The dynamics of consensus in group decision making: investigating the pairwise interactions between fuzzy preferences.

In this paper we present an overview of the soft consensus model in group decision making and we investigate the dynamical patterns generated by the fundamental pairwise preference interactions on which the model is based. The dynamical mechanism of the soft consensus model is driven by the minimization of a cost function combining a collective measure of dissensus with an individual mechanism of opinion changing aversion. The dissensus measure plays a key role in the model and induces a network of pairwise interactions between the individual preferences. The structure of fuzzy relations is present at both the individual and the collective levels of description of the soft consensus model: pairwise preference intensities between alternatives at the individual level, and pairwise interaction coefficients between decision makers at the collective level. The collective measure of dissensus is based on non linear scaling functions of the linguistic quantifier type and expresses the degree to which most of the decision makers disagree with respect to their preferences regarding the most relevant alternatives. The graded notion of consensus underlying the dissensus measure is central to the dynamical unfolding of the model. The original formulation of the soft consensus model in terms of standard numerical preferences has been recently extended in order to allow decision makers to express their preferences by means of triangular fuzzy numbers. An appropriate notion of distance between triangular fuzzy numbers has been chosen for the construction of the collective dissensus measure. In the extended formulation of the soft consensus model the extra degrees of freedom associated with the triangular fuzzy preferences, combined with non linear nature of the pairwise preference interactions, generate various interesting and suggestive dynamical patterns. In the present paper we investigate these dynamical patterns which are illustrated by means of a number of computer simulations.

Evaluation of e-learning web sites using fuzzy axiomatic design based approach

High quality web site has been generally recognized as a critical enabler to conduct online business. Numerous studies exist in the literature to measure the business performance in relation to web site quality. In this paper, an axiomatic design based approach for fuzzy group decision making is adopted to evaluate the quality of e-learning web sites. Another multi-criteria decision making technique, namely fuzzy TOPSIS, is applied in order to validate the outcome. The methodology proposed in this paper has the advantage of incorporating requirements and enabling reductions in the problem size, as compared to fuzzy TOPSIS. A case study focusing on Turkish e-learning websites is presented, and based on the empirical findings, managerial implications and recommendations for future research are offered

Dealing with Incomplete Information in Linguistic Group Decision Making by Means of Interval Type-2 Fuzzy Sets

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Nowadays in the social network based decision making processes, as the ones involved in e-commerce and e-democracy, multiple users with di erent backgrounds may take part and diverse alternatives might be involved. This diversity enriches the process but at the same time increases the uncertainty in the opinions. This uncertainty can be considered from two di erent perspectives: (i) the uncertainty in the meaning of the words given as preferences, that is motivated by the heterogeneity of the decision makers, (ii) the uncertainty inherent to any decision making process that may lead to an expert not being able to provide all their judgments. The main objective of this contribution is to address these two type of uncertainty. To do so the following approaches are proposed: Firstly, in order to capture, process and keep the uncertainty in the meaning of the linguistic assumption the Interval Type 2 Fuzzy Sets are introduced as a way to model the experts linguistic judgments. Secondly, a measure of the coherence of the information provided by each decision maker is proposed. Finally, a consistency based completion approach is introduced to deal with the uncertainty presented in the expert judgments. The proposed approach is tested in an e-democracy decision making scenario

Managing Incomplete Preference Relations in Decision Making: A Review and Future Trends

In decision making, situations where all experts are able to efficiently express their preferences over all the available options are the exception rather than the rule. Indeed, the above scenario requires all experts to possess a precise or sufficient level of knowledge of the whole problem to tackle, including the ability to discriminate the degree up to which some options are better than others. These assumptions can be seen unrealistic in many decision making situations, especially those involving a large number of alternatives to choose from and/or conflicting and dynamic sources of information. Some methodologies widely adopted in these situations are to discard or to rate more negatively those experts that provide preferences with missing values. However, incomplete information is not equivalent to low quality information, and consequently these methodologies could lead to biased or even bad solutions since useful information might not being taken properly into account in the decision process. Therefore, alternative approaches to manage incomplete preference relations that estimates the missing information in decision making are desirable and possible. This paper presents and analyses methods and processes developed on this area towards the estimation of missing preferences in decision making, and highlights some areas for future research

A review of fuzzy AHP methods for decision-making with subjective judgements

Analytic Hierarchy Process (AHP) is a broadly applied multi-criteria decision-making method to determine the weights of criteria and priorities of alternatives in a structured manner based on pairwise comparison. As subjective judgments during comparison might be imprecise, fuzzy sets have been combined with AHP. This is referred to as fuzzy AHP or FAHP. An increasing amount of papers are published which describe different ways to derive the weights/priorities from a fuzzy comparison matrix, but seldomly set out the relative benefits of each approach so that the choice of the approach seems arbitrary. A review of various fuzzy AHP techniques is required to guide both academic and industrial experts to choose suitable techniques for a specific practical context. This paper reviews the literature published since 2008 where fuzzy AHP is applied to decision-making problems in industry, particularly the various selection problems. The techniques are categorised by the four aspects of developing a fuzzy AHP model: (i) representation of the relative importance for pairwise comparison, (ii) aggregation of fuzzy sets for group decisions and weights/priorities, (iii) defuzzification of a fuzzy set to a crisp value for final comparison, and (iv) consistency measurement of the judgements. These techniques are discussed in terms of their underlying principles, origins, strengths and weakness. Summary tables and specification charts are provided to guide the selection of suitable techniques. Tips for building a fuzzy AHP model are also included and six open questions are posed for future work

Comprehensive Power Transformers Evaluation based on Multi-Criteria Decision-Making Approach

Selection of adequate power transformers is among the most important factors for ensuring well-operated and optimized power generation and distribution systems, which imposes the need for applying optimization methods in order to obtain comprehensive evaluation process. In the paper, a multi-criteria group decision-making supportive model for the power transformer evaluation is proposed; the model is based on integration of the Analytic Hierarchy Process (AHP) and the compromise ranking method with fuzzy Set Theory. The AHP method was utilized in order to estimate the criteria relative weights, whereas the compromise ranking method was used for alternative assessment and compromise ranking. Integration of the fuzzy logic within the proposed model allows dealing with problem of the ambiguities of human perceptions and provides more rational results. A numerical example illustrates the proposed methodology on the real MCDM problem of power transformers selection

Consistency based completion approaches of incomplete preference relations in uncertain decision contexts.

Uncertainty, hesitation and vagueness are inherent to human beings when articulating opinions and preferences. Therefore in decision making situations it might well be the case that experts are unable to express their opinions in an accurate way. Under these circumstances, various families of preference relations (PRs) have been proposed (linguistic, intuitionistic and interval fuzzy PRs) to allow the experts to manifest some degree of hesitation when enunciating their opinions. An extreme case of uncertainty happens when an expert is unable to differentiate the degree up to which one preference is preferred to another. Henceforth, incomplete preference relations are possible. It is worth to bear in mind that incomplete information does not mean low quality information, on the contrary, in many occasions experts might prefer no to provide information in other to keep consistency. Consequently mechanism to deal with incomplete information in decision making are necessary. This contribution presents the main consistency based completion approaches to estimate incomplete preference values in linguistic, intuitionistic and interval fuzzy PRs

Methodology for the evaluation and design of projects considering multiple criteria and uncertainty. Application to the development of energy projects in rural areas

Tesi en modalitat de compendi de publicacionsIn 2015, the United Nations defined the Sustainable Development Goals in a transition towards a world without poverty and where human rights, equity and sustainability are prioritized. In particular, modern energy services are considered crucial not only to achieve universal access to energy by 2030, but due to their contribution to alleviate chronical poverty, reduce food insecurity, promote the access to modern information in schools and enhance the start of productive activities. However, the aim of global access by 2030 is still far from being complete, with more than 700 million people living in rural areas without access to electricity and using firewood and other polluting traditional biomass for cooking and heating. Decentralized energy systems are gaining attention as a more feasible solution than grid extension to provide energy to rural and inaccessible areas. The evaluation and design of decentralized systems is a complex process that needs to take into account multiple alternatives and criteria to ensure a long-term sustainability, but usually available studies in literature focus exclusively in technical and economic aspects. Also, the minority of studies following a multicriteria decision-making approach underestimate the effect of the potential lack of confidence of the experts and users consulted to weight the importance of each criterion or to evaluate a specific alternative. In this context, the objective of this thesis is to develop multicriteria procedures considering uncertainty to increase the robustness of the results. These procedures are applied to projects that foster access to energy services and promote therefore the development of rural and underprivileged areas. The thesis begins with two multicriteria procedures presented for the evaluation and the design, respectively, of rural electrification projects. These procedures are applied to two real case studies in Peru and Nigeria. Both applications provide valuable insights, for local authorities and other promoters of electrification systems in similar contexts, regarding which technologies and configurations to use in determined circumstances. At the same time, the analysis carried out enable an improvement regarding the robustness of results through the consideration of the lack of confidence of the opinions collected about the importance of the criteria and the evaluation of the alternatives. In this regard, A Methodology for Multicriteria Decision-making considering Uncertainty (MIMDU) is then developed based on fuzzy numbers to include the lack of confidence experts and users might have when weighting a criterion or evaluating an alternative. The methodology designed includes a novel procedure to quantify human opinions with non-pre-defined fuzzy numbers and a systematic process to calculate diverse rankings of alternatives and provide complimentary information that leads to a more robust decision-making. Indeed, the potential of the methodology is illustrated with an example case that shows how the lack of confidence can affect the alternatives ranking and the subsequent decision. Finally, the methodology is applied to a real case study in Colombia to select the best alternative for digestate post-treatment before its application to agricultural soil as a fertilizer. The use of MIMDU presents three major beneficial outcomes for multicriteria decision-making to foster rural development. First, the consideration of the lack of confidence of the respondents can reduce the pressure they might feel when providing an answer without complete knowledge. Second, it allows a more accurate quantification of the opinions given, turning, for example, more hesitant answers into less reliable evaluations of an alternative, that worsens its final ranking. And third, more robust decisions can be taken due to the major precision in the modelling of opinions and the possibility of comparing crisp and fuzzy-based rankings of the alternatives.Dins dels objectius de desenvolupament sostenibles, els serveis energètics moderns es consideren crucials no només per aconseguir l'accés universal a l'energia el 2030, sinó per la seva contribució a pal·liar la pobresa crònica, reduir la inseguretat alimentària, promoure l'accés a la informació moderna a les escoles i permetre l'inici d'activitats productives. Tot i això, l’objectiu d’accés mundial per al 2030 encara està lluny d’acomplir-se, ja que més de 700 milions de persones viuen a les zones rurals sense accés a l’electricitat i utilitzen llenya i altres biomasses tradicionals contaminants per cuinar i escalfar. Els sistemes energètics descentralitzats guanyen pes respecte l’extensió de la xarxa per proporcionar energia a zones rurals i inaccessibles. L’avaluació i el disseny d’aquests sistemes és un procés complex que ha de tenir en compte múltiples alternatives i criteris per garantir una sostenibilitat a llarg termini, però els estudis de literatura disponibles generalment se centren exclusivament en aspectes tècniques i econòmiques. A més, la minoria d’estudis que segueixen un enfocament multicriteri subestimen l’efecte de la manca de confiança potencial dels experts i usuaris consultats per ponderar la importància de cada criteri o avaluar una alternativa específica. En aquest context, l'objectiu d'aquesta tesi és desenvolupar procediments multicriteri considerant la incertesa per afavorir l’obtenció de resultats robustos. Aquests procediments s’apliquen a projectes que afavoreixen l’accés als serveis energètics i promouen, per tant, el desenvolupament de zones rurals i desfavorides. La tesi comença amb dos procediments multicriteri presentats per a l'avaluació i el disseny, respectivament, de projectes d'electrificació rural. Aquests procediments s'apliquen a dos casos pràctics reals al Perú i Nigèria. Ambdues aplicacions proporcionen informació valuosa, per a les autoritats locals i altres promotors de sistemes d’electrificació en contextos similars, sobre quines tecnologies i configuracions a utilitzar en determinades circumstàncies. Al mateix temps, les anàlisis realitzades permeten una millora en quant a la solidesa dels resultats mitjançant la consideració de la manca de confiança de les opinions recollides sobre la importància dels criteris i l’avaluació de les alternatives. Per fer-ho, es desenvolupa una metodologia per a la presa de decisions multicriteri que té en compte la incertesa (MIMDU) basada en nombres difusos per incloure la manca de confiança que els experts i usuaris podrien tenir quan ponderen un criteri o avaluen una alternativa. La metodologia dissenyada inclou un nou procediment per quantificar opinions humanes amb nombres difusos no predefinits i un procés sistemàtic per calcular diversos rànquings d’alternatives i proporcionar informació complementària que condueix a una presa de decisions més robusta. De fet, el potencial de la metodologia s’il·lustra amb un cas d’exemple que mostra com la manca de confiança pot afectar el rànquing d’alternatives i la decisió posterior. Finalment, la metodologia s'aplica a un estudi de cas real a Colòmbia per seleccionar la millor alternativa per al post-tractament del digestat abans de la seva aplicació a sòl agrícola com a fertilitzant. L’ús de MIMDU presenta tres grans beneficis per a la presa de decisions multicriteri per fomentar el desenvolupament rural. En primer lloc, la consideració de la manca de confiança dels enquestats pot reduir la pressió que podrien sentir al donar una resposta sense coneixement complet. En segon lloc, permet una quantificació més precisa de les opinions donades, convertint, per exemple, respostes més dubtoses en avaluacions menys fiables d’una alternativa, que empitjora la seva classificació final. I, en tercer lloc, es poden prendre decisions més robustes a causa de la precisió en la modelització d’opinionsEn 2015, la Organización de las Naciones Unidas definió los Objetivos de Desarrollo Sostenible en una transición hacia un mundo sin pobreza y donde se priorizan los derechos humanos, la equidad y la sostenibilidad. En particular, los servicios energéticos modernos se consideran cruciales no solo para lograr el acceso universal a la energía en 2030, sino por su contribución para aliviar la pobreza crónica, reducir la inseguridad alimentaria, promover el acceso a la información en las escuelas y permitir el inicio de actividades productivas. Sin embargo, el objetivo de acceso global a la energía para 2030 aún está lejos de ser completo, con más de 700 millones de personas viviendo en áreas rurales sin acceso a electricidad y utilizando leña y otra biomasa tradicional contaminante, para cocinar y calentar. Los sistemas de energía descentralizados están ganando peso respecto a la extensión de la red para proporcionar energía a áreas rurales e inaccesibles. La evaluación y el diseño de sistemas descentralizados es un proceso complejo que precisa considerar múltiples alternativas y criterios para que sea sostenible a largo plazo, pero los estudios disponibles en la literatura generalmente se enfocan exclusivamente en aspectos técnicos y económicos. Asimismo, la minoría de estudios que siguen un enfoque de toma de decisiones multicriterio subestiman el efecto de la potencial falta de confianza de los expertos y usuarios consultados para ponderar la importancia de cada criterio o para evaluar una alternativa específica. En este contexto, el objetivo de esta tesis es desarrollar procedimientos multicriterio considerando la incertidumbre para aumentar la robustez de los resultados. Estos procedimientos se aplican a proyectos que fomentan el acceso a los servicios energéticos y, por tanto, promueven el desarrollo de zonas rurales y desfavorecidas. La tesis comienza con dos procedimientos multicriterio presentados para la evaluación y el diseño, respectivamente, de proyectos de electrificación rural. Estos procedimientos se aplican a dos estudios de casos reales en Perú y Nigeria. Ambas aplicaciones pueden proporcionar información valiosa, para las autoridades locales y otros promotores de sistemas de electrificación en contextos similares, sobre qué tecnologías y configuraciones utilizar en determinadas circunstancias. Al mismo tiempo, los análisis realizados permiten una mejora en cuanto a la robustez de los resultados a través de la consideración de la falta de confianza de las opiniones recogidas acerca de la importancia de los criterios y de la evaluación de las alternativas. Para ello, se desarrolla una Metodología para la toma de decisiones multicriterio considerando la incertidumbre (MIMDU) basada en números difusos para incluir la falta de confianza que los expertos y los usuarios pueden tener al ponderar un criterio o evaluar una alternativa La metodología diseñada incluye un procedimiento novedoso para cuantificar opiniones humanas con números difusos no predefinidos y un proceso sistemático para proponer rankings de alternativas y brindar información complementaria que conduce a una toma de decisiones más robusta. El potencial de la metodología se ilustra con un caso de ejemplo que muestra cómo la falta de confianza puede afectar el ranking de alternativas y la decisión posterior. Finalmente, la metodología diseñada se aplica a un estudio de caso real en Colombia para seleccionar la mejor alternativa para el digestato post-tratamiento previo a su aplicación al suelo agrícola como fertilizante. El uso de MIMDU presenta tres importantes beneficios para la toma de decisiones multicriterio en contextos de desarrollo rural. En primer lugar, la consideración de la falta de confianza de los encuestados puede reducir la presión al dar una respuesta sin un conocimiento completo. En segundo lugar, permite una cuantificación más precisa de las opiniones emitidas, convirtiendo, por ejemplo, respuestas más vacilantes en valoraciones menos fiables de una alternativa, que empeora su clasificación final. Y tercero, se pueden tomar decisiones más sólidas debido a la mayor precisión en el modelado de opiniones y la posibilidad de comparar rankings deterministas y difusos de las alternativas.Postprint (published version

Collaborative elicitation to select a sustainable biogas desulfurization technique for landfills

[EN] The 2015 Paris Agreement within the United Nations Framework Convention on Climate Change establishes three key ways for the reduction of the emissions of Greenhouse Effect Gases: mitigation, adaptation and resilience of ecosystems. In this context, one of the major goals for methane recovery from waste is the process of obtaining biogas from biomass or waste, a form of fuel with zero impact on the carbon footprint of the planet. All possible uses of biogas depend mainly on the degree of purification obtained. The removal of hydrogen sulfide (H2S) is the main weakness in using biogas in industrial applications. If the use of biogas is intended for engines, turbines or to enrich the biogas to obtain natural gas, lowering the levels of H2S will be necessary, in order to avoid corrosion in gas lines and in engines. Biogas desulfurization can be achieved through different techniques: physical, chemical, biological or hybrid procedures. Selecting the most sustainable technique to clean biogas entails a complex problem, which involves the analysis of these desulfurization treatments under different criteria. In this paper, we present a novel collaborative elicitation to select the consensus procedure for the reduction of the concentration of H2S in biogases from landfills. The elicitation technique is based on fuzzy set theory and VIKOR method in order to handle intangible data and to avoid potential bias by the panelists. The proposed hybrid method guarantees traceability and transparency to achieve consensus among the panel of experts during the decision making procedure.Curiel-Esparza, J.; Reyes-Medina, M.; Martín Utrillas, MG.; Martínez-García, MP.; Canto-Perello, J. (2019). Collaborative elicitation to select a sustainable biogas desulfurization technique for landfills. Journal of Cleaner Production. 212:1334-1344. doi:10.1016/j.jclepro.2018.12.095S1334134421