Begell House Inc.
International Journal for Uncertainty Quantification
IJUQ
2152-5080
7
5
2017
APPLICATIONS OF NEUTROSOPHIC CUBIC SETS IN MULTI-CRITERIA DECISION-MAKING
377-394
10.1615/Int.J.UncertaintyQuantification.2017020446
Jianming
Zhan
Department of Mathematics, Hubei University for Nationalities, Enshi, 445000, P.R. China
Madad
Khan
Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad,
Pakistan
Muhammad
Gulistan
Department of Mathematics, Hazara University Mansehra, Pakistan
Ahmed
Ali
Department of Mathematics, Hazara University Mansehra, Pakistan
neutrosophic cubic set
average operator
geometric operator
accuracy functions
multicriteria decision-making
In this paper, we investigate the concepts of the weighted average operator (ΑW) and weighted geometric operator (ςW) on neutrosophic cubic sets (NCSs) to aggregate the neutrosophic cubic information. Moreover, on the basis of ΑW and ςW and certain functions, including score, certainty, and accuracy, we develop our algorithm to multiple-criteria decision-making in NCSs, in which the assessment standards of another possibility on the characteristics yield the technique of neutrosophic cubic numbers (NCNs) to choose the greatest necessary ones. Finally, we provide a mathematical example of the technique to determine the application and usefulness of the established technique.
ALGORITHMS FOR INTERVAL NEUTROSOPHIC MULTIPLE ATTRIBUTE DECISION-MAKING BASED ON MABAC, SIMILARITY MEASURE, AND EDAS
395-421
10.1615/Int.J.UncertaintyQuantification.2017020416
Xindong
Peng
School of Information Sciences and Engineering, Shaoguan University, Shaoguan, 521005,
China
Jingguo
Dai
School of Information Sciences and Engineering, Shaoguan University, Shaoguan, 521005, China
similarity measure
combined weights
interval neutrosophic set
MABAC
EDAS
In this paper, we define a new axiomatic definition of interval neutrosophic similarity measure, which is presented
by interval neutrosophic number (INN). Later, the objective weights of various attributes are determined via Shannon
entropy theory; meanwhile, we develop the combined weights, which can show both subjective information and objective
information. Then, we present three approaches to solve interval neutrosophic decision-making problems by multiattributive border approximation area comparison (MABAC), evaluation based on distance from average solution
(EDAS), and similarity measure. Finally, the effectiveness and feasibility of algorithms are conceived by two illustrative examples.
DISTANCE MEASURES BETWEEN THE COMPLEX INTUITIONISTIC FUZZY SETS AND THEIR APPLICATIONS TO THE DECISION-MAKING PROCESS
423-439
10.1615/Int.J.UncertaintyQuantification.2017020356
Dimple
Rani
School of Mathematics, Thapar University, Patiala 147004, Punjab, India
Harish
Garg
School of Mathematics, Thapar Institute of Engineering and Technology (Deemed University)
Patiala 147004, Punjab, India
complex intuitionistic fuzzy set
membership degrees
distance measures
decision-making
The complex intuitionistic fuzzy set (CIFS) is one of the extensions of the intuitionistic fuzzy set in which the range of the membership function is extended from the subset of the real number to the unit disc. In this environment, the main objective of the present work is to develop some series of distance measures by using Hamming, Euclidean, and
Hausdorff metrics. Based on these measures, various desirable relations have been studied in detail. Further, based on these distance measures, a decision-making method has been presented for finding the best alternative under the set of the feasible one. Illustrative examples from the field of pattern recognition as well as medical diagnosis have been taken to validate the approach.
BLOCK AND MULTILEVEL PRECONDITIONING FOR STOCHASTIC GALERKIN PROBLEMS WITH LOGNORMALLY DISTRIBUTED PARAMETERS AND TENSOR PRODUCT POLYNOMIALS
441-462
10.1615/Int.J.UncertaintyQuantification.2017020377
Ivana
Pultarová
Mathematical Institute, Faculty of Mathematics and Physics, Charles University, Sokolovská
83, 186 75 Prague 8, Czech Republic, and Department of Mathematics, Faculty of Civil
Engineering, Czech Technical University in Prague, Thákurova 7, 166 29 Prague 6, Czech
Republic
stochastic Galerkin method
stochastic finite element method
uncertainty quantification
polynomial chaos
algebraic multilevel preconditioning
block-diagonal preconditioning
The stochastic Galerkin method is a popular numerical method for solution of differential equations with randomly
distributed data. We focus on isotropic elliptic problems with lognormally distributed coefficients. We study the block-diagonal preconditioning and the algebraic multilevel preconditioning based on the block splitting according to some hierarchy of approximation spaces for the stochastic part of the solution. We introduce upper bounds for the resulting condition numbers, and we derive a tool for obtaining sharp guaranteed upper bounds for the strengthened Cauchy-Bunyakovsky-Schwarz constant, which can serve as an indicator of the efficiency of some of these preconditioning
methods. The presented multilevel approach yields a tool for efficient guaranteed two-sided a posteriori estimates of
algebraic errors and for adaptive algorithms as well.
A NEW IMPROVED SCORE FUNCTION OF AN INTERVAL-VALUED PYTHAGOREAN FUZZY SET BASED TOPSIS METHOD
463-474
10.1615/Int.J.UncertaintyQuantification.2017020197
Harish
Garg
School of Mathematics, Thapar Institute of Engineering and Technology (Deemed University)
Patiala 147004, Punjab, India
Pythagorean fuzzy set
multicriteria decision-making
TOPSIS
score function
interval-valued numbers
In the present study, an improved score function for the ranking order of interval-valued Pythagorean fuzzy sets
(IVPFSs) has been proposed. Based on it, a Pythagorean fuzzy technique for order of preference by similarity to
ideal solution (TOPSIS) method by taking the preferences of the experts in the form of interval-valued intuitionistic
Pythagorean fuzzy decision matrices has been presented. A positive and negative ideal separation measures solution
has been computed based on the proposed score function to determine the relative closeness coefficient and hence the
most desirable one/s is/are selected. Finally, an illustrative example for a multicriteria decision-making (MCDM) problem
has been taken to demonstrate the proposed approach.