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conference paper

A New Distance on Generalized Fuzzy Numbers and a Glimpse on Their Properties

Conference of the European Society for Fuzzy Logic and Technology, EUSFLAT 2017, Warsaw, Poland.

Normalization is the dominant but inexact method to handle any nonnormal fuzzy sets data. This stems from the fact that normalization ignores some parts of such data in order to prepare them for being used in computational operations. A subset of such data which satisfi es the property of convexity is called Generalized Fuzzy Numbers (GFN). In this paper, a new  distance is presented on the set of GFNs. In the special case, when GFNs are normal (i.e. Fuzzy Numbers), the proposed distance is converted to a well-known distance which in the fuzzy literature has already been proved to be a metric. Also, some of the features of the proposed distance are studied
through several examples.

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A New Approach to Locate the Hippocampus Nest in Brain MR Images

3rd International Conference on Pattern Recognition and Image Analysis (IPRIA 2017) (2017) Shahrekord, Iran. 

(The Best Paper Award)

Hippocampal shrinkage is a main biomarker for the
detection of Alzheimer’s disease and Temporal lobe Epilepsy (TLE). Mostly, developing methods for the hippocampus segmentation are unable to initialize automatically due to its low contrast boundary and uncertain position with respect to the wide range of human brain size. This paper will describe how to reduce the search area in brain MRI to determine the hippocampus location by setting a cuboid slice-based nest for the hippocampus called CSNHC surrounding this structure. The proposed algorithm applies a 3D skull stripping method using BET to extract the brain volume, following by the distance estimation from the first slice that brain volume is seen to the first slice including the hippocampus in the coronal, axial and sagittal views. Finally, ground truths for three different dataset including 68 MR
images are used to validate our results.

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conference paper

A New Distance on a Specific Subset of Fuzzy Sets

8th International Joint Conference on Computational Intelligence (IJCCI 2016) –  FCTA, (2016), Porto, Portugal.

In this paper, first we propose a definition for fuzzy LR sets and then we present a method to assigning distance between these form of fuzzy sets. We show that this distance is a metric on the set of all trapezoidal fuzzy sets with the same height and all trapezoidal fuzzy numbers and is a pseudo-metric on the set of all fuzzy sets.

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Fuzzy Function Approximation by Using Radial Basis Function Interpolation

4th Joint Congress on Fuzzy and Intelligent Systems (CFIS), (2015) Zahedan, Iran.

In the present paper, Radial Basis Function interpolations are applied to approximate a fuzzy function $\tilde{f}:\R\rightarrow \mathcal{F}(\R)$,
on a discrete point set $X=\{x_1,x_2,\ldots,x_n\}$, by a fuzzy valued function $\tilde{S}$. RBFs are based on linear combinations of terms which include a single univariate function. Applying RBF to approximate a fuzzy function, a linear system will be obtain which by defining coefficient vector, target function will be approximiated. Finally for showing the efficiency of the method we give some numerical examples.

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conference paper

Solving the Heat Partial Differential Equation by using Bivariate B-splines and Tensor Product

44th Annual Iranian Mathematics Conference, (AIMC44), (2013) Ferdowsi University of Mashhad, Iran.

This paper is in Persian.

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conference paper

Application of Homotopy Perturbation Method to Fuzzy Nonlinear Klein-Gordon Equation with Variable Coefficients

13th Iranian Conference on Fuzzy Systems (IFSC), (2013) Qazvin, Iran.

In this paper, the author will first propose fuzzy nonlinear Klein-Gordon equation and then an application of He’s homotopy perturbation method is applied to solve this equation via the same strategy as Buckley- Feuring solution and Seikkala solution. Numerical illustrations that include fuzzy nonlinear Klein-Gordon equations are investigated to show the effectiveness and convenience of the method.

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Solving Fredholm Integral Equations by Discrete Least Squares Method

44th Annual Iranian Mathematics Conference, (AIMC44) (2013), Ferdowsi University of Mashhad, Iran.

In this paper we use Discrete Least Squares Method (DLSM )to solve Fredholm Integral Equations. In this method we take $n+1$ distinct points on interval $[a,b]$ and we apply discrete norm 2 for the residual function, in this case the computations is relatively simple and straightforward in comparing to Least Squares Method (LSM) also the error of DLSM will be smaller than the error of LSM. We present some illustrative examples to show the efficiency of this method.

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Image Reconstruction by Moving Least Squares

1st Seminar on Harmonic Analysis and Applications, (2013) Isfahan University of Technology, Iran.

In this work we represent some useful results of the moving least squares method and apply them to  reconstruct images and we obtain the approximation of an image by this method.

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A New Parametric Distance and Using it to Find the Nearest Approximation of a Fuzzy Number

11th Iranian Conference of Fuzzy Systems, (2011) Zahedan, Iran.

Application of fuzzy logic and fuzzy mathematics are increasing widely all around the world. This paper mainly intends to propose a new approach to compute the distance between fuzzy numbers. This new  distance, is a meter on the set of all fuzzy numbers with continuous left and right spread functions.Using this metric we can approximate parametric fuzzy number with polynomial parametric fuzzy
numbers.

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A New Approach of a Variational Iteration Method for Nonlinear Partial Differential Equations with Exponential Nonlinearity

41st Annual Iranian Mathematics Conference  (AIMC41), (2010), Urmia, Iran.

In this work, new approach of the variational iteration method by using $r$ terms of Taylor’s series is applied for solving nonlinear partial differential equations with exponential non-linearity. Numerical results are revealing its effectiveness and simplicity.

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