta tesis doctoral propone afrontar la gestión del mantenimiento a través del desarrollo de tres líneas principales de investigación estrechamente vinculadas. ¿ La primera es el núcleo, e ilustra la mayoría de los aspectos metodológicos de la tesis. Se refiere al uso de métodos MCDM para apoyar decisiones estratégicas de mantenimiento, y para hacer frente a la incertidumbre que afecta a los datos/evaluaciones, incluso cuando están involucrados varios responsables (expertos en mantenimiento) en la toma de decisiones. ¿ La segunda línea desarrolla análisis de fiabilidad para sistemas complejos reales (también en términos de fiabilidad humana) sobre cuya base se debe implementar cualquier actividad de mantenimiento. Estos análisis consideran la configuración de fiabilidad de los componentes del sistema en estudio y las características específicas del entorno operativo. ¿ La tercera línea de investigación aborda aspectos metodológicos importantes de la gestión de mantenimiento y enfatiza la necesidad de monitorizar el funcionamiento de las actividades de mantenimiento y de evaluar su efectividad utilizando indicadores adecuados. Se ha elaborado una amplia gama de casos de estudio del mundo real para evaluar la eficacia de los métodos MCDM en el mantenimiento y así probar la utilidad del enfoque propuesto.[CA] Aquesta tesi doctoral proposa l'ús de mètodes de presa de decisions multi-criteri (MCDM, per les seves inicials en anglès) com a eina estratègica per donar suport a la gestió del manteniment de sistemes complexos. El desenvolupament d'aquesta tesi doctoral s'emmarca dins d'un acord de cotutela entre la Università degli Studi di Palermo (UNIPA) i la Universitat Politècnica de València (UPV), dins dels seus respectius programes de doctorat en 'Enginyeria d'Innovació Tecnològica' i ' Matemàtiques '. Aquests programes estan estretament vinculats a través del tòpic MCDM, ja que proporciona eines crucials per gestionar el manteniment de sistemes complexos reals utilitzant anàlisis matemàtics profunds. El propòsit d'aquesta sinergia és tenir en compte de forma sòlida la incertesa en atribuir avaluacions subjectius, recopilar i sintetitzar judicis atribuïts per diversos responsables de la presa de decisions, i tractar amb conjunts grans d'aquests elements en els problemes plantejats. El tema principal del present treball de doctorat es la gestió de les activitats de manteniment per augmentar els nivells d'innovació tecnològica i el rendiment dels sistemes complexos. Qualsevol sistema pot ser considerat objecte d'estudi, inclosos els sistemes de producció i els de prestació de serveis, entre d'altres, mitjançant l'avaluació dels seus contextos reals. Aquesta tesi doctoral proposa afrontar la gestió del manteniment mitjançant el desenvolupament de tres línies principals d'investigació estretament vinculades. ¿ La primera és el nucli, i il·lustra la majoria dels aspectes metodològics de la tesi. Es refereix a l'ús de mètodes MCDM per donar suport a decisions estratègiques de manteniment, i per fer front a la incertesa que afecta les dades/avaluacions, fins i tot quan estan involucrats diversos responsables (experts en manteniment) en la presa de decisions. ¿ La segona línia desenvolupa anàlisis de fiabilitat per a sistemes complexos reals (també en termes de fiabilitat humana) sobre la qual base s'ha d'implementar qualsevol activitat de manteniment. Aquestes anàlisis consideren la configuració de fiabilitat dels components del sistema en estudi i les característiques específiques de l'entorn operatiu. ¿ La tercera línia d'investigació aborda aspectes metodològics importants de la gestió de manteniment i emfatitza la necessitat de monitoritzar el funcionament de les activitats de manteniment i d'avaluar la seva efectivitat utilitzant indicadors adequats. S'ha elaborat una àmplia gamma de casos d'estudi del món real per avaluar l'eficàcia dels mètodes MCDM en el manteniment i així provar la utilitat de l'enfocament proposat.[EN] This doctoral thesis proposes using multi-criteria decision making (MCDM) methods as a strategic tool to support maintenance management of complex systems. The development of this doctoral thesis is framed within a cotutelle (co-tutoring) agreement between the Università degli Studi di Palermo (UNIPA) and the Universitat Politècnica de València (UPV), within their respective programmes of doctorates in 'Technological Innovation Engineering' and 'Mathematics'. Regarding this thesis, these programmes are closely linked through the topic of MCDM, providing crucial tools to manage maintenance of real complex systems by applying in-depth mathematical analyses. The purpose of this connection is to robustly take into account uncertainty in attributing subjective evaluations, collecting and synthetizing judgments attributed by various decision makers, and dealing with large sets of elements characterising the faced issue. The main topic of the present doctoral work is the management of maintenance activities to increase the levels of technological innovation and performance of the analysed complex systems. All kinds of systems can be considered as objects of study, including production systems and service delivery systems, among others, by evaluating their real contexts. Thus, this doctoral thesis proposes facing maintenance management through the development of three tightly linked main research lines. ¿ The first is the core and illustrates most of the methodological aspects of the thesis. It refers to the use of MCDM methods for supporting strategic maintenance decisions, and dealing with uncertainty affecting data/evaluations even when several decision makers are involved (experts in maintenance). ¿ The second line develops reliability analyses for real complex systems (also in terms of human reliability analysis) on the basis of which any maintenance activity must be implemented. These analyses are approached by considering the reliability configuration of both the components belonging to the system under study and the specific features of the operational environment. ¿ The third research line focuses on important methodological aspects to support maintenance management, and emphasises the need to monitor the performance of maintenance activities and evaluate their effectiveness using suitable indicators. A wide range of real real-world case studies has been faced to evaluate the effectiveness of MCDM methods in maintenance and then prove the usefulness of the proposed approach.Carpitella, S. (2019). Multi-criteria decision methods to support the maintenance management of complex systems [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/11911

Applying the Analytic Hierarchy Process to Oil Sands Environmental Compliance Risk Management

Oil companies in Alberta, Canada, invested $32 billion on new oil sands projects in 2013. Despite the size of this investment, there is a demonstrable deficiency in the uniformity and understanding of environmental legislation requirements that manifest into increased project compliance risks. This descriptive study developed 2 prioritized lists of environmental regulatory compliance risks and mitigation strategies and used multi-criteria decision theory for its theoretical framework. Information from compiled lists of environmental compliance risks and mitigation strategies was used to generate a specialized pairwise survey, which was piloted by 5 subject matter experts (SMEs). The survey was validated by a sample of 16 SMEs, after which the Analytic Hierarchy Process (AHP) was used to rank a total of 33 compliance risks and 12 mitigation strategy criteria. A key finding was that the AHP is a suitable tool for ranking of compliance risks and mitigation strategies. Several working hypotheses were also tested regarding how SMEs prioritized 1 compliance risk or mitigation strategy compared to another. The AHP showed that regulatory compliance, company reputation, environmental compliance, and economics ranked the highest and that a multi criteria mitigation strategy for environmental compliance ranked the highest. The study results will inform Alberta oil sands industry leaders about the ranking and utility of specific compliance risks and mitigations strategies, enabling them to focus on actions that will generate legislative and public trust. Oil sands leaders implementing a risk management program using the risks and mitigation strategies identified in this study will contribute to environmental conservation, economic growth, and positive social change

Improving decision quality in the analytic hierarchy process implementation through knowledge management strategies.

The Analytic Hierarchy Process (AHP) is a multi-attribute decision making method that structures a decision problem hierarchically in terms of its objective, attributes, sub-attributes, and alternatives.AHP model selection methodology. Two AHP hierarchies were developed to advance knowledge with respect to AHP application. (1) A decision hierarchy comprised of four attributes and fifteen sub-attributes was developed and can be used by organizations to assess capital investment projects. (2) The application of the capital investment decision hierarchy produced cost and quality measurement data that can be used to evaluate alternative AHP models. (3) An AHP model selection methodology, including a decision hierarchy comprised of cost and quality attributes and sub-attributes was developed. The methodology can be used to select the most appropriate AHP model to use in prioritizing capital investment projects from the three AHP models used in this experimental process. AHP model alternative priority weightings with respect to sub-attributes were established through AHP implementation cost and decision quality data obtained through this experimental research. (4) An AHP model selection decision tree was developed to determine the most appropriate AHP model based on cost and quality attribute and sub-attribute priority weightings. (Abstract shortened by UMI.)This dissertation research made contributions in two categories: (1) analysis of AHP decision cost and quality, and (2) AHP model selection methodology. The specific contributions within each category are:The goals of this dissertation were to evaluate the impact of knowledge management strategies on AHP decision cost and quality outcomes and to develop an AHP model selection methodology.Analysis of AHP decision cost and quality. Based on the relative importance of quality and cost, recommendations are made for the use of knowledge management strategies and group size. (1) The use of knowledge management strategies did not significantly improve decision quality with respect to group consistency, individual consensus or group consensus. (2) A group size of seven versus a group size of five significantly improved decision quality with respect to group consistency. (3) The use of knowledge management strategies did not significantly increase mental workload; tasks performed using electronic meeting technology resulted in significantly lower mental workload

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