Begell House
International Journal for Uncertainty Quantification
International Journal for Uncertainty Quantification
2152-5080
8
6
2018
AN APPROXIMATION THEORETIC PERSPECTIVE OF SOBOL' INDICES WITH DEPENDENT VARIABLES
The Sobol' indices are a recognized tool in global sensitivity analysis. When the uncertain variables in a model are statistically independent, the Sobol' indices may be easily interpreted and utilized. However, their interpretation and utility is more challenging with statistically dependent variables. This article develops an approximation theoretic perspective to interpret Sobol' indices in the presence of variable dependencies. The value of this perspective is demonstrated in the context of dimension reduction, a common application of the Sobol' indices. Theoretical analysis and illustrative examples are provided.
Joseph L.
Hart
Department of Mathematics, North Carolina State University, Raleigh, North Carolina
27695-8205
P. A.
Gremaud
Department of Mathematics, North Carolina State University, Raleigh, North Carolina
27695-8205
483-193
TIME AND FREQUENCY DOMAIN METHODS FOR BASIS SELECTION IN RANDOM LINEAR DYNAMICAL SYSTEMS
Polynomial chaos methods have been extensively used to analyze systems in uncertainty quantification. Furthermore,
several approaches exist to determine a low-dimensional approximation (or sparse approximation) for some quantity of
interest in a model, where just a few orthogonal basis polynomials are required. We consider linear dynamical systems consisting of ordinary differential equations with random variables. The aim of this paper is to explore methods for producing low-dimensional approximations of the quantity of interest further. We investigate two numerical techniques to compute a low-dimensional representation, which both fit the approximation to a set of samples in the time domain. On the one hand, a frequency domain analysis of a stochastic Galerkin system yields the selection of the basis polynomials. It follows a linear least squares problem. On the other hand, a sparse minimization yields the choice of the basis polynomials by information from the time domain only. An orthogonal matching pursuit produces an approximate solution of the minimization problem. We compare the two approaches using a test example from a mechanical application.
John D.
Jakeman
Center for Computing Research, Sandia National Laboratories, P.O. Box 5800, MS 1318,
Albuquerque, New Mexico, 87185-1320, USA
Roland
Pulch
Department of Mathematics and Computer Science, Ernst-Moritz-Arndt-Universitat Greifswald, Walther-Rathenau-Strasse 47, D-17487 Greifswald, Germany
495-510
NEUTROSOPHIC FILTERS IN PSEUDO-BCI ALGEBRAS
The concept of the neutrosophic set was introduced by Smarandache; it is a mathematical tool for handling problems
involving imprecise, indeterminacy and inconsistent data. The notion of pseudo-BCI algebra was introduced by Dudek
and Jun; it is a kind of nonclassical logic algebra and has a close connection with various noncommutative fuzzy
logics. In this paper, neutrosophic set theory is applied to pseudo-BCI algebras. The new concepts of neutrosophic
filter, neutrosophic normal filter, antigrouped neutrosophic filter, and neutrosophic p-filter in pseudo-BCI algebras are
proposed, and their basic properties are presented. Moreover, by using the concept of (alpha, beta, gamma)-level set in neutrosophic sets, the relationships between fuzzy filters and neutrosophic filters are discussed.
Xiaohong
Zhang
Department of Mathematics, Shaanxi University of Science & Technology, Xi'an, 710021,
People's Republic of China; Department of Mathematics, Shanghai Maritime University, Shanghai, 201306, People's
Republic of China
Xiaoyan
Mao
College of Science and Technology, Ningbo University, Ningbo, 315212, People's Republic of
China
Yuntian
Wu
Department of Mathematics, Shaanxi University of Science & Technology, Xi'an, 710021,
People's Republic of China
Xuehuan
Zhai
Department of Mathematics, Shaanxi University of Science & Technology, Xi'an, 710021,
People's Republic of China
511-526
A SIMPLIFIED METHOD FOR COMPUTING INTERVAL-VALUED EQUAL SURPLUS DIVISION VALUES OF INTERVAL-VALUED COOPERATIVE GAMES
Cooperative games with coalitions' values represented by intervals, which are often called interval-valued (IV) cooperative games, have currently become a hot research topic. For single-valued solutions of IV cooperative games, if the Moore's interval subtraction were used, then some unreasonable conclusions and issues result. This paper focuses on developing a simplified method without using the Moore's interval subtraction for solving the IV equal division values and IV equal surplus division values of IV cooperative games. In the methods, through defining some weaker coalition monotonicity-like conditions, it is proven that both equal division value and equal surplus division value of the defined associated cooperative game are monotonic and nondecreasing functions of the parameter α. Hence, the IV equal division values and IV equal surplus division values of IV cooperative games can be directly and explicitly obtained through determining their lower and upper bounds by using the lower and upper bounds of the IV coalitions' values, respectively. The method proposed in this paper uses coalition monotonicity-like conditions rather than the Moore's interval subtraction and hereby can effectively avoid the issues resulting from it. Moreover, some important properties of the IV equal division values and IV equal surplus division values of IV cooperative games are discussed. Finally, real numerical examples are used to demonstrate the feasibility and applicability of the methods proposed in this paper.
Deng-Feng
Li
School of Economics and Management, Fuzhou University, Fuzhou, Fujian 350108, China
Yin-Fang
Ye
School of Economics and Management, Fuzhou University, Fuzhou, Fujian 350108, China
527-542
FUZZY AGGREGATION OPERATORS WITH APPLICATION IN THE ENERGY PERFORMANCE OF BUILDINGS
In this paper, new aggregation operators are introduced in order to develop scoring and classifying methods in decision
sciences. The proposed operators are applied to evaluate and score the energy performance of residential buildings. At
first, a classical linear regression approach and a random forests method are applied to calculate the effects of eight
building factors on heating load (HL) and cooling load (CL) of residential buildings. Then, two novel definitions of
discrete fuzzy integrals, i.e., the Frank and Weber integrals, are adopted to score each building according to its energy efficiency. To evaluate the proposed fuzzy operators, we apply them on a standard dataset of 768 diverse residential buildings, a so-called energy efficiency dataset. The results of the energy performance by using Frank and Weber integrals on the energy efficiency dataset are compared with the outcomes of two traditional methods, i.e., TOPSIS and the Choquet integral, two popular approaches of scoring, and it is shown that the proposed fuzzy operators outperform the traditional methods.
Sadegh
Abbaszadeh
Department of Computer Sciences, Payame Noor University, Tehran, Iran
Alireza
Tavakoli
CS Group of Mathematics Department, Shahid Beheshti University, Tehran, Iran
Marjan
Movahedan
Department of Computer Science, University of Regina, Regina, Canada
Peide
Liu
School of Management Science and Engineering, Shandong University of Finance and
Economics, Jinan Shandong 250014, China; School of Economics and Management, Civil Aviation University of China, Tianjin 300300,
China
543-560