Begell House Inc. International Journal for Uncertainty Quantification IJUQ 2152-5080 8 6 2018
AN APPROXIMATION THEORETIC PERSPECTIVE OF SOBOL' INDICES WITH DEPENDENT VARIABLES 483-493 10.1615/Int.J.UncertaintyQuantification.2018026498 Joseph Hart Department of Mathematics, North Carolina State University, Raleigh, NC Pierre A. Gremaud Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695-8205 global sensitivity analysis Sobol' indices 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.
TIME AND FREQUENCY DOMAIN METHODS FOR BASIS SELECTION IN RANDOM LINEAR DYNAMICAL SYSTEMS 495-510 10.1615/Int.J.UncertaintyQuantification.2018026902 John D. Jakeman Sandia National Laboratories, Albuquerque, NM, USA Roland Pulch Department of Mathematics and Computer Science University of Greifswald Domstraße 11, 17489 Greifswald, Germany linear dynamical system random variable orthogonal basis polynomial chaos stochastic Galerkin method least squares problem orthogonal matching pursuit uncertainty quantification 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.
NEUTROSOPHIC FILTERS IN PSEUDO-BCI ALGEBRAS 511-526 10.1615/Int.J.UncertaintyQuantification.2018022057 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 neutrosophic set fuzzy set pseudo-BCI algebra neutrosophic filter fuzzy filter 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.
A SIMPLIFIED METHOD FOR COMPUTING INTERVAL-VALUED EQUAL SURPLUS DIVISION VALUES OF INTERVAL-VALUED COOPERATIVE GAMES 527-542 10.1615/Int.J.UncertaintyQuantification.2018021714 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 game theory cooperative game equal division value equal surplus division value interval computing fuzzy set 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.
PRICING ASIAN OPTIONS IN AN UNCERTAIN STOCK MODEL WITH FLOATING INTEREST RATE 543-557 10.1615/Int.J.UncertaintyQuantification.2018025270 Weiwei Wang School of Science, Nanjing University of Science and Technology, Nanjing 210094, China Ping Chen School of Science, Nanjing University of Science and Technology, Nanjing 210094, China uncertainty theory uncertain differential equation stock model option pricing Option pricing has always been an important issue in the financial field. Unlike the classical stochastic theory, we investigate the valuation of Asian options under the assumption that the risk factors are described by uncertain processes. Early researchers have presented some uncertain stock models to simulate the financial market. In this paper, we propose a new uncertain stock model with floating interest rate, where the process of interest rate is assumed to be the uncertain counterpart of the Cox-Ingersoll-Ross (CIR) model. Subsequently, Asian option pricing formulas of the proposed model are derived and some mathematical properties of the formulas are studied. Finally, some numerical algorithms are designed to calculate the prices of Asian options and some numerical examples are performed.
FUZZY AGGREGATION OPERATORS WITH APPLICATION IN THE ENERGY PERFORMANCE OF BUILDINGS 559-575 10.1615/Int.J.UncertaintyQuantification.2018024815 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 fuzzy integral monotone measure energy performance TOPSIS 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.
INDEX, VOLUME 8, 2018 576-582 10.1615/Int.J.UncertaintyQuantification.v8.i6.70