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Recognizing when heuristics can approximate minimum vertex covers is complete for parallel access to NP

Edith Hemaspaandra, Jörg Rothe, Holger Spakowski (2010)

RAIRO - Theoretical Informatics and Applications

For both the edge deletion heuristic and the maximum-degree greedy heuristic, we study the problem of recognizing those graphs for which that heuristic can approximate the size of a minimum vertex cover within a constant factor of r, where r is a fixed rational number. Our main results are that these problems are complete for the class of problems solvable via parallel access to NP. To achieve these main results, we also show that the restriction of the vertex cover problem to those...

Reconstructing a neural net from its output.

Charles Fefferman (1994)

Revista Matemática Iberoamericana

Neural nets were originally introduced as highly simplified systems of the neural system. Today they are widely used in technology and studied theoretically by scientists from several disciplines. (See e.g. [N]). However they remain little understood. (...)

Recovering an algebraic curve using its projections from different points. Applications to static and dynamic computational vision

Jeremy Yirmeyahu Kaminski, Michael Fryers, Mina Teicher (2005)

Journal of the European Mathematical Society

We study some geometric configurations related to projections of an irreducible algebraic curve embedded in ℂ ℙ 3 onto embedded projective planes. These configurations are motivated by applications to static and dynamic computational vision. More precisely, we study how an irreducible closed algebraic curve X embedded in ℂ ℙ 3 , of degree d and genus g , can be recovered using its projections from points onto embedded projective planes. The embeddings are unknown. The only input is the defining equation of...

Refinement of a fuzzy control rule set.

Antonio González, Raúl Pérez (1998)

Mathware and Soft Computing

Fuzzy logic controller performance depends on the fuzzy control rule set. This set can be obtained either by an expert or from a learning algorithm through a set of examples. Recently, we have developed SLAVE an inductive learning algorithm capable of identifying fuzzy systems. The refinement of the rules proposed by SLAVE (or by an expert) can be very important in order to improve the accuracy of the model and in order to simplify the description of the system. The refinement algorithm is based...

Relational Formal Characterization of Rough Sets

Adam Grabowski (2013)

Formalized Mathematics

The notion of a rough set, developed by Pawlak [10], is an important tool to describe situation of incomplete or partially unknown information. In this article, which is essentially the continuation of [6], we try to give the characterization of approximation operators in terms of ordinary properties of underlying relations (some of them, as serial and mediate relations, were not available in the Mizar Mathematical Library). Here we drop the classical equivalence- and tolerance-based models of rough...

Relations of granular worlds

Witold Pedrycz, George Vukovich (2002)

International Journal of Applied Mathematics and Computer Science

In this study, we are concerned with a two-objective development of information granules completed on a basis of numeric data. The first goal of this design concerns revealing and representing a structure in a data set. As such it is very much oriented towards coping with the underlying it relational aspects of the experimental data. The second goal deals with a formation of a mapping between information granules constructed in two spaces (thus it concentrates on the it directional aspect of information...

Relative sets and rough sets

Amin Mousavi, Parviz Jabedar-Maralani (2001)

International Journal of Applied Mathematics and Computer Science

In this paper, by defining a pair of classical sets as a relative set, an extension of the classical set algebra which is a counterpart of Belnap's four-valued logic is achieved. Every relative set partitions all objects into four distinct regions corresponding to four truth-values of Belnap's logic. Like truth-values of Belnap's logic, relative sets have two orderings; one is an order of inclusion and the other is an order of knowledge or information. By defining a rough set as a pair of definable...

Relevance and redundancy in fuzzy classification systems.

Ana Del Amo, Daniel Gómez, Javier Montero, Gregory S. Biging (2001)

Mathware and Soft Computing

Fuzzy classification systems is defined in this paper as an aggregative model, in such a way that Ruspini classical definition of fuzzy partition appears as a particular case. Once a basic recursive model has been accepted, we then propose to analyze relevance and redundancy in order to allow the possibility of learning from previous experiences. All these concepts are applied to a real picture, showing that our approach allows to check quality of such a classification system.

Reliable robust path planning with application to mobile robots

Romain Pepy, Michel Kieffer, Eric Walter (2009)

International Journal of Applied Mathematics and Computer Science

This paper is devoted to path planning when the safety of the system considered has to be guaranteed in the presence of bounded uncertainty affecting its model. A new path planner addresses this problem by combining Rapidly-exploring Random Trees (RRT) and a set representation of uncertain states. An idealized algorithm is presented first, before a description of one of its possible implementations, where compact sets are wrapped into boxes. The resulting path planner is then used for nonholonomic...

Representación de datos de conjuntos aproximados mediante diagramas de decisión binarios.

Alex Muir, Ivo Düntsch, Günther Gediga (2004)

RACSAM

A new information system representation, which inherently represents indiscernibility is presented. The basic structure of this representation is a Binary Decision Diagram. We offer testing results for converting large data sets into a Binary Decision Diagram Information System representation, and show how indiscernibility can be efficiently determined. Furthermore, a Binary Decision Diagram is used in place of a relative discernibility matrix to allow for more efficient determination of the discernibility...

Representation of fuzzy knowledge bases using Petri nets: operation in the truth space.

Alberto Bugarín, Senén Barro (1996)

Mathware and Soft Computing

In this paper the execution of Fuzzy Knowledge Bases in the truth space is briefly analyzed. The computational efficiency of the process is significantly increased by means of a parameterized description based on the linguistic truth values described by Baldwin. This permits executing the Fuzzy Knowledge Base through operations involving only simple numerical values, thus avoiding the direct analytic manipulation of possibility distributions. A Petri Net-based formalism that permits representing...

Restricted ideals and the groupability property. Tools for temporal reasoning

J. Martínez, P. Cordero, G. Gutiérrez, I. P. de Guzmán (2003)

Kybernetika

In the field of automatic proving, the study of the sets of prime implicants or implicates of a formula has proven to be very important. If we focus on non-classical logics and, in particular, on temporal logics, such study is useful even if it is restricted to the set of unitary implicants/implicates [P. Cordero, M. Enciso, and I. de Guzmán: Structure theorems for closed sets of implicates/implicants in temporal logic. (Lecture Notes in Artificial Intelligence 1695.) Springer–Verlag, Berlin 1999]....

ReSySTER: A hybrid recommender system for Scrum team roles based on fuzzy and rough sets

Ricardo Colomo-Palacios, Israel González-Carrasco, José Luis López-Cuadrado, Ángel García-Crespo (2012)

International Journal of Applied Mathematics and Computer Science

Agile development is a crucial issue within software engineering because one of the goals of any project leader is to increase the speed and flexibility in the development of new commercial products. In this sense, project managers must find the best resource configuration for each of the work packages necessary for the management of software development processes in order to keep the team motivated and committed to the project and to improve productivity and quality. This paper presents ReSySTER,...

Right division in Moufang loops

Maria de Lourdes M. Giuliani, Kenneth Walter Johnson (2010)

Commentationes Mathematicae Universitatis Carolinae

If ( G , · ) is a group, and the operation ( * ) is defined by x * y = x · y - 1 then by direct verification ( G , * ) is a quasigroup which satisfies the identity ( x * y ) * ( z * y ) = x * z . Conversely, if one starts with a quasigroup satisfying the latter identity the group ( G , · ) can be constructed, so that in effect ( G , · ) is determined by its right division operation. Here the analogous situation is examined for a Moufang loop. Subtleties arise which are not present in the group case since there is a choice of defining identities and the identities produced by...

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