1,721,021 research outputs found
Automatic Generation of Fuzzy Rules and its Applications in Medical Diagnosis
No full textFuzzy Rule Learner (FURL) is a the- ory revision approach to fuzzy rules learning based on Hierarchical Pri- oritized Structures. Each new level is composed from exceptions to rules from the preceding levels. The new rules are chosen in order to elimi- nate the biggest classification errors found in the training data. FURL may me combined with many tech- niques used to interpret rule bases in fuzzy controllers.
In the traditional approaches to fuzzy approximation, the learning of rules has an undesirable effect. When many new rules are added, the interpretation of the rule base tends to one of its extreme values, thus we loose its informational value. In this paper, we suggest and test two methods which may overcome this drawback, negated antecedents and a controller with conditionally firing rules. We show that they allow to improve the performance of systems based on learning of fuzzy rules, namely the Fuzzy Rule Learner. The methods are tested on ECG and Multiple Sclerosis Disease datasets
On interval homogeneous orthomodular lattices
Full text linksummary:An orthomodular lattice is said to be interval homogeneous (resp. centrally interval homogeneous) if it is -complete and satisfies the following property: Whenever is isomorphic to an interval, , in then is isomorphic to each interval with and (resp. the same condition as above only under the assumption that all elements , , , are central in ). Let us denote by Inthom (resp. Inthom) the class of all interval homogeneous orthomodular lattices (resp. centrally interval homogeneous orthomodular lattices). We first show that the class Inthom is considerably large — it contains any Boolean -algebra, any block-finite -complete orthomodular lattice, any Hilbert space projection lattice and several other examples. Then we prove that belongs to Inthom exactly when the Cantor-Bernstein-Tarski theorem holds in . This makes it desirable to know whether there exist -complete orthomodular lattices which do not belong to Inthom. Such examples indeed exist as we than establish. At the end we consider the class Inthom. We find that each -complete orthomodular lattice belongs to Inthom, establishing an orthomodular version of Cantor-Bernstein-Tarski theorem. With the help of this result, we settle the Tarski cube problem for the -complete orthomodular lattices
Yosida-Hewitt and Lebesgue decompositions of states on orthomodular posets
No full textAbstractOrthomodular posets are usually used as event structures of quantum mechanical systems. The states of the systems are described by probability measures (also called states) on it. It is well known that the family of all states on an orthomodular poset is a convex set, compact with respect to the product topology. This suggests using geometrical results to study its structure. In this line, we deal with the problem of the decomposition of states on orthomodular posets with respect to a given face of the state space. For particular choices of this face, we obtain, e.g., Lebesgue-type and Yosida–Hewitt decompositions as special cases. Considering, in particular, the problem of existence and uniqueness of such decompositions, we generalize to this setting numerous results obtained earlier only for orthomodular lattices and orthocomplete orthomodular posets
A Cantor-Bernstein theorem for -complete MV-algebras
No full textsummary:The Cantor-Bernstein theorem was extended to -complete boolean algebras by Sikorski and Tarski. Chang’s MV-algebras are a nontrivial generalization of boolean algebras: they stand to the infinite-valued calculus of Łukasiewicz as boolean algebras stand to the classical two-valued calculus. In this paper we further generalize the Cantor-Bernstein theorem to -complete MV-algebras, and compare it to a related result proved by Jakubík for certain complete MV-algebras
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