A kernel-based framework for learning graded relations from data

Driven by a large number of potential applications in areas like bioinformatics, information retrieval and social network analysis, the problem setting of inferring relations between pairs of data objects has recently been investigated quite intensively in the machine learning community. To this end, current approaches typically consider datasets containing crisp relations, so that standard classification methods can be adopted. However, relations between objects like similarities and preferences are often expressed in a graded manner in real-world applications. A general kernel-based framework for learning relations from data is introduced here. It extends existing approaches because both crisp and graded relations are considered, and it unifies existing approaches because different types of graded relations can be modeled, including symmetric and reciprocal relations. This framework establishes important links between recent developments in fuzzy set theory and machine learning. Its usefulness is demonstrated through various experiments on synthetic and real-world data.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Transitive matrices, strict preference and intensity operators

Let X be a set of alternatives and a_{ij} a positive number expressing how much the alternative x_{i} is preferred to the alternative x_{j}. Under suitable hypothesis of no indifference and transitivity over the pairwise comparison matrix A= (a_{ij}), the alternatives can be ordered as a chain . Then a coherent priority vector is a vector giving a weighted ranking agreeing with the obtained chain and an intensity vector is a coherent priority vector encoding information about the intensities of the preferences. In the paper we look for operators F that, acting on the row vectors translate the matrix A in an intensity vector

On the geometric mean method for incomplete pairwise comparisons

When creating the ranking based on the pairwise comparisons very often, we face difficulties in completing all the results of direct comparisons. In this case, the solution is to use the ranking method based on the incomplete PC matrix. The article presents the extension of the well known geometric mean method for incomplete PC matrices. The description of the methods is accompanied by theoretical considerations showing the existence of the solution and the optimality of the proposed approach.Comment: 15 page

Improvement in Weighting Assignment Process in Analytic Hierarchy Process by Introducing Suggestion Matrix and Likert Scale

Analytic Hierarchy Process (AHP) has been widely used in varieties of decision making processes among several alternatives, where data on pair-wise comparisons are aggregated and the degree of importance of each alternative is quantified. The process of assigning importance or priorities against the alternatives has inherent limitations, which lead to higher possibility of inconsistency. This paper focuses on two basic limitations of the AHP, first one is its inconsistency generated from huge comparisons in judgment matrix and the second one is the use of ranking weightages given by AHP. To eliminate these limitations, this research paper recommends to calculate relative importance among alternatives from the ratings assigned from Likert scale to form a suggestion matrix with zero percent CR before judgment matrix which gives privilege to decision makers to change relative importance within the range of CR. This process intensifies the effectiveness of AHP by reducing time consumption through optimizing inconsistency

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

Ordering vs. AHP. Does the intensity used in the decision support techniques compensate?

The manifestation of the intensity in the judgment of one alternative versus another in the peer comparison processes is a central element in some decision support techniques, such as the Analytical Hierarchy Process (AHP). However, its contribution regarding quality (expected performance) with respect to the priority vector has not been evaluated so far. Using the Intentional Bounded Rationality Methodology (IBRM), this work analyzes the gains obtained from requiring the decision-maker to report an intensity judgment in pairs (AHP) with respect to a technique that only requires expressing a preference (Ordering). The results show that when decision-makers have low levels of expertise, it is possible that a less informative and computational cheap technique (Ordering) performs better than a more informative and computational expensive one (AHP). When decision-makers have medium and high levels of expertise, AHP technique obtains modest gains with respect to the Ordering technique. This study proposes a cost-benefit analysis of decision support techniques contrasting the gains of a technique that requires more resources (AHP) against other that require less resources (Ordering). Our results can change the managing approach of the information obtained from experts’ judgments

Ordering vs. AHP. Does the intensity used in the decision support techniques compensate?

The manifestation of the intensity in the judgment of one alternative versus another in the peer comparison processes is a central element in some decision support techniques, such as the Analytical Hierarchy Process (AHP). However, its contribution regarding quality (expected performance) with respect to the priority vector has not been evaluated so far. Using the Intentional Bounded Rationality Methodology (IBRM), this work analyzes the gains obtained from requiring the decision-maker to report an intensity judgment in pairs (AHP) with respect to a technique that only requires expressing a preference (Ordering). The results show that when decision-makers have low levels of expertise, it is possible that a less informative and computational cheap technique (Ordering) performs better than a more informative and computational expensive one (AHP). When decision-makers have medium and high levels of expertise, AHP technique obtains modest gains with respect to the Ordering technique. This study proposes a cost-benefit analysis of decision support techniques contrasting the gains of a technique that requires more resources (AHP) against other that require less resources (Ordering). Our results can change the managing approach of the information obtained from experts’ judgments.Spanish Ministerio de Economía y Competitividad, [ECO2017-86305-C4-3-R]Diputación General de Arag´on (DGA) and the European Social Fund [CREVALOR]CUD (UZCUD2017-SOC-04)Spanish State Research Agency under Project PID2019-103880RB-I00/AEI/https://doi.org/10.13039/501, 100,011,033 and PID2020-113338RB-I0