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2001 | Buch

A Natural Deduction System for Intuitionistic Fuzzy Logic Kapitel lesen Erstes Kapitel lesen

Lectures on Soft Computing and Fuzzy Logic

herausgegeben von: Prof. Antonio Di Nola, Prof. Giangiacomo Gerla

Verlag: Physica-Verlag HD

Buchreihe : Advances in Intelligent and Soft Computing

Enthalten in: Professional Book Archive

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Über dieses Buch

The present volume collects selected papers arising from lectures delivered by the authors at the School on Fuzzy Logic and Soft Computing held during the years 1996/97/98/99 and sponsored by the Salerno University. The authors contributing to this volume agreed with editors to write down, to enlarge and, in many cases, to rethink their original lectures, in order to offer to readership, a more compact presentation of the proposed topics. The aim of the volume is to offer a picture, as a job in progress, of the effort that is coming in founding and developing soft computing's techniques. The volume contains papers aimed to report on recent results containing genuinely logical aspects of fuzzy logic. The topics treated in this area cover algebraic aspects of Lukasiewicz Logic, Fuzzy Logic as the logic of continuous t-norms, Intuitionistic Fuzzy Logic. Aspects of fuzzy logic based on similar­ ity relation are presented in connection with the problem of flexible querying in deductive database. Departing from fuzzy logic, some papers present re­ sults in Probability Logic treating computational aspects, results based on indishernability relation and a non commutative version of generalized effect algebras. Several strict applications of soft computing are presented in the book. Indeed we find applications ranging among pattern recognition, image and signal processing, evolutionary agents, fuzzy cellular networks, classi­ fication in fuzzy environments. The volume is then intended to serve as a reference work for foundational logico-algebraic aspect of Soft Computing and for concrete applications of soft computing technologies.

Inhaltsverzeichnis

Frontmatter
A Natural Deduction System for Intuitionistic Fuzzy Logic
Abstract
Intuitionistic fuzzy logic IF was introduced by Takeuti and Titani. This logic coincides with the first-order Gödel logic based on the real unit interval [0,1] as set of truth-values. We present a natural deduction system NIF for IF. NIF is defined by suitably translating a first-order extension of Avron’s hypersequent calculus for Gödel logic. Soundness, completeness and normal form theorems for NIF are provided.
Matthias Baaz, Agata Ciabattoni, Christian G. Fermüller
Minimal Ideals and the Socle in MV-algebras
Abstract
We borrow from ring theory the well known notions of essential ideal and socle reversing them profitably in a MV-algebra A and proving that the socle is the l.w.b. of the minimals and the g.l.b. of the essentials in the lattice of the ideal of A. We also characterize non-essential prime ideals of A as the isolated points in the hull-kernel topology of the minimals The above concepts are in particular studied in the MV-algebra of continuous functions from a compact Hausdorff topological space into [0, 1].
Peter L. Belluce, Salvatore Sessa
Industrial Applications of Soft Computing
Abstract
In this paper two industrial applications of soft computing methodologies, developed by STMicroelectronics, are described. The main idea, in designing dedicated ICs based on soft computing paradigm, is to produce competitive devices characterized by high MIQ (Machine Intelligence Quotient).
Marco Branciforte, Riccardo Caponetto, Mario Lavorgna, Luigi Occhipinti
Spatial Diversity in Reaction-Diffusion Fuzzy Cellular Networks
Abstract
This paper deals with two main points. Firstly, a new type of Reaction-Diffusion Fuzzy Cellular Network, suitable to describe complex phenomena is defined. The second part of the work is devoted to investigate on the role played by diversity in this type of networks. In particular, the regularizing role of non organized spatial perturbation introduced in the membership functions of the proposed architecture is analyzed.
Maide Bucolo, Maria Chiara Cutuli, Luigi Fortuna, Alessandro Rizzo
An Evolutionary View to the Design of Soft-Computing Agents
Abstract
Among the possible experiments aiming to enhance Actors (active objects) to have a behavior compatible with the requirements traditionally identified for Agents, here we discuss those integrating an evolutionary fuzzy reasoning module into Actors. The resulting framework, based on the notion of FuzzyEvoAgent, allows to realise societies of Agents evolving as a result of interactions with the environment. We propose here: 1. a formal definition of FuzzyEvoAgents; 2. an architecture in Java and 3. an application to a simple scenario in artificial life (pray and predator). The results shown in this paper confirm that the evolutionary fuzzy framework may represent an important component for ensuring the autonomy of Agents, i.e. the ability to learn from interactions with the environment.
Stefano A. Cerri, Vincenzo Loia
Finiteness and Duality in MV-algebras Theory
Abstract
Some results about finiteness properties of MV-algebras and some dualities between categories of MV-algebras and categories of certain ordered structures are presented. Actually, finite MV-algebras are presented as algebras of words. Moreover, it is presented a duality between the category of MV-algebras which are finitely generated, having finite spectrum, and the category of finite linear dual Heyting algebras.
Antonio Di Nola, Revaz Grigolia
Generalized Pseudo-Effect Algebras
Abstract
We introduce generalized pseudo-effect algebras as a non-commutative version of generalized effect algebras.
The importance of the algebras of the latter type in quantum physics is based on the fact that they reflect the inner structure of subsets of the positive cone of the group of self-adjoint operators in a Hilbert space. The new algebras are designed to model subsets of group cones as well; but now the underlying po-group may be chosen arbitrarily, in particular it does not need to be abelian.
We raise the question when a generalized pseudo-effect algebra is actually representable in the positive cone of a po-group. We are able to give an affirmative answer for two special cases. Both times a property of Riesz kind is involved, defined for our algebra in a similar manner as known for po-groups.
Anatolij Dvurečenskij, Thomas Vetterlein
Extension Principle and Probabilistic Inferential Process
Abstract
In this work we sketch out a method to design expert systems, probabilistic in nature. The inferential engine we propose is a data-base storing information about a set of “past cases ”.
Giangiacomo Gerla, Domenico Calabró, Luciana Scarpati
An Algebraic Tool for Classification in Fuzzy Environments
Abstract
This paper illustrates the behavior of a commutative l-monoid, endowed with a suitable operation of composition, as regards the problem of classification with fuzzy attributes. The concepts of relevance and similarity are introduced, then a mechanism for weighing the attributes is shown. Finally, a case study concerning graphology is illustrated in
Antonio Gisolfi, Luigi Di Lascio, Enrico Fischetti
Free BL Δ Algebras
Abstract
We prove that the BL algebra consisting of the ordinal sum of n + 1 copies of the standard MV-algebra on [0,1] generates the variety generated by all n generated BL algebras.
Franco Montagna
Natural Duality as a Tool to Study Algebras Arising from Logics
Abstract
MV-algebras are the algebraic counterpart of Lukasiewicz’s infinite-valued logic, just as Boolean algebras correspond to the classical propositional calculus. The finitely generated subvarieties of the variety M of all MV-algebras are generated by a finite number of finite chains.
We present Davey and Werner’s theory of natural duality, illustrated by its application to a few classes of algebras arising from classical and non-classical logics. We insist on the subvarieties of M generated by one finite chain, for which some simple applications of the dualities are proposed.
Philippe Niederkorn
The Principles of Fuzzy Logic: Its Mathematical and Computational Aspects
Abstract
Our aim in this chapter is to give a brief overview of the main aspects of fuzzy logic. We introduce the concept of fuzzy logic and discuss its philosophical background. We argue that people encounter a phenomenon of indeterminacy which has two complementary facets, namely uncertainty and vagueness. Fuzzy logic is then considered as a mathematical model useful for modelling of the latter. Furthermore, we outline the theory of special structures, which are suitable for representation of the structure of truth values.
Vilém Novák, Irina Perfilieva
Fuzzy Systems and Data Mining
Abstract
Data mining and fuzzy systems share an important common feature that is information granulation. Information granules, and fuzzy sets exploited in the setting of this study, are used to reveal stable, transparent and meaningful patterns in databases. While there exists panoply of various forms of patterns, we focus on associations and rules as the two commonly encountered constructs that exist both in data mining and fuzzy systems. Associations are modeled in the language of fuzzy relations and are direction-free concepts meaning that they are not concerned as to the question “what implies what”. Rules, on the other hand, are direction — based constructs with clearly delineated cause and effect (condition and conclusion). Moreover, it is shown that associations and rules are tied together: associations may entail rules but no other way around. We discuss the role of information granularity in determining consistency of the rules and analyze an impact that linguistic quantification of fuzzy sets has on the consistency of the individual rules. An idea of rule growing is also discussed.
Witold Pedrycz
Flexible Querying in Deductive Database
Abstract
In this paper we frame the approach proposed in [9] in the field of Deductive Databases. Approximate information can be managed by introducing a similarity relation R in the set of predicate names and object names of the language. The notion of fuzzy least Herbrand model is also introduced.
Maria I. Sessa
Neural Networks for Pattern Recognition, Image and Signal Processing
Abstract
In this paper Neural Networks are presented in the context of Statistical Pattern Recognition, focusing the attention on all the steps needed to classify and interpolate input data. Standard multi-layer models are briefly illustrated, and then proved to be good instruments for data interpolation and Bayesian classification. Furthermore, Neural Networks are presented in the pre-processing stage, both for input reduction and clustering. Finally, two applications to signal and image processing are summarized to show the potentiality of Neural Network based systems in real world Statistical Pattern Recognition problems.
Roberto Tagliaferri
Computational Aspects of Probability Logics
Abstract
This paper gives an overview of recent results about the computational complexity of the problem of checking the coherence for a partial probability assessment. Moreover, a decision procedure which works directly on the Boolean relations by simplification rules and by elimination of Boolean variables is presented.
Sauro Tulipani
Survey of Theory and Applications of Łukasiewicz-Pavelka Fuzzy Logic
Abstract
We demonstrate how approximate reasoning, many classification tasks, case-based reasoning, etc. can be viewed as applications of many valued similarity and, thus Lukasiewicz-Pavelka logic.
Esko Turunen
Metadaten
Titel
Lectures on Soft Computing and Fuzzy Logic
herausgegeben von
Prof. Antonio Di Nola
Prof. Giangiacomo Gerla
Copyright-Jahr
2001
Verlag
Physica-Verlag HD
Electronic ISBN
978-3-7908-1818-5
Print ISBN
978-3-7908-1396-8
DOI
https://doi.org/10.1007/978-3-7908-1818-5