Gotowa bibliografia na temat „Fuzzy modal logics”

Ce manuscrit est dédié à l'étude des logiques modales floues qui formalisent le raisonnement (paraconsistant) sur l'incertitude. Ici, l'interprétation d'«information (données) incertain(es)» inclut toute combinaison des trois propriétés suivantes. Premièrement, l'information peur être quantifiée, i.e., la proposition est associée à un degré de vérité plutôt qu'une valeur de vérité. Deuxièmement, l'information peut être incomplète. Troisièmement, l'information peut être contradictoire.Toutes les logiques étudiees se divisent en deux groupes. Les plus «traditionnelles» dont la sémantique est construite sur des modèles de Kripke où les formules (et parfois, même des relations d'accessibilité) prennent des valeurs dans [0,1] constituent le premier groupe. Le second groupe contient des logiques dites «bi-stratifiées». Ici, le langage est composé de trois parties: la strate intérieure, la strate extérieure, et la modalité non-nichante. On interprète la modalité comme une mesure sur l'univers (e.g., une mesure de probabilité, fonction de croyance, fonction de plausibilité, etc.) correspondante au degré de (in)certitude de l'agent dans une proposition donnée. Le raisonnement sur cette (in)certitude est conduit dans la strate extérieure. Les cadres dans des logiques bi-stratifiées sont alors des ensembles munis de mesures.Chacun de ces deux genres de logiques correspond à l'une des façons d'interpréter l'incertitude. Dans le cas moins formel, nous utiliserons les logiques avec la sémantique de Kripke. Dans le cas plus formel où l'on assume que le degré de certitude se comporte comme une mesure d'incertitude concrète, nous utiliserons les logiques bi-stratifiées<br>This dissertation is devoted to the study of fuzzy modal logics that formalise (paraconsistent) reasoning about uncertainty. The understanding of ‘uncertain information (data)’ here includes any combination of the following three characteristics. First, the information can be graded, i.e., the statement is equipped with a truth degree rather than a truth value. Second, the information can be incomplete. Third, the information can be contradictory.All the logics in question can be divided into two kinds. First, the more ‘traditional’ modal logics defined on [0,1]-valued Kripke models (possibly, with fuzzy accessibility relations) whose language includes modal operators interpreted as infima and suprema of values in the accessible states.The second kind of logics contains so-called ‘two-layered’ logics. In this framework, the language is divided into three parts: the inner layer, the outer layer, and the non-nesting modality. The idea is to use the inner-layer language to describe events, interpret the modality as a measure on the set of events (e.g., as a probability function, belief function, plausibility, etc.) corresponding to the degree of the agent's (un)certainty in a given event, and then reason about this (un)certainty in the outer-layer language. A frame in a two-layered logic is, thus, a set with a measure defined thereon.These two kinds of logics correspond to two ways of interpreting uncertainty. In the less formal one, we will be using the logics with the Kripke-frame semantics. In the more formal case where the degree of one's certainty or belief is assumed to behave as a concrete uncertainty measure, we will use the two-layered logics

Made available in DSpace on 2015-03-03T15:47:48Z (GMT). No. of bitstreams: 1 AdrianoAD_DISSERT.pdf: 771338 bytes, checksum: 06adea5feab9914c5a48eb146511b556 (MD5) Previous issue date: 2013-11-19<br>Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior<br>I thank to my advisor, Jo?o Marcos, for the intellectual support and patience that devoted me along graduate years. With his friendship, his ability to see problems of the better point of view and his love in to make Logic, he became a great inspiration for me. I thank to my committee members: Claudia Nalon, Elaine Pimentel and Benjamin Bedregal. These make a rigorous lecture of my work and give me valuable suggestions to make it better. I am grateful to the Post-Graduate Program in Systems and Computation that accepted me as student and provided to me the propitious environment to develop my research. I thank also to the CAPES for a 21 months fellowship. Thanks to my research group, LoLITA (Logic, Language, Information, Theory and Applications). In this group I have the opportunity to make some friends. Someone of them I knew in my early classes, they are: Sanderson, Haniel and Carol Blasio. Others I knew during the course, among them I?d like to cite: Patrick, Claudio, Flaulles and Ronildo. I thank to Severino Linhares and Maria Linhares who gently hosted me at your home in my first months in Natal. This couple jointly with my colleagues of student flat Fernado, Don?tila and Aline are my nuclear family in Natal. I thank my fianc?e Lucl?cia for her precious a ective support and to understand my absence at home during my master. I thank also my parents Manoel and Zenilda, my siblings Alexandre, Paulo and Paula.Without their confidence and encouragement I wouldn?t achieve success in this journey. If you want the hits, be prepared for the misses Carl Yastrzemski<br>Esta disserta??o trata do enriquecimento de l?gicas modais. O termo enriquecimento ? usado em dois sentidos distintos. No primeiro deles, de fundo sem?ntico, propomos uma sem?ntica difusa para diversas l?gicas modais normais e demonstramos um resultado de completude para uma extensa classe dessas l?gicas enriquecidas com m?ltiplas inst?ncias do axioma da conflu?ncia. Um fato curioso a respeito dessa sem?ntica ? que ela se comporta como as sem?nticas de Kripke usuais. O outro enriquecimento diz respeito ? expressividade da l?gica e se d? por meio da adi??o de novos conectivos, especialmente de nega??es modais. Neste sentido, estudamos inicialmente o fragmento da l?gica cl?ssica positiva estendido com uma nega??o modal paraconsistente e mostramos que essa linguagem ? forte o suficiente para expressar as linguagens modais normais. Vemos que tamb?m ? poss?vel definir uma nega??o modal paracompleta e conectivos de restaura??o que internalizam as no??es de consist?ncia e determina??o a n?vel da linguagem-objeto. Esta l?gica constitui-se em uma L?gica da Inconsist?ncia Formal e em uma L?gica da Indetermina??o Formal. Em tais l?gicas, com o objetivo de recuperar infer?ncias cl?ssicas perdidas, demonstram-se Teoremas de Ajuste de Derivabilidade. No caso da l?gica estendida com uma nega??o paraconsistente, se removermos a implica??o ainda lidaremos com uma linguagem bastante rica, com ambas nega??es paranormais e seus respectivos conectivos de restaura??o. Sobre esta linguagem estudamos a l?gica modal normal minimal definida por meio de um c?lculo de Gentzen apropriado, ? diferen?a dos demais sistemas estudados at? ent?o, que s?o apresentados via c?lculo de Hilbert. Em seguida ap?s demonstrarmos a completude do sistema dedutivo associado a este c?lculo, introduzimos algumas extens?es desse sistema e buscamos Teoremas de Ajuste de Derivabilidade adequados

According to Zadeh, the term “fuzzy logic” has two different meanings: wide and narrow. In a narrow sense it is a logical system which aims a formalization of approximate reasoning, and so it can be considered an extension of many-valued logic. However, Zadeh also says that the agenda of fuzzy logic is quite different from that of traditional many-valued logic, as it addresses concepts like linguistic variable, fuzzy if-then rule, linguistic quantifiers etc. Hájek, in the preface of his foundational book Metamathematics of Fuzzy Logic, agrees with Zadeh’s distinction, but stressing that formal calculi of many-valued logics are the kernel of the so-called Basic Fuzzy logic (BL), having continuous triangular norms (t-norm) and their residua as semantics for the conjunction and implication respectively, and of its most prominent extensions, namely Lukasiewicz, Gödel and Product fuzzy logics. Taking advantage of the fact that a t-norm has residuum if, and only if, it is left-continuous, the logic of the left-continuous t-norms, called MTL, was soon after introduced. On the other hand, classical modal logic is an active field of mathematical logic, originally introduced at the beginning of the XXth century for philosophical purposes, that more recently has shown to be very successful in many other areas, specially in computer science. That are the most well-known semantics for classical modal logics. Modal expansions of non-classical logics, in particular of many-valued logics, have also been studied in the literature. In this thesis we focus on the study of some modal logics over MTL, using natural generalizations of the classical Kripke relational structures where propositions at possible words can be many-valued, but keeping classical accessibility relations. In more detail, the main goal of this thesis has been to study modal expansions of the logic of a left-continuous t-norm, defined over the language of MTL expanded with rational truth-constants and the Monteiro-Baaz Delta-operator, whose intended (standard) semantics is given by Kripke models with crisp accessibility relations and taking the unit real interval [0, 1] as set of truth-values. To get complete axiomatizations, already known techniques based on the canonical model construction are uses, but this requires to ensure that the underlying (propositional) fuzzy logic is strongly standard complete. This constraint leads us to consider axiomatic systems with infinitary inference rules, already at the propositional level. A second goal of the thesis has been to also develop and automated reasoning software tool to solve satisfiability and logical consequence problems for some of the fuzzy logic modal logics considered. This dissertation is structured in four parts. After a gentle introduction, Part I contains the needed preliminaries for the thesis be as self-contained as possible. Most of the theoretical results are developed in Parts II and III. Part II focuses on solving some problems concerning the strong standard completeness of underlying non-modal expansions. We first present and axiomatic system for the non-nodal propositional logic of a left-continuous t-norm who makes use of a unique infinitary inference rule, the “density rule”, that solves several problems pointed out in the literature. We further expand this axiomatic system in order to also characterize arbitrary operations over [0, 1] satisfying certain regularity conditions. However, since this axiomatic system turn out to be not well-behaved for the modal expansion, we search for alternative axiomatizations with some particular kind of inference rules (that will be called conjunctive). Unfortunately, this kind of axiomatization does not necessarily exist for all left-continuous t-norms (in particular, it does not exist for the Gödel logic case), but we identify a wide class of t-norms for which it works. This “well-behaved” t-norms include all ordinal sums of Lukasiewiczand Product t-norms. Part III focuses on the modal expansion of the logics presented before. We propose axiomatic systems (which are, as expected, modal expansions of the ones given in the previous part) respectively strongly complete with respect to local and global Kripke semantics defined over frames with crisp accessibility relations and worlds evaluated over a “well-behaved” left-continuous t-norm. We also study some properties and extensions of these logics and also show how to use it for axiomatizing the possibilistic logic over the very same t-norm. Later on, we characterize the algebraic companion of these modal logics, provide some algebraic completeness results and study the relation between their Kripke and algebraic semantics. Finally, Part IV of the thesis is devoted to a software application, mNiB-LoS, who uses Satisfability Modulo Theories in order to build an automated reasoning system to reason over modal logics evaluated over BL algebras. The acronym of this applications stands for a modal Nice BL-logics Solver. The use of BL logics along this part is motivated by the fact that continuous t-norms can be represented as ordinal sums of three particular t-norms: Gödel, Lukasiewicz and Product ones. It is then possible to show that these t-norms have alternative characterizations that, although equivalent from the point of view of the logic, have strong differences for what concerns the design, implementation and efficiency of the application. For practical reasons, the modal structures included in the solver are limited to the finite ones (with no bound on the cardinality).

Master’s thesis deals with mathematical operation with fuzzy numbers. The first part of the thesis deals with theoretical knowledge of fuzzy arithmetic and defines fuzzy sets, fuzzy numbers, universum and five membership function used in program. In the concrete it describes – cut method for dealing with fuzzy numbers as with limited interval for specific level which simplifies computation. The second part of the thesis contains description of programmed module for mathematical operation with fuzzy numbers. There is described creation of user interface which is using to set parameters of computation. There are also described support functions which make operation with fuzzy numbers possible and operation ensures output.

Two fuzzy controllers are presented. A fuzzy controller with intermediate variable designed for cascade control purposes is presented as the FCIV controller. An intermediate variable and a new set of fuzzy logic rules are added to a conventional Fuzzy Logic Controller (FLC) to build the Fuzzy Controller with Intermediate Variable (FCIV). The new controller was tested in the control of a nonlinear chemical process, and its performance was compared to several other controllers. The FCIV shows the best control performance regarding stability and robustness. The new controller also has an acceptable performance when noise is added to the sensor signal. An optimization program has been used to determine the optimum tuning parameters for all controllers to control a chemical process. This program allows obtaining the tuning parameters for a minimum IAE (Integral absolute of the error). The second controller presented uses fuzzy logic to improve the performance of the convention al internal model controller (IMC). This controller is called FAIMCr (Fuzzy Adaptive Internal Model Controller). Twofuzzy modules plus a filter tuning equation are added to the conventional IMC to achieve the objective. The first fuzzy module, the IMCFAM, determines the process parameters changes. The second fuzzy module, the IMCFF, provides stability to the control system, and a tuning equation is developed for the filter time constant based on the process parameters. The results show the FAIMCr providing a robust response and overcoming stability problems. Adding noise to the sensor signal does not affect the performance of the FAIMC.The contributions presented in this work include:The development of a fuzzy controller with intermediate variable for cascade control purposes. An adaptive model controller which uses fuzzy logic to predict the process parameters changes for the IMC controller. An IMC filter tuning equation to update the filter time constant based in the process paramete rs values. A variable fuzzy filter for the internal model controller (IMC) useful to provide stability to the control system.

This diploma thesis deals with the evaluation of offers with the usage of fuzzy logic. It describes methods and processes of a model building. The aim is to make a decision – making model that helps a customer to make decisions between more properties.

The presented diploma thesis deals with the evaluation of suppliers for the company Ferrit using fuzzy logic. The main part of the diploma thesis deals with the creation of proposals for the solution of the evaluation of suppliers of a selected company. Decision models are created in Microsoft Excel and MATLAB. The comparison of the results of both proposed models is the content of the part of the work.

Master's thesis deals with a design of models that allow selection of the most suitable contractor for construction of a company's new branch. Models are based on utilization of basic principles of fuzzy logic. Proposed fuzzy models allow evaluation of individual offers and serve as support in decision-making process.