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A Mathematical Setting for Fuzzy Logics
 International Journal of Uncertainty, Fuzziness and KnowledgeBased Systems
"... The setup of a mathematical propositional logic is given in algebraic terms, describing exactly when two choices of truth value algebras give the same logic. The propositional logic obtained when the algebra of truth values is the real numbers in the unit interval equipped with minimum, maximum and: ..."
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The setup of a mathematical propositional logic is given in algebraic terms, describing exactly when two choices of truth value algebras give the same logic. The propositional logic obtained when the algebra of truth values is the real numbers in the unit interval equipped with minimum, maximum and:x = 1 x for conjunction, disjunction and negation, respectively, is the standard propositional fuzzy logic. This is shown to be the same as threevalued logic. The propositional logic obtained when the algebra of truth values is the set f(a; b) j a b and a; b 2 [0; 1]g of subintervals of the unit interval with componentwise operations, is propositional intervalvalued fuzzy logic. This is shown to be the same as the logic given by a certain four element lattice of truth values. Since both of these logics are equivalent to ones given by …nite algebras, it follows that there are …nite algorithms for determining when two statements are logically equivalent within either of these logics. On this topic, normal forms are discussed for both of these logics.
Focused Web Crawling: A Generic Framework for Specifying the User Interest and for Adaptive Crawling Strategies
, 2001
"... Compared to the standard web search engines, focused crawlers yield good recall as well as good precision by restricting themselves to a limited domain. In this paper, we do not introduce another focused crawler, but we introduce a generic framework for focused crawling consisting of two major ..."
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Compared to the standard web search engines, focused crawlers yield good recall as well as good precision by restricting themselves to a limited domain. In this paper, we do not introduce another focused crawler, but we introduce a generic framework for focused crawling consisting of two major components: (1) Specification of the user interest and measuring the resulting relevance of a given web page. The proposed method of specifying the user interest by a formula combining atomic topics significantly improves the expressive power of the user. (2) Crawling strategy. Ordering the links at the crawl frontier is a challenging task since pages of a low relevance may be on a path to highly relevant pages. Thus, tunneling may be necessary. The explicit specification of the user interest allows us to define topicspecific strategies for tunneling. Our system Ariadne is a prototype implementation of the proposed framework. An experimental evaluation of different crawling strategies demonstrates the performance gain obtained by focusing a crawl and by dynamically adapting the focus. 1
Algebraic aspects of fuzzy sets and fuzzy logics
 Proc. Work. on Current Trends and Development in Fuzzy Logic, ThessalonikiGreece
, 1998
"... This paper is expository. It is mainly a survey of some of our work on the algebraic systems that arise in fuzzy set theory and logic. We include some of the proofs here ..."
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This paper is expository. It is mainly a survey of some of our work on the algebraic systems that arise in fuzzy set theory and logic. We include some of the proofs here
On ignorance and contradiction considered as truth values, personal communication
"... A critical view of the alleged significance of Belnap fourvalued logic for reasoning under inconsistent and incomplete information is provided. The difficulty lies in the confusion between truthvalues and information states, when reasoning about Boolean propositions. So our critique is along the l ..."
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A critical view of the alleged significance of Belnap fourvalued logic for reasoning under inconsistent and incomplete information is provided. The difficulty lies in the confusion between truthvalues and information states, when reasoning about Boolean propositions. So our critique is along the lines of previous debates on the relevance of manyvalued logics and especially of the extension of the Boolean truthtables to more than two values as a tool for reasoning about uncertainty. The critique also questions the significance of partial logic. 1
StateAggregation Algorithms for Learning Probabilistic Models for Robot Control
, 2002
"... This thesis addresses the problem of learning probabilistic representations of dynamical systems with nonlinear dynamics and hidden state in the form of partially observable Markov decision process (POMDP) models, with the explicit purpose of using these models for robot control. In contrast to the ..."
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This thesis addresses the problem of learning probabilistic representations of dynamical systems with nonlinear dynamics and hidden state in the form of partially observable Markov decision process (POMDP) models, with the explicit purpose of using these models for robot control. In contrast to the usual approach to learning probabilistic models, which is based on iterative adjustment of probabilities so as to improve the likelihood of the observed data, the algorithms proposed in this thesis take a different approach  they reduce the learning problem to that of state aggregation by clustering in an embedding space of delayed coordinates, and subsequently estimating transition probabilities between aggregated states (clusters). This approach has close ties to the dominant methods for system identification in the field of control engineering, although the characteristics of POMDP models require very different algorithmic solutions.
Machine Learning for Computer Graphics: A Manifesto and Tutorial
, 2003
"... I argue that computer graphics can benefit from a deeper use of machine learning techniques. I give an overview of what learning has to offer the graphics community, with an emphasis on Bayesian techniques. I also attempt to address some misconceptions about learning, and to give a very brief tutori ..."
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Cited by 8 (0 self)
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I argue that computer graphics can benefit from a deeper use of machine learning techniques. I give an overview of what learning has to offer the graphics community, with an emphasis on Bayesian techniques. I also attempt to address some misconceptions about learning, and to give a very brief tutorial on Bayesian reasoning.
A Semantics for Fuzzy Logic
 Soft Computing
, 1997
"... We present a semantics for certain Fuzzy Logics of vagueness by identifying the fuzzy truth value an agent gives to a proposition with the number of independent arguments that the agent can muster in favour of that proposition. Introduction In the literature the expression `Fuzzy Logic' is us ..."
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We present a semantics for certain Fuzzy Logics of vagueness by identifying the fuzzy truth value an agent gives to a proposition with the number of independent arguments that the agent can muster in favour of that proposition. Introduction In the literature the expression `Fuzzy Logic' is used in two separate ways (at least). One is where `truth values' are intended to stand for measures of belief (or condence, or certainty of some sort) and the expression `Fuzzy Logic' is taken as a synonym for the assumption that belief values are truth functional. That is, if w() denotes an agent's belief value (on the usual scale [0; 1]) for 2 SL, where SL is the set of sentences from a nite propositional language L built up using the connectives :; ^; _ (we shall consider implication later), then w satises w(:) = F: (w()); w( ^ ) = F^ (w(); w()); w( _ ) = F_ (w(); w()); (1) for some xed functions F: : [0; 1] ! [0; 1] and F^ ; F_ : [0; 1] 2 ! [0; 1]; where ; 2 SL. Two p...
Fuzzyshell: A largescale expert system shell using fuzzy logic for uncertainty reasoning
 IEEE Trans. Fuzzy Syst
, 1998
"... Abstract — There exist in the literature today many contributions dealing with the incorporation of fuzzy logic in expert systems. However, unfortunately, much of what has been proposed can only be applied to smallscale expert systems; that is, when the number of rules is in the dozens as opposed t ..."
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Abstract — There exist in the literature today many contributions dealing with the incorporation of fuzzy logic in expert systems. However, unfortunately, much of what has been proposed can only be applied to smallscale expert systems; that is, when the number of rules is in the dozens as opposed to in the hundreds. The more traditional (nonfuzzy) expert systems are able to cope with large numbers of rules by using Rete networks for maintaining matches of all the rules and all the facts. (A Rete network obviates the need to match the rules with the facts on every cycle of the inference engine.) In this paper, we present a more general Rete network that is particularly suitable for reasoning with fuzzy logic. The generalized Rete network consists of a cascade of three networks: the pattern network, the join network, and the evidence aggregation network. The first two layers are modified versions of similar layers for the traditional Rete networks and the last, the aggregation layer, is a new concept that allows fuzzy evidence to be aggregated when fuzzy inferences are made about the same fuzzy variable by different rules. Index Terms—Expert system, fuzzy logic, Rete network. I.
Generating fc fuzzy rule systems from data using evolution strategies
 IEEE Transactions on Systems, Man and Cybernetics  Part B: Cybernetics
, 1999
"... Abstract — Sophisticated fuzzy rule systems are supposed to be flexible, complete, consistent and compact (FC 3). Flexibility, completeness and consistency are essential for fuzzy systems to exhibit an excellent performance and to have a clear physical meaning, while compactness is crucial when the ..."
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Abstract — Sophisticated fuzzy rule systems are supposed to be flexible, complete, consistent and compact (FC 3). Flexibility, completeness and consistency are essential for fuzzy systems to exhibit an excellent performance and to have a clear physical meaning, while compactness is crucial when the number of the input variables increases. However, the completeness and consistency conditions are often violated if a fuzzy system is generated from data collected from real world applications. In an attempt to develop FC 3 fuzzy systems, a systematic design paradigm is proposed using evolution strategies. The structure of the fuzzy rules, which determines the compactness of the fuzzy systems, is evolved along with the parameters of the fuzzy systems. Special attention has been paid to the completeness and consistency of the rule base. The completeness is guaranteed by checking the completeness of the fuzzy partitioning of input variables and the completeness of the rule structure. An index of inconsistency is suggested with the help of a fuzzy similarity measure, which can prevent the algorithm from generating rules that seriously contradict with each other or with the heuristic knowledge. In addition, soft Tnorm and BADD defuzzification are introduced and optimized to increase the flexibility of the fuzzy system. The proposed approach is applied to the design of distance controller for cars. It is verified that a FC 3 fuzzy system works very well both for training and test driving situations, especially when the training data are insufficient. Index Terms—Compactness, completeness, consistency, evolution strategies, flexibility, fuzzy rule systems.