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51
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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Cited by 10 (5 self)
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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
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.
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 used in ..."
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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.
Supervaluation semantics for an inland water feature ontology
 Proceedings of the 19th International Joint Conference on Artificial Intelligence (IJCAI05
, 2005
"... This paper describes an ontology for inland water features built using formal conceptual analysis and supervaluation semantics. The first is used to generate a complete lattice of the water domain, whereas supervaluation semantics is used to model the various (possibly incompatible) interpretations ..."
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This paper describes an ontology for inland water features built using formal conceptual analysis and supervaluation semantics. The first is used to generate a complete lattice of the water domain, whereas supervaluation semantics is used to model the various (possibly incompatible) interpretations of terms in the ontology. We also present an algorithm for a mechanism of individuation and classification of water features, from snapshots of river networks, according to the proposed ontology. 1
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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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.
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.
Bayesian networks inference algorithm to implement Dempster Shafer theory in reliability analysis
 Reliability Engineering and System Safety
, 2008
"... Abstract: This paper deals with the use of Bayesian networks to compute system reliability. The reliability analysis problem is described and the usual methods for quantitative reliability analysis are presented within a case study. Some drawbacks that justify the use of Bayesian networks are identi ..."
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Abstract: This paper deals with the use of Bayesian networks to compute system reliability. The reliability analysis problem is described and the usual methods for quantitative reliability analysis are presented within a case study. Some drawbacks that justify the use of Bayesian networks are identified. The basic concepts of the Bayesian networks application to reliability analysis are introduced and a model to compute the reliability for the case study is presented. Dempster Shafer theory to treat epistemic uncertainty in reliability analysis is then discussed and its basic concepts that can be applied thanks to the Bayesian network inference algorithm are introduced. Finally, it is shown, with a numerical example, how Bayesian networks ’ inference algorithms compute complex system reliability and what the Dempster Shafer theory can provide to reliability analysis.
Fuzzy Logics Arising from Strict De Morgan Systems
 IN PROCEEDINGS OF LINZ ’99: TOPOLOGICAL AND ALGEBRAIC STRUCTURES
, 1999
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