Abstract: Motivated by the recent work of Herbert, Hayen, Macaskill and Walter [Interval estimation for the difference of two independent variances. Communications in Statistics, Simulation and Computation, 40: 744-758, 2011.], we investigate, in this paper, new confidence intervals for the difference between two normal population variances based on the generalized confidence interval of Weerahandi [Generalized Confidence Intervals. Journal of the American Statistical Association, 88(423): 899-905, 1993.] and the closed form method of variance estimation of Zou, Huo and Taleban [Simple confidence intervals for lognormal means and their differences with environmental applications. Environmetrics 20: 172-180, 2009]. Monte Carlo simulation results indicate that our proposed confidence intervals give a better coverage probability than that of the existing confidence interval. Also two new confidence intervals perform similarly based on their coverage probabilities and their average length widths.
Abstract: Different types of aggregation operators such as the
ordered weighted quasi-arithmetic mean (Quasi-OWA) operator and
the normalized Hamming distance are studied. We introduce the use
of the OWA operator in generalized distances such as the quasiarithmetic
distance. We will call these new distance aggregation the
ordered weighted quasi-arithmetic distance (Quasi-OWAD) operator.
We develop a general overview of this type of generalization and
study some of their main properties such as the distinction between
descending and ascending orders. We also consider different families
of Quasi-OWAD operators such as the Minkowski ordered weighted
averaging distance (MOWAD) operator, the ordered weighted
averaging distance (OWAD) operator, the Euclidean ordered
weighted averaging distance (EOWAD) operator, the normalized
quasi-arithmetic distance, etc.
Abstract: We present the induced generalized hybrid
averaging (IGHA) operator. It is a new aggregation operator
that generalizes the hybrid averaging (HA) by using
generalized means and order inducing variables. With this
formulation, we get a wide range of mean operators such as
the induced HA (IHA), the induced hybrid quadratic
averaging (IHQA), the HA, etc. The ordered weighted
averaging (OWA) operator and the weighted average (WA)
are included as special cases of the HA operator. Therefore,
with this generalization we can obtain a wide range of
aggregation operators such as the induced generalized OWA
(IGOWA), the generalized OWA (GOWA), etc. We further
generalize the IGHA operator by using quasi-arithmetic
means. Then, we get the Quasi-IHA operator. Finally, we also
develop an illustrative example of the new approach in a
financial decision making problem. The main advantage of the
IGHA is that it gives a more complete view of the decision
problem to the decision maker because it considers a wide
range of situations depending on the operator used.
Abstract: The multiindex Mittag-Leffler (M-L) function and the multiindex Dzrbashjan-Gelfond-Leontiev (D-G-L) differentiation and integration play a very pivotal role in the theory and applications of generalized fractional calculus. The object of this paper is to investigate the relations that exist between the Riemann-Liouville fractional calculus and multiindex Dzrbashjan-Gelfond-Leontiev differentiation and integration with multiindex Mittag-Leffler function.
Abstract: The aim of this paper is to introduce the concepts of τ1τ2-regular generalized star star closed sets , τ1τ2-regular generalized star star open sets and study their basic properties in bitopological spaces.
Abstract: Using the idea of prime and semiprime bi-ideals of
rings, the concept of prime and semiprime generalized bi-ideals of
rings is introduced, which is an extension of the concept of prime and
semiprime bi-ideals of rings and some interesting characterizations
of prime and semiprime generalized bi-ideals are obtained. Also,
we give the relationship between the Baer radical and prime and
semiprime generalized bi-ideals of rings in the same way as of biideals
of rings which was studied by Roux.
Abstract: Due to the tremendous amount of information provided
by the World Wide Web (WWW) developing methods for mining
the structure of web-based documents is of considerable interest. In
this paper we present a similarity measure for graphs representing
web-based hypertext structures. Our similarity measure is mainly
based on a novel representation of a graph as linear integer strings,
whose components represent structural properties of the graph. The
similarity of two graphs is then defined as the optimal alignment of
the underlying property strings. In this paper we apply the well known
technique of sequence alignments for solving a novel and challenging
problem: Measuring the structural similarity of generalized trees.
In other words: We first transform our graphs considered as high
dimensional objects in linear structures. Then we derive similarity
values from the alignments of the property strings in order to
measure the structural similarity of generalized trees. Hence, we
transform a graph similarity problem to a string similarity problem for
developing a efficient graph similarity measure. We demonstrate that
our similarity measure captures important structural information by
applying it to two different test sets consisting of graphs representing
web-based document structures.
Abstract: In this paper, we use Generalized Hamiltonian systems approach to synchronize a modified sixth-order Chua's circuit, which generates hyperchaotic dynamics. Synchronization is obtained between the master and slave dynamics with the slave being given by an observer. We apply this approach to transmit private information (analog and binary), while the encoding remains potentially secure.
Abstract: In the present paper, we consider the generalized form of Baskakov Durrmeyer operators to study the rate of convergence, in simultaneous approximation for functions having derivatives of bounded variation.
Abstract: We study different types of aggregation operators such
as the ordered weighted averaging (OWA) operator and the
generalized OWA (GOWA) operator. We analyze the use of OWA
operators in the Minkowski distance. We will call these new distance
aggregation operator the Minkowski ordered weighted averaging
distance (MOWAD) operator. We give a general overview of this
type of generalization and study some of their main properties. We
also analyze a wide range of particular cases found in this
generalization such as the ordered weighted averaging distance
(OWAD) operator, the Euclidean ordered weighted averaging
distance (EOWAD) operator, the normalized Minkowski distance,
etc. Finally, we give an illustrative example of the new approach
where we can see the different results obtained by using different
aggregation operators.
Abstract: We present a method for the selection of students
in interdisciplinary studies based on the hybrid averaging
operator. We assume that the available information given in
the problem is uncertain so it is necessary to use interval
numbers. Therefore, we suggest a new type of hybrid
aggregation called uncertain induced generalized hybrid
averaging (UIGHA) operator. It is an aggregation operator
that considers the weighted average (WA) and the ordered
weighted averaging (OWA) operator in the same formulation.
Therefore, we are able to consider the degree of optimism of
the decision maker and grades of importance in the same
approach. By using interval numbers, we are able to represent
the information considering the best and worst possible results
so the decision maker gets a more complete view of the
decision problem. We develop an illustrative example of the
proposed scheme in the selection of students in
interdisciplinary studies. We see that with the use of the
UIGHA operator we get a more complete representation of the
selection problem. Then, the decision maker is able to
consider a wide range of alternatives depending on his
interests. We also show other potential applications that could
be used by using the UIGHA operator in educational problems
about selection of different types of resources such as
students, professors, etc.
Abstract: Strong law of large numbers and complete convergence for sequences of *-mixing random variables are investigated. In particular, Teicher-s strong law of large numbers for independent random variables are generalized to the case of *-mixing random sequences and extended to independent and identically distributed Marcinkiewicz Law of large numbers for *-mixing.
Abstract: .Hardware realization of a Neural Network (NN), to a large extent depends on the efficient implementation of a single neuron. FPGA-based reconfigurable computing architectures are suitable for hardware implementation of neural networks. FPGA realization of ANNs with a large number of neurons is still a challenging task. This paper discusses the issues involved in implementation of a multi-input neuron with linear/nonlinear excitation functions using FPGA. Implementation method with resource/speed tradeoff is proposed to handle signed decimal numbers. The VHDL coding developed is tested using Xilinx XC V50hq240 Chip. To improve the speed of operation a lookup table method is used. The problems involved in using a lookup table (LUT) for a nonlinear function is discussed. The percentage saving in resource and the improvement in speed with an LUT for a neuron is reported. An attempt is also made to derive a generalized formula for a multi-input neuron that facilitates to estimate approximately the total resource requirement and speed achievable for a given multilayer neural network. This facilitates the designer to choose the FPGA capacity for a given application. Using the proposed method of implementation a neural network based application, namely, a Space vector modulator for a vector-controlled drive is presented
Abstract: The focus in this work is to assess which method
allows a better forecasting of malaria cases in Bujumbura ( Burundi)
when taking into account association between climatic factors and
the disease. For the period 1996-2007, real monthly data on both
malaria epidemiology and climate in Bujumbura are described and
analyzed. We propose a hierarchical approach to achieve our
objective. We first fit a Generalized Additive Model to malaria cases
to obtain an accurate predictor, which is then used to predict future
observations. Various well-known forecasting methods are compared
leading to different results. Based on in-sample mean average
percentage error (MAPE), the multiplicative exponential smoothing
state space model with multiplicative error and seasonality performed
better.
Abstract: Three novel and significant contributions are made in
this paper Firstly, non-recursive formulation of Haar connection
coefficients, pioneered by the present authors is presented, which
can be computed very efficiently and avoid stack and memory
overflows. Secondly, the generalized approach for state analysis of
singular bilinear time-invariant (TI) and time-varying (TV) systems
is presented; vis-˜a-vis diversified and complex works reported by
different authors. Thirdly, a generalized approach for parameter
estimation of bilinear TI and TV systems is also proposed. The unified
framework of the proposed method is very significant in that the
digital hardware once-designed can be used to perform the complex
tasks of state analysis and parameter estimation of different types
of bilinear systems single-handedly. The simplicity, effectiveness and
generalized nature of the proposed method is established by applying
it to different types of bilinear systems for the two tasks.
Abstract: In this paper we propose and examine an Adaptive
Neuro-Fuzzy Inference System (ANFIS) in Smoothing Transition
Autoregressive (STAR) modeling. Because STAR models follow
fuzzy logic approach, in the non-linear part fuzzy rules can be
incorporated or other training or computational methods can be
applied as the error backpropagation algorithm instead to nonlinear
squares. Furthermore, additional fuzzy membership functions can be
examined, beside the logistic and exponential, like the triangle,
Gaussian and Generalized Bell functions among others. We examine
two macroeconomic variables of US economy, the inflation rate and
the 6-monthly treasury bills interest rates.
Abstract: Discrete Cosine Transform (DCT) based transform coding is very popular in image, video and speech compression due to its good energy compaction and decorrelating properties. However, at low bit rates, the reconstructed images generally suffer from visually annoying blocking artifacts as a result of coarse quantization. Lapped transform was proposed as an alternative to the DCT with reduced blocking artifacts and increased coding gain. Lapped transforms are popular for their good performance, robustness against oversmoothing and availability of fast implementation algorithms. However, there is no proper study reported in the literature regarding the statistical distributions of block Lapped Orthogonal Transform (LOT) and Lapped Biorthogonal Transform (LBT) coefficients. This study performs two goodness-of-fit tests, the Kolmogorov-Smirnov (KS) test and the 2- test, to determine the distribution that best fits the LOT and LBT coefficients. The experimental results show that the distribution of a majority of the significant AC coefficients can be modeled by the Generalized Gaussian distribution. The knowledge of the statistical distribution of transform coefficients greatly helps in the design of optimal quantizers that may lead to minimum distortion and hence achieve optimal coding efficiency.
Abstract: A new Feed-Forward/Feedback Generalized
Minimum Variance Pole-placement Controller to incorporate the
robustness of classical pole-placement into the flexibility of
generalized minimum variance self-tuning controller for Single-Input
Single-Output (SISO) has been proposed in this paper. The design,
which provides the user with an adaptive mechanism, which ensures
that the closed loop poles are, located at their pre-specified positions.
In addition, the controller design which has a feed-forward/feedback
structure overcomes the certain limitations existing in similar poleplacement
control designs whilst retaining the simplicity of
adaptation mechanisms used in other designs. It tracks set-point
changes with the desired speed of response, penalizes excessive
control action, and can be applied to non-minimum phase systems.
Besides, at steady state, the controller has the ability to regulate the
constant load disturbance to zero. Example simulation results using
both simulated and real plant models demonstrate the effectiveness of
the proposed controller.
Abstract: Ranking of fuzzy numbers play an important role in
decision making, optimization, forecasting etc. Fuzzy numbers must
be ranked before an action is taken by a decision maker. In this
paper, with the help of several counter examples it is proved that
ranking method proposed by Chen and Chen (Expert Systems with
Applications 36 (2009) 6833-6842) is incorrect. The main aim of this
paper is to propose a new approach for the ranking of generalized
trapezoidal fuzzy numbers. The main advantage of the proposed
approach is that the proposed approach provide the correct ordering
of generalized and normal trapezoidal fuzzy numbers and also the
proposed approach is very simple and easy to apply in the real life
problems. It is shown that proposed ranking function satisfies all
the reasonable properties of fuzzy quantities proposed by Wang and
Kerre (Fuzzy Sets and Systems 118 (2001) 375-385).
Abstract: In this paper, solution of fuzzy differential equation
under general differentiability is obtained by simulink. The simulink
solution is equivalent or very close to the exact solution of the
problem. Accuracy of the simulink solution to this problem is
qualitatively better. An illustrative numerical example is presented
for the proposed method.