Begell House Inc.
International Journal for Uncertainty Quantification
IJUQ
2152-5080
8
2
2018
INTERVAL-VALUED COMPLEX FUZZY SOFT SET AND ITS APPLICATION
101-117
Ganeshsree
Selvachandran
Department of Actuarial Science and Applied Statistics, Faculty of Business & Information
Science, UCSI University, Jalan Menara Gading, 56000 Cheras, Kuala Lumpur, Malayasia
Prem Kumar
Singh
Amity Institute of Information Technology, Amity University, Sector-125, Noida – 201313,
UP, India
This paper is focused on handling complex data sets using the properties of interval-valued complex fuzzy sets (IVCFSs). We extend the IV-CFS model to include a generalization parameter that reflects the opinion of experts to validate the information provided by the users. Our proposed generalized interval-valued complex fuzzy soft set model allows users to indicate their confidence in the data through the interval-based membership structure. The built-in validation mechanism in the model provides a robust framework that allows experts to ratify the individual hesitancy of the users supplying data to the system. To further enhance the utility of the proposed model, we introduce a weighted geometric aggregation operator and an accompanying score function. This aggregation operator reduces the multiple components in the proposed model into a single component with the aim of analyzing the decision-making process in a precise manner. An application of the aggregation operator and score function is demonstrated via a MADM problem related to measuring the effects of the implementation of TPPA by the Malaysian government on selected sectors of the Malaysian economy, and the time taken for these effects to manifest itself on the economic sectors that are considered. The results derived from this method is then corroborated using the interval-valued complex fuzzy concept lattice method.
A NOTE ON "NOVEL SINGLE-VALUED NEUTROSOPHIC AGGREGATED OPERATORS UNDER FRANK NORM OPERATION AND ITS APPLICATION TO DECISION-MAKING PROCESS"
119-121
Akansha
Mishra
School of Mathematics, Thapar Institute of Engineering and Technology Patiala, Punjab, India
Nancy and Garg (Int. J. Uncertain. Quan., 6(4):361–375, 2016) proposed a single-valued neutrosophic Frank weighted
averaging operator and a single-valued neutrosophic Frank weighted geometric aggregation operator. To show the
validity of these operators, they proved that these operators satisfy the idempotency, monotonicity, and boundedness properties. After a deep study, it is observed that the statement and proof of the monotonicity property proposed by Nancy and Garg is not valid. Therefore, the aggregation operators proposed by Nancy and Garg are not valid as for a valid aggregation operator, the monotonicity property should necessarily be satisfied.
A PARTIAL LEAST-SQUARES PATH MODEL FOR MULTIATTRIBUTE DECISION-MAKING UNDER FUZZY ENVIRONMENT
123-141
Xiaohong
Chen
School of Business, Central South University, Changsha 410083, China; Key Laboratory of Hunan Province for Mobile Intelligence, Hunan University of Commerce, Changsha 410205, China
Hui
Li
School of Business, Central South University, Changsha 410083, China
Chunqiao
Tan
School of Business, Central South University, Changsha 410083, China; School of Economics and Management, Nanjing University of Information Science and Technology, Nanjing 210044, China
In practical multiattribute decision-making problems, attributes are often correlated and some attributes (latent attributes) that play significant parts in evaluating alternatives cannot be directly observed, leading to an incorrect result. This paper proposes a partial least-squares path model for multiattribute decision-making under a triangular fuzzy environment, which not only addresses interaction between attributes but also fully reveals the effects of latent attributes on the evaluation of alternatives, and their weights are objectively assigned. First, utilizing a least-squares method, a triangular fuzzy regression model is built with the defuzzification of the residual sum of squares. On the basis of a triangular fuzzy regression model, an iterative algorithm is proposed for a triangular fuzzy partial least-squares path model. Four indexes are given to investigate the goodness of the proposed model. Then the procedure of the triangular
fuzzy partial least-squares path model-based multiattribute decision-making is introduced. Finally, an illustrated
example is provided to demonstrate the feasibility and validity of the proposed method.
UTILIZING ADJOINT-BASED ERROR ESTIMATES FOR SURROGATE MODELS TO ACCURATELY PREDICT PROBABILITIES OF EVENTS
143-159
Troy
Butler
Department of Mathematical and Statistical Sciences, University of Colorado Denver, Colorado
80217, USA
Timothy
Wildey
Optimization and Uncertainty Quantification Department, Sandia National Laboratories,
Albuquerque, New Mexico 87185, USA
We develop a procedure to utilize error estimates for samples of a surrogate model to compute robust upper and lower bounds on estimates of probabilities of events. We show that these error estimates can also be used in an adaptive algorithm to simultaneously reduce the computational cost and increase the accuracy in estimating probabilities of events using computationally expensive high-fidelity models. Specifically, we introduce the notion of reliability of a sample of a surrogate model, and we prove that utilizing the surrogate model for the reliable samples and the high-fidelity model for the unreliable samples gives precisely the same estimate of the probability of the output event as would be obtained by evaluation of the original model for each sample. The adaptive algorithm uses the additional evaluations of the high-fidelity model for the unreliable samples to locally improve the surrogate model near the limit state, which significantly reduces the number of high-fidelity model evaluations as the limit state is resolved. Numerical results based on a recently developed adjoint-based approach for estimating the error in samples of a surrogate are provided to demonstrate (1) the robustness of the bounds on the probability of an event, and (2) that the adaptive enhancement algorithm provides a more accurate estimate of the probability of the QoI event than standard response surface approximation methods at a lower computational cost.
A NOVEL HYBRID APPROACH FOR SIMPLIFIED NEUTROSOPHIC DECISION-MAKING WITH COMPLETELY UNKNOWN WEIGHT INFORMATION
161-173
Gökçe Dilek
Küçük
Department of Mathematics, Faculty of Art and Science, Igdir University, Igdir, Turkey
R?dvan
Şahin
Bayburt University
The simplified neutrosophic set (SNS) is a useful model to describe the indeterminacy information which widely exists
in the real world. In this paper, we develop a multicriteria decision-making (MCDM) method under simplified
neutrosophic environment in which the information about weights of criteria is completely unknown, and the decision
criterion values take the form of simplified neutrosophic numbers (SNNs). In order to determine the weighting vector
of the criteria, we establish an optimization model based on the basic ideal of the traditional gray relational analysis
(GRA) method. By solving this model, we get a simple and exact formula which can be used to determine the criterion
weights. Moreover, we utilize the dice similarity measure to determine the similarity measures between each alternative
decision and the related ideal decisions. Then, based on the traditional GRA method and the technique for order preference by similarity to ideal solution (TOPSIS), some calculation steps are presented for solving a simplified neutrosophic multicriteria decision-making problem with completely unknown weight information. To avoid information loss, this model does not use the aggregation process of decision information. Comparisons of the suggested methodology with other methods are also made. Finally, a numerical example and an experimental analysis are proposed to illustrate the application of the proposed model.
FAST AND FLEXIBLE UNCERTAINTY QUANTIFICATION THROUGH A DATA-DRIVEN SURROGATE MODEL
175-192
Felix
Dietrich
Technical University of Munich, Garching, 85747, Germany
Florian
Künzner
Technical University of Munich, Garching, 85747, Germany
Tobias
Neckel
Technical University of Munich, Garching, 85747, Germany
Gerta
Köster
Munich University of Applied Sciences, Munich, 80335, Germany
Hans-Joachim
Bungartz
Technical University of Munich, Garching, 85747, Germany
To assess a computer model's descriptive and predictive power, the model's response to uncertainties in the input must be quantified. However, simulations of complex systems typically need a lot of computational resources, and thus
prohibit exhaustive sweeps of high-dimensional spaces. Moreover, the time available to compute a result for decision systems is often very limited. In this paper, we construct a data-driven surrogate model from time delays of observations of a complex, microscopic model. We employ diffusion maps to reduce the dimensionality of the delay space. The surrogate model allows faster generation of the quantity of interest over time than the original, microscopic model. It is a nonintrusive method, and hence does not need access to the model formulation. In contrast to most other surrogate approaches, the construction allows quantities of interest that are not closed dynamically, because a closed state space is constructed through Takens delay embedding. Also, the surrogate can be stored to and loaded from storage with very little effort. The surrogate model is decoupled from the original model, and the fast execution speed allows us to quickly evaluate many different parameter distributions. We demonstrate the capability of the approach in combination with forward UQ on a parametrized Burgers' equation, and the microscopic simulation of a train station. The surrogate model can accurately capture the dynamical features in both examples, with relative errors always smaller than 10%. The simulation time in the real-world example can be reduced by an order of magnitude.