Catálogo de publicaciones - libros

The most problematic and challenging issues in fuzzy modeling of nonlinear system dynamics deal with robustness and interpretability. Traditional data-driven approaches, especially when the data set is not adequate, may lead to a model that results to be either unable to reproduce the system dynamics or numerically unstable or unintelligible. This paper demonstrates that Qualitative Reasoning plays a crucial role to significantly improve both robustness and interpretability. In the modeling framework we propose both fuzzy partition of input-output variables and the fuzzy rule base are built on the available deep knowledge represented through qualitative models. This leads to a clear and neat model structure that does describe the system dynamics, and the parameters of which have a physically significant meaning. Moreover, it allows us to properly constrain the parameter optimization problem, with a consequent gain in numerical stability. The obtained substantial improvement of model robustness and interpretability in “actual” physical terms lays the groundwork for new application perspectives of fuzzy models.

This paper reviews and analyzes the performance of the TaSe-II model, carrying out a statistical comparison among different TSK fuzzy system configurations for function approximation. The TaSe-II model, using a special type of rule antecedents, utilizes the Taylor Series Expansion of a function around a point to provide interpretability to the local models in a TSK approximator using a low number of rules. Here we will review the TaSe model basics and endow it with a full learning algorithm for function approximation from a set of I/O data points. Finally we present an ANOVA analysis about the modification of the different blocks that intervene in a TSK fuzzy model whose results support the use of the TaSe-II model.

We provide non-deterministic semantics for the 3 basic paraconsistent C-systems (also known as ), , and , as well as to all 9 extensions of them by one or two of the schemata ¬(Λ¬) ⊃ ∘  and  ⊃ ¬¬. This includes da Costa’s original (which is equivalent to ). Our semantics is 3-valued for the systems without , and infinite-valued for the systems with it. We prove that these results cannot be improved: neither of the systems without has either a finite characteristic ordinary matrix or a two-valued characteristic non-deterministic matrix, and neither of the systems with has a finite characteristic non-deterministic matrix. Still, our semantics suffices for providing decision procedures for all the systems investigated.

In this paper we introduce TCTL, a dense-time extension of the multi-valued Computation Tree Logic (CTL) in [1]. Alternatively, TCTL is a multi-valued extension of TCTL [2] over quasi-boolean algebras. A multi-valued quotient is defined which enables to reduce dense-time TCTL model checking to the untimed case.

We construct a class of Łukasiewicz formulae whose associated McNaughton functions constitute a family of Schauder hats having special properties. Our technique is inspired by the well-known algorithm of Brun [3,4,2] for simultaneous diopanthine approximations. As a first application of Brun hats we construct normal forms for co-atomic Łukasiewicz logics. We also show how to combine Brun hats to obtain normal forms for all finite-valued Łukasiewicz logics.

MTL is the logic of all left-continuous -norms and their residua. Its algebraic semantics is constituted by the variety (MTL) of MTL-algebras. Among schematic extensions of MTL there are infinite-valued logics such that the finitely generated free algebras in the corresponding subvariety () of (MTL) are finite. In this paper we focus on Gödel and Nilpotent Minimum logics. We give concrete representations of their associated free algebras in terms of finite algebras of sections over finite posets.

Learning rules with exceptions may be of interest, especially if the exceptions are not important in some sense. Standard Inductive Logic Programming (ILP) algorithms and classical first order logic are not well-suited for managing rules with exceptions. Indeed, a hypothesis that is induced accumulates all the exceptions of the rules contained in it. Moreover, with multiple-class problems, classifying an example in two different classes (even if one is the right one) is not correct, so a rule that contains some exceptions may prevent another rule which has no exception from being useful. This paper proposes a new possibilistic logic framework for weighted ILP. It induces rules which are progressively more and more accurate, and allows us to manage exceptions by controlling their accumulation. In this setting, we first propose an algorithm for learning rules when the background knowledge and the examples are stratified into layers having different levels of priority or certainty. This allows the induction of general but uncertain rules together with more specific and less uncertain rules. A second algorithm is presented, which does not require an initial weighted database, but still learn a default set of rules in the possibilistic setting.

We present a simple, yet general top-down query answering procedure for normal logic programs over lattices and bilattices, where functions may appear in the rule bodies. Its interest relies on the fact that many approaches to paraconsistency and uncertainty in logic programs with or without non-monotonic negation are based on bilattices or lattices, respectively.

The notion of conditional possibility derived from marginal possibility measures has received different treatments. However, as shown by Bouchon-Meunier et al., conditional possibility can be introduced as a primitive notion generalizing simple possibility measures. In this paper, following an approach already adopted by the author w.r.t. conditional probability, we build up the fuzzy modal logic Π, relying on the fuzzy logic  ∏, so as to reason about coherent conditional possibilities and necessities. First we apply a modal operator ⋄ over conditional events ∣ to obtain modal formulas of the type (|) whose reading is “∣ is possible”. Then we define the truth-value of the modal formulas as corresponding to a conditional possibility measure. The logic Π is shown to be strongly complete for finite theories w.r.t. to the class of the introduced conditional possibility Kripke structures. Then, we show that any rational assessment of conditional possibilities is coherent iff a suitable defined theory over Π is consistent. We also prove compactness for rational coherent assessments of conditional possibilities. Finally, we derive the notion of generalized conditional necessity from that of generalized conditional possibility, and we show how to represent them introducing the logic Π.

This paper is devoted to a logical and algebraic treatment of conditional probability. Unlike the other approaches to this problem (cf [7],[10]) we base our work on the notion of (cf [4]). Thus we define the fuzzy modal logic (Ł) with modalities for , built up over the many-valued logic Ł (obtained by adding to the Rational Łukasiewicz logic the Baaz connective Δ). The main result of this paper tells us that it is possible to characterize the coherence of an assessment of conditional probability by the consistence of a suitable theory over (Ł).