On the Relationship Between the Generalized Equality Classifier and ART 2 Neural Networks

In this paper, we introduce the Generalized Equality Classifier (GEC) for use as an unsupervised clustering algorithm in categorizing analog data. GEC is based on a formal definition of inexact equality originally developed for voting in fault tolerant software applications. GEC is defined using a metric space framework. The only parameter in GEC is a scalar threshold which defines the approximate equality of two patterns. Here, we compare the characteristics of GEC to the ART2-A algorithm (Carpenter, Grossberg, and Rosen, 1991). In particular, we show that GEC with the Hamming distance performs the same optimization as ART2. Moreover, GEC has lower computational requirements than AR12 on serial machines

On the Relationship Between the Generalized Equality Classifier and ART 2 Neural Networks

In this paper, we introduce the Generalized Equality Classifier (GEC) for use as an unsupervised clustering algorithm in categorizing analog data. GEC is based on a formal definition of inexact equality originally developed for voting in fault tolerant software applications. GEC is defined using a metric space framework. The only parameter in GEC is a scalar threshold which defines the approximate equality of two patterns. Here, we compare the characteristics of GEC to the ART2-A algorithm (Carpenter, Grossberg, and Rosen, 1991). In particular, we show that GEC with the Hamming distance performs the same optimization as ART2. Moreover, GEC has lower computational requirements than AR12 on serial machines

Fuzzy inequational logic

We present a logic for reasoning about graded inequalities which generalizes the ordinary inequational logic used in universal algebra. The logic deals with atomic predicate formulas of the form of inequalities between terms and formalizes their semantic entailment and provability in graded setting which allows to draw partially true conclusions from partially true assumptions. We follow the Pavelka approach and define general degrees of semantic entailment and provability using complete residuated lattices as structures of truth degrees. We prove the logic is Pavelka-style complete. Furthermore, we present a logic for reasoning about graded if-then rules which is obtained as particular case of the general result

Computing a T-transitive lower approximation or opening of a proximity relation

Fuzzy Sets and Systems. IMPACT FACTOR: 1,181. Fuzzy Sets and Systems. IMPACT FACTOR: 1,181. Since transitivity is quite often violated even by decision makers that accept transitivity in their preferences as a condition for consistency, a standard approach to deal with intransitive preference elicitations is the search for a close enough transitive preference relation, assuming that such a violation is mainly due to decision maker estimation errors. In some way, the more number of elicitations, the more probable inconsistency is. This is mostly the case within a fuzzy framework, even when the number of alternatives or object to be classified is relatively small. In this paper we propose a fast method to compute a T-indistinguishability from a reflexive and symmetric fuzzy relation, being T any left-continuous t-norm. The computed approximation we propose will take O(n3) time complexity, where n is the number of elements under consideration, and is expected to produce a T-transitive opening. To the authors¿ knowledge, there are no other proposed algorithm that computes T-transitive lower approximations or openings while preserving the reflexivity and symmetry properties

Efficient Discovery of Ontology Functional Dependencies

Poor data quality has become a pervasive issue due to the increasing complexity and size of modern datasets. Constraint based data cleaning techniques rely on integrity constraints as a benchmark to identify and correct errors. Data values that do not satisfy the given set of constraints are flagged as dirty, and data updates are made to re-align the data and the constraints. However, many errors often require user input to resolve due to domain expertise defining specific terminology and relationships. For example, in pharmaceuticals, 'Advil' \emph{is-a} brand name for 'ibuprofen' that can be captured in a pharmaceutical ontology. While functional dependencies (FDs) have traditionally been used in existing data cleaning solutions to model syntactic equivalence, they are not able to model broader relationships (e.g., is-a) defined by an ontology. In this paper, we take a first step towards extending the set of data quality constraints used in data cleaning by defining and discovering \emph{Ontology Functional Dependencies} (OFDs). We lay out theoretical and practical foundations for OFDs, including a set of sound and complete axioms, and a linear inference procedure. We then develop effective algorithms for discovering OFDs, and a set of optimizations that efficiently prune the search space. Our experimental evaluation using real data show the scalability and accuracy of our algorithms.Comment: 12 page

Accept & Reject Statement-Based Uncertainty Models

We develop a framework for modelling and reasoning with uncertainty based on accept and reject statements about gambles. It generalises the frameworks found in the literature based on statements of acceptability, desirability, or favourability and clarifies their relative position. Next to the statement-based formulation, we also provide a translation in terms of preference relations, discuss---as a bridge to existing frameworks---a number of simplified variants, and show the relationship with prevision-based uncertainty models. We furthermore provide an application to modelling symmetry judgements.Comment: 35 pages, 17 figure