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Belief functions induced by multimodal probability density functions, an application to the search and rescue problem

P.-E. Doré, A. Martin, I. Abi-Zeid, A.-L. Jousselme, P. Maupin (2011)

RAIRO - Operations Research

In this paper, we propose a new method to generate a continuous belief functions from a multimodal probability distribution function defined over a continuous domain. We generalize Smets' approach in the sense that focal elements of the resulting continuous belief function can be disjoint sets of the extended real space of dimension n. We then derive the continuous belief function from multimodal probability density functions using the least commitment principle. We illustrate the approach on two...

Bias-variance decomposition in Genetic Programming

Taras Kowaliw, René Doursat (2016)

Open Mathematics

We study properties of Linear Genetic Programming (LGP) through several regression and classification benchmarks. In each problem, we decompose the results into bias and variance components, and explore the effect of varying certain key parameters on the overall error and its decomposed contributions. These parameters are the maximum program size, the initial population, and the function set used. We confirm and quantify several insights into the practical usage of GP, most notably that (a) the...

Bi-directional nearness in a network by AHP (Analytic Hierarchy Process) and ANP (Analytic Network Process)

Kazutomo Nishizawa (2010)

RAIRO - Operations Research

In this paper we study bi-directional nearness in a network based on AHP (Analytic Hierarchy Process) and ANP (Analytic Network Process). Usually we use forward (one-dimensional) direction nearness based on Euclidean distance. Even if the nearest point to i is point j, the nearest point to j is not necessarily point i. Sowe propose the concept of bi-directional nearness defined by AHP'ssynthesizing of weights “for” direction and “from” direction. This concept of distance is a relative distance...

Binary Relations-based Rough Sets – an Automated Approach

Adam Grabowski (2016)

Formalized Mathematics

Rough sets, developed by Zdzisław Pawlak [12], are an important tool to describe the state of incomplete or partially unknown information. In this article, which is essentially the continuation of [8], 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 [11]). Here we drop the classical equivalence- and tolerance-based models of rough...

Bio-inspired decentralized autonomous robot mobile navigation control for multi agent systems

Alejandro Rodriguez-Angeles, Luis-Fernando Vazquez Chavez (2018)

Kybernetika

This article proposes a decentralized navigation controller for a group of differential mobile robots that yields autonomous navigation, which allows reaching a certain desired position with a specific desired orientation, while avoiding collisions with dynamic and static obstacles. The navigation controller is constituted by two control loops, the so-called external control loop is based on crowd dynamics, it brings autonomous navigation properties to the system, the internal control loop transforms...

Bounds of graph parameters for global constraints

Nicolas Beldiceanu, Thierry Petit, Guillaume Rochart (2006)

RAIRO - Operations Research - Recherche Opérationnelle

This article presents a basic scheme for deriving systematically a filtering algorithm from the graph properties based representation of global constraints. This scheme is based on the bounds of the graph parameters used in the description of a global constraint. The article provides bounds for the most common used graph parameters.

Bounds of graph parameters for global constraints

Nicolas Beldiceanu, Thierry Petit, Guillaume Rochart (2007)

RAIRO - Operations Research

This article presents a basic scheme for deriving systematically a filtering algorithm from the graph properties based representation of global constraints. This scheme is based on the bounds of the graph parameters used in the description of a global constraint. The article provides bounds for the most common used graph parameters.

Building a knowledge base for correspondence analysis.

M.ª Carmen Bravo Llatas (1994)

Qüestiió

This paper introduces a statistical strategy for Correspondence Analysis. A formal description of the choices, actions and decisions taken during data analysis is built. Rules and heuristics have been obtained from the application of this technique to real case studies.The strategy proposed checks suitability of certain types of data matrices for this analysis and also considers a guidance and interpretation of the application of this technique. Some algorithmic-like rules are presented and specific...

Building adaptive tests using Bayesian networks

Jiří Vomlel (2004)

Kybernetika

We propose a framework for building decision strategies using Bayesian network models and discuss its application to adaptive testing. Dynamic programming and A O algorithm are used to find optimal adaptive tests. The proposed A O algorithm is based on a new admissible heuristic function.

Calculations of graded ill-known sets

Masahiro Inuiguchi (2014)

Kybernetika

To represent a set whose members are known partially, the graded ill-known set is proposed. In this paper, we investigate calculations of function values of graded ill-known sets. Because a graded ill-known set is characterized by a possibility distribution in the power set, the calculations of function values of graded ill-known sets are based on the extension principle but generally complex. To reduce the complexity, lower and upper approximations of a given graded ill-known set are used at the...

Can interestingness measures be usefully visualized?

Robert Susmaga, Izabela Szczech (2015)

International Journal of Applied Mathematics and Computer Science

The paper presents visualization techniques for interestingness measures. The process of measure visualization provides useful insights into different domain areas of the visualized measures and thus effectively assists their comprehension and selection for different knowledge discovery tasks. Assuming a common domain form of the visualized measures, a set of contingency tables, which consists of all possible tables having the same total number of observations, is constructed. These originally four-dimensional...

Capital budgeting problems with fuzzy cash flows.

Christer Carlsson, Robert Fuller (1999)

Mathware and Soft Computing

We consider the internal rate of return (IRR) decision rule in capital budgeting problems with fuzzy cash flows. The possibility distribution of the IRR at any r ≥ 0, is defined to be the degree of possibility that the (fuzzy) net present value of the project with discount factor r equals to zero. Generalizing our earlier results on fuzzy capital budegeting problems [Car99] we show that the possibility distribution of the {IRR} is a highly nonlinear function which is getting more and more unbalanced...

Cascading classifiers

Ethem Alpaydin, Cenk Kaynak (1998)

Kybernetika

We propose a multistage recognition method built as a cascade of a linear parametric model and a k -nearest neighbor ( k -NN) nonparametric classifier. The linear model learns a “rule” and the k -NN learns the “exceptions” rejected by the “rule.” Because the rule-learner handles a large percentage of the examples using a simple and general rule, only a small subset of the training set is stored as exceptions during training. Similarly during testing, most patterns are handled by the rule -learner and...

Cayley's Theorem

Artur Korniłowicz (2011)

Formalized Mathematics

The article formalizes the Cayley's theorem saying that every group G is isomorphic to a subgroup of the symmetric group on G.

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