Fuzzy Mathematics

This book provides a timely overview of topics in fuzzy mathematics. It lays the foundation for further research and applications in a broad range of areas. It contains break-through analysis on how results from the many variations and extensions of fuzzy set theory can be obtained from known results of traditional fuzzy set theory. The book contains not only theoretical results, but a wide range of applications in areas such as decision analysis, optimal allocation in possibilistics and mixed models, pattern classification, credibility measures, algorithms for modeling uncertain data, and numerical methods for solving fuzzy linear systems. The book offers an excellent reference for advanced undergraduate and graduate students in applied and theoretical fuzzy mathematics. Researchers and referees in fuzzy set theory will find the book to be of extreme value

Moral Luck in Medical Ethics and Practical Politics

Typically we maintain two incompatible standards towards right action and good character, and the tension between these polarities creates the paradox of moral luck. In practice we regard actions as right or wrong, and character as good or bad, partly according to what happens as a result of the agent's decision. Yet we also think that people should not be held responsible for matters beyond their control. This split underpins Kant's assertion that only the good will is securely good, that its goodness is impervious to outcome ill-luck. Some commentators, such as Martha Nussbaum and to some extent Bernard Williams, think that this simply writes off the paradox. Williams asserts that the paradox is insoluble, and that its inescapability threatens the notion of agent responsibility. In contrast Thomas Nagel argues that agents' most cherished projects may be indeed be subject to luck, but that does not mean that their deepest motivations are moral. This, I suggest, is one of several means whereby we might limit the effect of the paradox without denying that the tension exists. But I also argue that it is wrong to accuse Kant of ignoring the paradox. Ethical consequentialists, on the other hand, appear to have no problem with moral luck, because the paradox depends on a dichotomy between the outside world and the locus of moral worth in the individual agent. But this turns out not to be true. The problem of moral luck is not some strange Kantian fixation, but a general dilemma: a variant on what Nagel terms "the problem of excess objectivity" which cuts across all of ethics and metaphysics. Retaining a broadly Kantian notion of agent-responsibility, but limiting what agents are responsible for, requires us to delineate the realm of ethics more narrowly than has been done by those who believe that the rational and/or prudential are coterminous with the ethical. This strategy for minimising the paradox's impact is explored in two areas from medical ethics, the allocation of scarce medical resources and informed consent, and two from public policy, secrecy and nuclear deterrence. Throughout, the analysis seeks to test Nagel's maxim that the best we can hope for is to act in such a manner that we would not have to revise our opinion of how we should have acted once the consequences of our actions become apparent

Surfaces de réponse sous incertitude normative : ambiguïté et agrégation dans une analyse ascendante de vulnérabilité des systèmes hydriques

L'incertitude profonde pesant sur l'évolution future des systèmes hydriques représente un défi considérable pour leur modélisation et planification. En réponse à ce défi, plusieurs approches, qualifiées d'ascendantes, proposent une inversion de paradigme, en employant une démarche d'aide à la décision robuste plutôt que prédictive. Parmi ces approches, la surface de réponse est un outil fréquent permettant de comparer des décisions alternatives sous forte incertitude. Cette méthode consiste à modéliser la performance d'un système hydrique pour un grand nombre de conditions possibles, échantillonnées en fonction d'un nombre limité de variables, nommées stresseurs, afin d'identifier deux ensembles : l'espace des conditions acceptables et l'espace des conditions inacceptables, selon que la performance simulée du système y satisfait ou non un seuil d'acceptabilité. Pour comparer différentes options envisagées, ce type de méthode nécessite cependant de départager, dans l'espace des conditions possibles, les régions acceptables ou inacceptables en traçant un front net et unique. Les recommandations de l'analyse sont donc soumises à une incertitude normative pesant sur ce front d'acceptabilité : comment définir une performance acceptable ? Acceptable pour qui ? La présente thèse de doctorat intègre l'effet de cette incertitude normative sur une surface de réponse à travers deux axes : ambiguïté et équité. L'ambiguïté est une incertitude normative sur la capacité des acteurs d'un système hydrique à fournir un seuil précis. L'équité porte sur les conséquences des choix d'agrégation des acteurs entre lesquels la performance du système peut varier considérablement. L'ambiguïté du seuil est traduite en logique floue et intégrée à l'incertitude hydroclimatique propre à la surface de réponse. Une méthodologie est proposée pour combiner deux incertitudes de nature très différente, la stochasticité de la surface de réponse et l'ambiguïté de son évaluation, à travers une régression logistique agrégée et une mesure de possibilité. La méthode est illustrée à travers une modélisation du système de réservoirs du Haut Saint-François (Québec méridional, Canada), sous l'angle de la protection face aux inondations. L'équité est analysée en paramétrant des méthodes d'agrégation selon différentes priorités et appliquées à un grand nombre d'usagers. Cela permet d'identifier quels niveaux d'agrégation conduisent à recommander une politique ou une autre. Un modèle multi-agent du système hydrique Jordanien est utilisé pour simuler l'approvisionnement inégal en eau potable des ménages et l'effet de différentes politiques de développement d'infrastructures ou de restructuration de l'approvisionnement. Les résultats montrent comment ces incertitudes normatives peuvent modifier la recommandation d'une analyse de vulnérabilité et comment intégrer ces incertitudes à la surface de réponse. Dans le cas du système du Haut Saint-François, les surfaces de réponse illustrent comment les niveaux de possibilité sont modifiés par le seuil flou et sa fonction d'appartenance, affectant potentiellement la recommandation. Dans le cas Jordanien, le choix d'agrégation modifie fortement la surface de réponse, parfois plus que les politiques augmentant les ressources disponibles. Les résultats montrent aussi les effets non-linéaires que divers types de distribution statistique de l'approvisionnement en eau peuvent avoir sur les surfaces de réponse. Les niveaux d'agrégation menant à différentes préférences sont identifiables, permettant d'établir une relation entre les options disponibles, choix social et incertitude profonde afin d'expliciter les arbitrages et favoriser la délibération. En proposant des outils pour intégrer ces incertitudes normatives aux approches ascendantes d'analyse des systèmes hydriques, ce travail ouvre également des pistes de recherche futures telles que la combinaison de ces deux approches par agrégation de seuils flous, ou leur inclusion au sein de cadres plus vastes d'analyse de vulnérabilité hydrique

Advances in Meta-Heuristic Optimization Algorithms in Big Data Text Clustering

This paper presents a comprehensive survey of the meta-heuristic optimization algorithms on the text clustering applications and highlights its main procedures. These Artificial Intelligence (AI) algorithms are recognized as promising swarm intelligence methods due to their successful ability to solve machine learning problems, especially text clustering problems. This paper reviews all of the relevant literature on meta-heuristic-based text clustering applications, including many variants, such as basic, modified, hybridized, and multi-objective methods. As well, the main procedures of text clustering and critical discussions are given. Hence, this review reports its advantages and disadvantages and recommends potential future research paths. The main keywords that have been considered in this paper are text, clustering, meta-heuristic, optimization, and algorithm

Funding strategies for defined benefit pension

The main area of concern of this thesis is the development of the area of pension mathematics dealing with the funding of Defined Benefit pension schemes. Particular attention is directed to the modelling of a stochastically evolving structure, whereby the demographic and financial variables may differ from the expectations, according to specific probability distributions. In such a framework, we investigate how to efficiently combine exogenous variables, such as the level of contributions and the asset allocation, with the goal of devising an optimal risk management of pension funds. The development of a stochastic model for the demographic evolution of the scheme is central for describing the dynamics of a pension scheme. Thus, the population plan theory, as presented in the literature, is extended, allowing for a random evolution of the membership population. Furthermore, the impact of this uncertainty is measured with and without the coexistence of a randomly evolving financial world. For a pension scheme, the main sources of funding are the contribution paid by the sponsor and the returns from investing the available funds. The way of combining these two sources of income is a key issue in the determination of the risk profile and the costs of implementing a pension plan. Using mathematical models and numerical algorithms, several contribution strategies are investigated, emphasising the aspects related to the risk and cost borne by the pension scheme. Specifically, the following intuitive insight, that a higher security is achieved by spending more, is found in analysing the profiles of different contribution strategies. Moreover, the impact on this trade-off between risk and cost is illustrated by separating the different effects of several sources of uncertainty. Finally, optimal contribution strategies are found analytically and numerically. The allocation of the available funds is also taken into account, with the specific aim of identifying the optimal proportions of investment in a range of three possible assets. This issue, which is part of a broader discussion on the fundamentals of pension funding, is also considered together with the choice of the contribution strategy. The main result is that, when the two strategies are contextually developed, optimality is reached when there is support between the two strategies. In other words, within certain boundaries, it is optimal to combine a contribution strategy, which extensively relies on investment returns, with a high proportion of risky assets in the investment portfolio. Avenues for further research are also suggested

Quantitative Techniques in Participatory Forest Management

Forest management has evolved from a mercantilist view to a multi-functional one that integrates economic, social, and ecological aspects. However, the issue of sustainability is not yet resolved. Quantitative Techniques in Participatory Forest Management brings together global research in three areas of application: inventory of the forest variables that determine the main environmental indices, description and design of new environmental indices, and the application of sustainability indices for regional implementations. All these quantitative techniques create the basis for the development of scientific methodologies of participatory sustainable forest management

Quantitative Techniques in Participatory Forest Management

Forest management has evolved from a mercantilist view to a multi-functional one that integrates economic, social, and ecological aspects. However, the issue of sustainability is not yet resolved. Quantitative Techniques in Participatory Forest Management brings together global research in three areas of application: inventory of the forest variables that determine the main environmental indices, description and design of new environmental indices, and the application of sustainability indices for regional implementations. All these quantitative techniques create the basis for the development of scientific methodologies of participatory sustainable forest management