Topic
Class (philosophy)
About: Class (philosophy) is a research topic. Over the lifetime, 821 publications have been published within this topic receiving 28000 citations.
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01 Jan 1989
TL;DR: The sought incomplete classification is implicitly described by a separate estimate for each identified class of nonspecial objects, and this estimate should be extremal and equal on all classes of the sought classification.
Abstract: The problem of incomplete classification is solved using a monotone system of a special kind. A classification method based on identification of the minimal cores of the monotone system is proposed. Existence conditions of a complete classification are given. The method is compared with previously published methods. Automatic classification methods, in addition to looking for complete classifications (i.e., partitioning of the initial set of objects), when classes are nonintersecting and form a covering of the entire set, also consider classifications with intersecting classes, with fuzzy classes, with macrostructure, etc. [1-3]. An independent group comprises incomplete classification methods, which identify a special class of “atypical” (background, special, or intermediate) objects and then assign the rest of the objects to nonintersecting classes [4-6]. Incomplete classifications are constructed when it is desirable to form classes comprising “strongly separated” subsets of objects, with all the background objects collected in a single class. This is archived either by two-step procedures, in which the first stage involving identification of the special objects is independent of the second stage involving classification proper, or by single-stage processing in which the classification functional is defined on the set of two-level classifications, thus complicating the discrete optimization problem. Moreover, both cases require specifying in advance the number of classes and the cardinality of the set of special objects, which leads to multi-alternative computations. Finally, most of the known algorithms are crudely approximate. In this paper, the sought incomplete classification is implicitly described by a separate estimate for each identified class of nonspecial objects, and this estimate should be extremal and equal on all classes of the sought classification. The proposed approach requires minimum prior information: we only need to know the measure of association of one object with a subset of objects. The number of classes and the number of objects identified, as special, is not fixed in advance. The proposed algorithm guarantees exact solution of the corresponding extremal problem.
11 citations
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TL;DR: In this paper, it was shown that Terao's celebrated addition-deletion theorem for free arrangements is combinatorial, i.e., whether you can apply it depends only on the intersection lattice of arrangements.
Abstract: In the theory of hyperplane arrangements, the most important and difficult problem is the combinatorial dependency of several properties. In this atricle, we prove that Terao's celebrated addition-deletion theorem for free arrangements is combinatorial, i.e., whether you can apply it depends only on the intersection lattice of arrangements. The proof is based on a classical technique. Since some parts are already completed recently, we prove the rest part, i.e., the combinatoriality of the addition theorem. As a corollary, we can define a new class of free arrangements called the additionally free arrangement of hyperplanes, which can be constructed from the empty arrangement by using only the addition theorem. Then we can show that Terao's conjecture is true in this class. As an application, we can show that every ideal-Shi arrangement is additionally free, implying that their freeness is combinatorial.
11 citations
TL;DR: This work discusses the algorithm PSO, its recent applications to find different types of efficient experimental designs, and provides resources, where codes for PSO and other metaheuristic algorithms and tutorials with examples are available.
Abstract: The class of nature‐inspired metaheuristic algorithms is increasingly used to tackle all kinds of optimization problems across disciplines. It also plays an important component in artificial intelligence and machine learning. Members in this class are general purpose optimization tools that virtually require no assumptions for them to be applicable. There are many such algorithms, and to fix ideas, we review one of its exemplary members called particle swarm optimization (PSO). We discuss the algorithm, its recent applications to find different types of efficient experimental designs, and provide resources, where codes for PSO and other metaheuristic algorithms and tutorials with examples are available.
11 citations
TL;DR: In this article , Paiva et al. give the concept of quasi-overlap functions on a finite chain L with n+2 elements and its arbitrary subchains together with three generalized forms of quasi overlap functions on any subchain of L. And then, they show some examples of quasi overlaps on L along with some of its specific subchains and study the idempotent property, Archimedean property and cancellation law.
11 citations
TL;DR: In this article, it is argued that only type-e expressions can be marked as a contrastive topic in a discourse contrasting individuals, equated with another type e expression in an equative frame, and anchor supplementing material.
Abstract: This paper presents three novel ways of testing which plural quantificational phrases can denote individuals (type e). Specifically, it is argued that only type-e expressions can (i) be marked as a contrastive topic in a discourse contrasting individuals, (ii) be equated with another type-e expression in an equative frame, and (iii) anchor supplementing material. The main empirical finding is that the class of quantifiers allowing type-e nominal denotations is larger than assumed on classic accounts like Reinhart 1997. Furthermore, this class is characterizable in semantic terms. The quantifiers that give rise to type-e meanings are "witnessable" in the sense of entailing the existence of an individual satisfying both their restrictor and their nuclear scope.
11 citations