Fuzzy Inference Systems for Risk Appraisal in Military Operational Planning

Advances in computing and mathematical techniques have given rise to increasingly complex models employed in the management of risk across numerous disciplines. While current military doctrine embraces sound practices for identifying, communicating, and mitigating risk, the complex nature of modern operational environments prevents the enumeration of risk factors and consequences necessary to leverage anything beyond rudimentary risk models. Efforts to model military operational risk in quantitative terms are stymied by the interaction of incomplete, inadequate, and unreliable knowledge. Specifically, it is evident that joint and inter-Service literature on risk are inconsistent, ill-defined, and prescribe imprecise approaches to codifying risk. Notably, the near-ubiquitous use of risk matrices (along with other qualitative methods), are demonstrably problematic at best, and downright harmful at worst, due to misunderstanding and misapplication of their quantitative implications. The use of fuzzy set theory is proposed to overcome the pervasive ambiguity of risk modeling encountered by today’s operational planners. Fuzzy logic is adept at addressing the problems caused by imperfect and imprecise knowledge, entangled causal relationships, and the linguistic input of expert opinion. To this end, a fuzzy inference system is constructed for the purpose of risk appraisal in military operational planning

Heterogeneous neural networks: theory and applications

Aquest treball presenta una classe de funcions que serveixen de models neuronals generalitzats per ser usats en xarxes neuronals artificials. Es defineixen com una mesura de similitud que actúa com una definició flexible de neurona vista com un reconeixedor de patrons. La similitud proporciona una marc conceptual i serveix de cobertura unificadora de molts models neuronals de la literatura i d'exploració de noves instàncies de models de neurona. La visió basada en similitud porta amb naturalitat a integrar informació heterogènia, com ara quantitats contínues i discretes (nominals i ordinals), i difuses ó imprecises. Els valors perduts es tracten de manera explícita. Una neurona d'aquesta classe s'anomena neurona heterogènia i qualsevol arquitectura neuronal que en faci ús serà una Xarxa Neuronal Heterogènia.En aquest treball ens concentrem en xarxes neuronals endavant, com focus inicial d'estudi. Els algorismes d'aprenentatge són basats en algorisms evolutius, especialment extesos per treballar amb informació heterogènia. En aquesta tesi es descriu com una certa classe de neurones heterogènies porten a xarxes neuronals que mostren un rendiment molt satisfactori, comparable o superior al de xarxes neuronals tradicionals (com el perceptró multicapa ó la xarxa de base radial), molt especialment en presència d'informació heterogènia, usual en les bases de dades actuals.This work presents a class of functions serving as generalized neuron models to be used in artificial neural networks. They are cast into the common framework of computing a similarity function, a flexible definition of a neuron as a pattern recognizer. The similarity endows the model with a clear conceptual view and serves as a unification cover for many of the existing neural models, including those classically used for the MultiLayer Perceptron (MLP) and most of those used in Radial Basis Function Networks (RBF). These families of models are conceptually unified and their relation is clarified. The possibilities of deriving new instances are explored and several neuron models --representative of their families-- are proposed. The similarity view naturally leads to further extensions of the models to handle heterogeneous information, that is to say, information coming from sources radically different in character, including continuous and discrete (ordinal) numerical quantities, nominal (categorical) quantities, and fuzzy quantities. Missing data are also explicitly considered. A neuron of this class is called an heterogeneous neuron and any neural structure making use of them is an Heterogeneous Neural Network (HNN), regardless of the specific architecture or learning algorithm. Among them, in this work we concentrate on feed-forward networks, as the initial focus of study. The learning procedures may include a great variety of techniques, basically divided in derivative-based methods (such as the conjugate gradient)and evolutionary ones (such as variants of genetic algorithms).In this Thesis we also explore a number of directions towards the construction of better neuron models --within an integrant envelope-- more adapted to the problems they are meant to solve.It is described how a certain generic class of heterogeneous models leads to a satisfactory performance, comparable, and often better, to that of classical neural models, especially in the presence of heterogeneous information, imprecise or incomplete data, in a wide range of domains, most of them corresponding to real-world problems.Postprint (published version

Fuzzy Sets, Fuzzy Logic and Their Applications 2020

The present book contains the 24 total articles accepted and published in the Special Issue “Fuzzy Sets, Fuzzy Logic and Their Applications, 2020” of the MDPI Mathematics journal, which covers a wide range of topics connected to the theory and applications of fuzzy sets and systems of fuzzy logic and their extensions/generalizations. These topics include, among others, elements from fuzzy graphs; fuzzy numbers; fuzzy equations; fuzzy linear spaces; intuitionistic fuzzy sets; soft sets; type-2 fuzzy sets, bipolar fuzzy sets, plithogenic sets, fuzzy decision making, fuzzy governance, fuzzy models in mathematics of finance, a philosophical treatise on the connection of the scientific reasoning with fuzzy logic, etc. It is hoped that the book will be interesting and useful for those working in the area of fuzzy sets, fuzzy systems and fuzzy logic, as well as for those with the proper mathematical background and willing to become familiar with recent advances in fuzzy mathematics, which has become prevalent in almost all sectors of the human life and activity