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2015
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On Fuzzy Topological Spaces Involving Boolean Algebraic Structures
On Fuzzy Topological Spaces Involving Boolean Algebraic Structures
en
en
The notion of fuzzy set was introduced by L.A. Zadeh as a generalization of the notion of classical set or crisp set. Fuzzy topological spaces were introduced by C.L. Chang and studied by many eminent authors like R. Lowen and C.K. Wong. A. Rosenfeld applied the notion of fuzzy set to algebra and introduced fuzzy subgroup of a group. Shaoquan Sun introduced the notion of fuzzy Boolean subalgebra in a Boolean algebra. In this paper, we will study fuzzy topology by involving the Boolean algebraic structure on it and introduce the notion of Boolean algebraic fuzzy topological spaces. We will examine many properties of these spaces and obtain many results.
252
260
P. K.
Sharma
Fuzzy topological space (FTS)
fuzzy Boolean subalgebra (FBSA)
Boolean algebraic fuzzy topological space (BAFTS)
fuzzy point (FP).
Article.1.pdf
[
[1]
C. L. Chang, Fuzzy Topological Spaces, J. Math. Anal. Appl., 24 (1968), 182-190
##[2]
R. Lowen, Fuzzy Topological Spaces and Fuzzy Compactness, J. Math. Anal. Appl., 56 (1976), 621-633
##[3]
A. Parvathi, K. N. Meenakshi, Fuzzy Topological Boolean Algebras, Indian J. pure appl. Math. , 28(12) (1997), 1639-1648
##[4]
A. Rosenfeld, Fuzzy Groups, J. Math. Anal. Appl., 35 (1971), 512-517
##[5]
Shaoquan Sun, Fuzzy subalgebras and Fuzzy ideals of Boolean algebra, Fuzzy Systems and Mathematics, 20(1) (2006), 90-94
##[6]
Shaoquan Sun, Generalized Fuzzy Subalgebras of Boolean Algebras, Proceedings of the 2009 International Workshop on Information Security and Application (IWISA 2009) Qingdao, November 21-22, China (2009)
##[7]
C. K. Wong, Fuzzy Topology, Products and Quotient Theorems, J. Math. Anal. Appl., 45 (1974), 512-521
##[8]
L. A. Zadeh, Fuzzy sets , Information and Control, 8 (1965), 338-353
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Elliott Mendelson, Schaum’s outline of Boolean Algebra and Switching Circuits, McGraw Hill, (1970), 07-041460
##[10]
N. Palaniappan, Fuzzy Topology, 2nd Edition Narosa Publishing House, India ()
]
A Review of Attention Models in Image Protrusion and Object Detection
A Review of Attention Models in Image Protrusion and Object Detection
en
en
Modelling in visual attention especially the stimulus-driven one, i.e. saliency-based attention, has been a very active research field during the recent 25 years. There are many attention models which, apart from being in other aspects, have been offered in successful functions of computer vision, moving robots, and cognitive systems. The present article surveys the primary concepts of visual attention, implemented in cognitive, Bayesian network, decision theories, and information theory in a computational perspective. It will demonstrate a categorization that provides a critical comparison of the approaches as well as their abilities and results. Specifically, the article formulates the criteria, derived from computational behaviors and studies in order to compare the quality of visual attention models.
261
271
Seyyed Mohammad Reza
Hashemi
Ali
Broumandnia
visual attention
bottom-up attention
top-down attention
saliency
eye movement
regions of interest
visual search.
Article.2.pdf
[
[1]
A. Borji, State-of-the-Art in Visual Attention Modeling, IEEE Transactions on Pattern Analysis And Machine Intelligence, Vol. 35 , No. 1, January. (2013)
##[2]
L. Itti, Models of Bottom-Up and Top-Down Visual Attention, PhD thesis, California Inst. of Technology (2000)
##[3]
L. Itti, C. Koch, E. Niebur, A Model of Saliency-Based Visual Attention for Rapid Scene Analysis, IEEE Trans. Pattern Analysis and Machine Intelligence, 20 (1998), 1254-1259
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Y. Zhai, M. Shah, Visual Attention Detection in Video Sequences Using Spatiotemporal Cues, Proc. ACM Int’l Conf., Multimedia (2006)
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L. Zhang, M. H. Tong, T. K. Marks, H. Shan, G. W. Cottrell, SUN: A Bayesian Framework for Saliency Using Natural Statistics, J. Vision, 8 (2008), 1-20
##[6]
L. Itti, Quantifying the Contribution of Low-Level Saliency to Human Eye Movements in Dynamic Scenes, Visual Cognition, 12 (2005), 1093-1123
##[7]
R. Rao, Bayesian Inference and Attentional Modulation in the Visual Cortex, NeuroReport, 16 (2005), 1843-1848
##[8]
Y.-S. Wang, C.-L. Tai, O. Sorkine, T.-Y. Lee, Optimized scale-and-stretch for image resizing, ACM Trans. on Graphics (Proc. of SIGGRAPH ASIA) 27(5), (2008)
##[9]
M. Ma, J. K. Guo, Automatic image cropping for mobile device with built-in camera, in [IEEE Consumer Communications and Networking Conference], (2004), 710-711
##[10]
Y. Guo, F. Liu, J. Shi, Z.-H. Zhou, M. Gleicher, Image retargeting using mesh parametrization, IEEE Trans. on Multimedia, 11(5) (2009), 856-867
##[11]
SMR. Hashemi, M. Kalantari, M. Zangian, Giving a New Method for Face Recognition Using Neural Networks, International Journal of Mechatronics, Electrical and Computer Technology, 4(11) (2014), 744-761
##[12]
SMR. Hashemi, M. Zangian, M. Shakeri, M. Faridpoor, Survey Article about Image Fuzzy Processing Algorithms, The Journal of Mathematics and Computer Science, 13 (2014), 26-40
##[13]
SMR. Hashemi, Review of algorithms changing image size, Cumhuriyet Science Journal, Vol. 36 , (2015)
]
Numerical Solution of Black-scholes Equation Using Bernstein Multi-scaling Functions
Numerical Solution of Black-scholes Equation Using Bernstein Multi-scaling Functions
en
en
A numerical method for solving Black-Scholes equation is presented. The method is based upon Bernstein multi-scaling basis approximations. The properties of Bernstein multi-scaling functions are first presented. These properties together with the forward Euler and Ritz-Galerkin method are then utilized to reduce the Black-Scholes equation to the solution of algebraic equations. Illustrative example is included to demonstrate the validity and applicability of the new technique.
272
280
M.
Moradipour
S. A.
Yousefi
Bernstein polynomial
Bernstein multi-scaling functions
Black-Scholes equation
Euler method
Ritz-Galerkin method.
Article.3.pdf
[
[1]
F. Black, M. Scholes, The pricing of options and corporate liabilities, Journal of Political Economy, (1973), 637-659
##[2]
J. C. Hull, Options, futures, and other derivatives, Pearson Prentice Hall, Upper Saddle River, NJ, 6.ed (2006)
##[3]
P. Wilmott, Introduces quantitative finance, John Wiley & Sons, (2007)
##[4]
Y. Achdu, O. Pironneau, Computational methods for option pricing, SIAM, (2005)
##[5]
D. J. Duffy, Finite Difference Methods in Financial Engineering, John Wiley & Sons, (2006)
##[6]
J. C. Cox, Option pricing: a simplified approach, Journal of Financial Economics, 7 (1979), 229-263
##[7]
M. Dehghan, S. Pourghanbar, Solution of the Black-Scholes equation for pricing of barrier option, Z. Naturforsch., 66 (2011), 289-296
##[8]
J. Ankudinova, M. Ehrhardt, On the numerical solution of nonlinear Black–Scholes equations, Computers and Mathematics with Applications, 56 (2008), 799-812
##[9]
R. Company, E. Navarro, J. R. Pintos, E. Ponsoda, Numerical solution of linear and nonlinear Black-Scholes option pricing equations, Computers and Mathematics with Applications , 56 (2008), 813-821
##[10]
M. Chawla, M. Al-zanaidi, D. Evans, Generalized Trapezoidal Formulas for the Black-Scholes Equation of Option Pricing, International Journal of Computer Mathematics, 80 (2003), 1521-1526
##[11]
M. Idrees Bhatti, P. Bracken, Solutions of differential equations in a Bernstein polynomial basis, J. Comput. Appl. Math., 205 (2007), 272-280
##[12]
S. A. Yousefi, M. Behroozifar, Operational matrices of Bernstein polynomials and their applications, International Journal of Systems Science, 41 (2010), 709-716
##[13]
S. A. Yousefi, B-polynomial multiwavelets approach for the solution of Abel's integral equation, International Journal of Computer Mathematics, 87 (2010), 310-316
]
Some Refinements of Jensens Inequality on Product Spaces
Some Refinements of Jensens Inequality on Product Spaces
en
en
In this paper, we give some refinements of the classical Jensen's inequality which generalizes some results already obtained in literatures.
281
286
Peter O.
Olanipekun
Adesanmi A.
Mogbademu
Convex function
Jensen's inequality
Fubini's theorem
\(L^p\) spaces.
Article.4.pdf
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[1]
E. Hewitt, K. Stromberg, Real and Abstract Analysis, Springer-Verlag, New York (1965)
##[2]
P. O. Olanipekun, A. A. Mogbademu, A note on generalization of classical Jensen's inequality, J. Math. Computer Sci. , 13 (2014), 68-70
##[3]
J. ROOIN, A refinement of Jensen's inequality, J. Inequal. Pure and Appl. Math., 6(2) Art. 38 (2005)
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W. RUDIN, Real and Complex Analysis, 3rd ed., McGraw-Hill , New York (1974)
]
A Modified Explicit Method for the Black-scholes Equation with Positivity Preserving Property
A Modified Explicit Method for the Black-scholes Equation with Positivity Preserving Property
en
en
In this paper, we show that the standard finite difference scheme can generate numerical drawbacks such
as spurious oscillations in the solution of the famous Black-Scholes partial differential equation, in the
presence of discontinuities. We propose a modification of this scheme based on a nonstandard
discretization. The proposed scheme is free of spurious oscillations and satisfies the positivity requirement,
as is demanded for the financial solution of the Black-Scholes equation.
287
293
M. Mehdizadeh
Khalsaraei
R. Shokri
Jahandizi
Black-Scholes equation
Nonstandard finite differences
Positivity preserving
Stability.
Article.5.pdf
[
[1]
W. F. Ames, Numerical Methods for Partial Differential Equations, Third Edition, Academic Press, San Diego (1992)
##[2]
B. M. Chen-Charpentier, H. V. Kojouharov, An unconditionally positivity preserving scheme for advectiondiffusion reaction equations, Mathematical and computer modelling, 57: 9 (2013), 2177-2185
##[3]
M. Mehdizadeh Khalsaraei, An improvement on the positivity results for 2-stage explicit Runge-Kutta methods, Journal of Computatinal and Applied mathematics, 235 (2010), 137-143
##[4]
M. Mehdizadeh Khalsaraei, F. Khodadoosti, A new total variation diminishing implicit nonstandard finite difference scheme for conservation laws, Computational Methods for Differential Equations, 2 (2014), 91-98
##[5]
M. Mehdizadeh Khalsaraei, F. Khodadoosti, Nonstandard finite difference schemes for differential equations, Sahand Commun. Math. Anal, 1 (2014), 47-54
##[6]
M. Mehdizadeh Khalsaraei, F. Khodadoosti, Qualitatively stability of nonstandard 2-stage explicit Runge-Kutta methods of order two, Computational Mathematics and Mathematical physics., 56 (2016), 235-242
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R. E. Mickens, Nonstandard Finite Difference Models of Differential Equations, World Scientific, Singapore (1994)
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M. Milev, A. Tagliani, Efficient implicit scheme with positivity preserving and smoothing properties, J. Comput. Appl. Math., 243 (2013), 1-9
##[9]
M. Milev, A. Tagliani, Numerical valuation of discrete double barrier options, Journal of Computational and Applied Mathematics, 233 (2010), 2468-2480
##[10]
M. Milev, A. Tagliani, Nonstandard finite difference schemes with application to finance: option pricing, Serdica Mathematical Journal, 36: 1 (2010), 75-88
##[11]
A. Tagliani, M. Milev, Discrete monitored barrier options by finite difference schemes, Math. and education in Math., 38 (2009), 81-89
]
Offenders Clustering Using Fcm and K-means
Offenders Clustering Using Fcm and K-means
en
en
One of the most applicable and successful methods to provide security in society is to use data mining techniques to recognize patterns of crimes. Data mining is a field that discovers hidden patterns of large amount of data in large data bases, and also extracts useful knowledge in every field which uses it. Clustering is a technique of data mining that divides data points into many groups so that the members of each group have the most similarity and the members from different groups have the least similarity. In this paper we cluster 100 offenders according to crime they have committed, using Fuzzy C-Means and K-Means algorithms in Matlab and Weka environments. Then we studied the intersections in efficient elements in crime occurrence in each cluster. We obtained interesting results coincided our real data. Hence we have created a pattern which is able to detect crime with considering other attributes, and reversely. It is clear that these detections can help to decrease the effects of crime. Note that Fuzzy C-Means algorithm has provided more accurate results in comparison with K-Means algorithm, because of considering fuzzy point of view and natural uncertainty in the real world.
294
301
Sara
Farzai
Davood
Ghasemi
Seyed Saeed Mirpour
Marzuni
Crime
Offender
Data Mining
Clustering.
Article.6.pdf
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A. Corapcıoglu, S. Erdogan , A Cross-Sectional Study on Expression of Anger and Factors Associated With Criminal Recidivism in Prisoners with Prior Offences, Forensic Science International, 140 (2004), 167-1746
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W. Chung, H. Ch. Chen, W. Chang, SH. Chou , Fighting Cybercrime: A Review and the Taiwan Experience, Decision Support Systems, 41 (2006), 669-682
##[3]
D. Karlis, L. Meligkotsidou , Finite Mixtures of Multivariate Poisson Distributions with Application, Journal of Statistical Planning and Inference, 137 (2007), 1942-1960
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J. I. Khan, S. S. Shaikh , Computing in Social Networks With Relationship Algebra, Journal of Network and Computer Applications, 31 (2008), 862-878
##[5]
Sh. T. Li, SH. CH. Kuo, F. CH. Tsai , An Intelligent Decision-Support Model Using FSOM and Rule Extraction for Crime Prevention, Expert Systems with Applications, 37 (2010), 7108-7119
##[6]
H. Liu, E. Brown Donald , Criminal Incident Prediction Using a Point- Pattern-Based Density Model, International Journal of Forecasting, 19 (2003), 603-622
##[7]
B. Moon, J. B. McCluskey, C. P. McCluskey , General Theory of Crime and Computer Crime: An Empirical Test, Journal of Criminal Justice, 38 (2010), 767-772
##[8]
G. C. Oatley, B. W. Ewart , Crimes Analysis Software: ‘Pins in Maps’, Clustering and Bayes Net Prediction, Expert Systems with Applications, 25 (2003), 569-588
##[9]
M. Sanoroyan , Neural Symptoms Norm in Men Prisoners, Notion and behavior, No. 4 (2005)
##[10]
L. A. Zadeh , Fuzzy sets, Information and Control, 8(3) (1965), 338-353
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P. Dadsetan, Criminal psychology, Samt publication, Tehran (2006)
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A. Sayyah , Universal Arabic-Farsi dictionary, 1st edition. , ()
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M. Keynia , Criminal psychology, 1st edition, Roshd publication (2005)
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, Iranian Human Rights, (Islamic criminal law), (2004)
]
Using Hybrid Metaheuristics Algorithm to Balancing Bicycle Sharing System
Using Hybrid Metaheuristics Algorithm to Balancing Bicycle Sharing System
en
en
Bike sharing system Balancing is an difficult and important issue due to the increasing popularity of this type of transportation, so we are dealing with a routing bicycles problem. In this system, there are several stations that bicycles are rented to individuals. The number of bicycles that can be embedded at each station with the same station's capacity is limited. The aim is to find the shortest possible time to start traveling from one station to the final destination station. In this article we study bike sharing system balancing problem in the real world (BBSP) by hybrid meta-discovery approach. Simulation results indicate an increase in the efficiency and speed of convergence rather than the earlier work.
302
309
Farzaneh
Fadaie
Seyyed Yaser Bozorgi
Rad
Bike sharing systems
Limitation programming
Particles mass
Optimization.
Article.7.pdf
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F. Fadaie, J. Vahidi , The optimal Bicycle Time sharing systems By Hybrid genetic algorithm and ant colony, The second National Conference on applied research in computer science and information technology, 26 Feb. (2015)
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]