Abstract: In this paper, the robust exponential stability problem of discrete-time uncertain stochastic neural networks with timevarying delays is investigated. By introducing a new augmented Lyapunov function, some delay-dependent stable results are obtained in terms of linear matrix inequality (LMI) technique. Compared with some existing results in the literature, the conservatism of the new criteria is reduced notably. Three numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed method.
Abstract: In this paper, the notion of Hyperbolic Klingenberg
plane is introduced via a set of axioms like as Affine Klingenberg
planes and Projective Klingenberg planes. Models of such planes are
constructed by deleting a certain number m of equivalence classes
of lines from a Projective Klingenberg plane. In the finite case, an
upper bound for m is established and some combinatoric properties
are investigated.
Abstract: This paper focuses on the problem of a common linear copositive Lyapunov function(CLCLF) existence for discrete-time switched positive linear systems(SPLSs) with bounded time-varying delays. In particular, applying system matrices, a special class of matrices are constructed in an appropriate manner. Our results reveal that the existence of a common copositive Lyapunov function can be related to the Schur stability of such matrices. A simple example is provided to illustrate the implication of our results.
Abstract: This paper aims at developing a multilevel fuzzy
decision support model for urban rail transit planning schemes in
China under the background that China is presently experiencing an
unprecedented construction of urban rail transit. In this study, an
appropriate model using multilevel fuzzy comprehensive evaluation
method is developed. In the decision process, the followings are
considered as the influential objectives: traveler attraction,
environment protection, project feasibility and operation. In addition,
consistent matrix analysis method is used to determine the weights
between objectives and the weights between the objectives-
sub-indictors, which reduces the work caused by repeated
establishment of the decision matrix on the basis of ensuring the
consistency of decision matrix. The application results show that
multilevel fuzzy decision model can perfectly deal with the
multivariable and multilevel decision process, which is particularly
useful in the resolution of multilevel decision-making problem of
urban rail transit planning schemes.
Abstract: The optimization problem using time scales is studied.
Time scale is a model of time. The language of time scales seems to
be an ideal tool to unify the continuous-time and the discrete-time
theories. In this work we present necessary conditions for a solution
of an optimization problem on time scales. To obtain that result we
use properties and results of the partial diamond-alpha derivatives for
continuous-multivariable functions. These results are also presented
here.
Abstract: The paper compares the treatment of fractions in a
typical undergraduate college curriculum and in abstract algebra
textbooks. It stresses that the main difference is that the
undergraduate curriculum treats equivalent fractions as equal, and
this treatment eventually leads to paradoxes and impairs the students-
ability to perceive ratios, proportions, radicals and rational exponents
adequately. The paper suggests a simplified version of rigorous
theory of fractions suitable for regular college curriculum.
Abstract: In this study, a minimal submaximal element of LIT(X) (the lattice of all intuitionistic topologies for X, ordered by inclusion) is determined. Afterwards, a new contractive property, intuitionistic mega-connectedness, is defined. We show that the submaximality and mega-connectedness are not complementary intuitionistic topological invariants by identifying those members of LIT(X) which are intuitionistic mega-connected.
Abstract: Developing a stable early warning system (EWS)
model that is capable to give an accurate prediction is a challenging
task. This paper introduces k-nearest neighbour (k-NN) method
which never been applied in predicting currency crisis before with the
aim of increasing the prediction accuracy. The proposed k-NN
performance depends on the choice of a distance that is used where in
our analysis; we take the Euclidean distance and the Manhattan as a
consideration. For the comparison, we employ three other methods
which are logistic regression analysis (logit), back-propagation neural
network (NN) and sequential minimal optimization (SMO). The
analysis using datasets from 8 countries and 13 macro-economic
indicators for each country shows that the proposed k-NN method
with k = 4 and Manhattan distance performs better than the other
methods.
Abstract: A series of microarray experiments produces observations
of differential expression for thousands of genes across multiple
conditions.
Principal component analysis(PCA) has been widely used in
multivariate data analysis to reduce the dimensionality of the data in
order to simplify subsequent analysis and allow for summarization of
the data in a parsimonious manner. PCA, which can be implemented
via a singular value decomposition(SVD), is useful for analysis of
microarray data.
For application of PCA using SVD we use the DNA microarray
data for the small round blue cell tumors(SRBCT) of childhood
by Khan et al.(2001). To decide the number of components which
account for sufficient amount of information we draw scree plot.
Biplot, a graphic display associated with PCA, reveals important
features that exhibit relationship between variables and also the
relationship of variables with observations.
Abstract: The general global behavior of particle S a non-linear (Q - xy)2 potential cannot be revealed a Poincare surface of section method (PSS) because inost trajectories take practically infinitely long time to integrate numerically before they come back to the surface. In this study as an alternative to PSS, a multiple scale perturbation is applied to analyze global adiabatic, non-adiabatic and chaotic behavior of particles in this potential. It was found that the results can be summarized as a form of a Fermi-like map. Additionally, this method gives a variation of global stochasticity criteria with Q.
Abstract: In conventional reliability assessment, the reliability data of system components are treated as crisp values. The collected data have some uncertainties due to errors by human beings/machines or any other sources. These uncertainty factors will limit the understanding of system component failure due to the reason of incomplete data. In these situations, we need to generalize classical methods to fuzzy environment for studying and analyzing the systems of interest. Fuzzy set theory has been proposed to handle such vagueness by generalizing the notion of membership in a set. Essentially, in a Fuzzy Set (FS) each element is associated with a point-value selected from the unit interval [0, 1], which is termed as the grade of membership in the set. A Vague Set (VS), as well as an Intuitionistic Fuzzy Set (IFS), is a further generalization of an FS. Instead of using point-based membership as in FS, interval-based membership is used in VS. The interval-based membership in VS is more expressive in capturing vagueness of data. In the present paper, vague set theory coupled with conventional Lambda-Tau method is presented for reliability analysis of repairable systems. The methodology uses Petri nets (PN) to model the system instead of fault tree because it allows efficient simultaneous generation of minimal cuts and path sets. The presented method is illustrated with the press unit of the paper mill.
Abstract: In this paper, we discuss the egalitarianism solution (ES) and center-of-gravity of the imputation-set value (CIV) for bicooperative games, which can be seen as the extensions of the solutions for traditional games given by Dutta and Ray [1] and Driessen and Funaki [2]. Furthermore, axiomatic systems for the given values are proposed. Finally, a numerical example is offered to illustrate the player ES and CTV.
Abstract: Abstract–Let k ≥ 3 be an integer, and let G be a graph of order n with n ≥ 9k +3- 42(k - 1)2 + 2. Then a spanning subgraph F of G is called a k-factor if dF (x) = k for each x ∈ V (G). A fractional k-factor is a way of assigning weights to the edges of a graph G (with all weights between 0 and 1) such that for each vertex the sum of the weights of the edges incident with that vertex is k. A graph G is a fractional k-deleted graph if there exists a fractional k-factor after deleting any edge of G. In this paper, it is proved that G is a fractional k-deleted graph if G satisfies δ(G) ≥ k + 1 and |NG(x) ∪ NG(y)| ≥ 1 2 (n + k - 2) for each pair of nonadjacent vertices x, y of G.
Abstract: The primary objective of the paper is to propose a new method for solving assignment problem under uncertain situation. In the classical assignment problem (AP), zpqdenotes the cost for assigning the qth job to the pth person which is deterministic in nature. Here in some uncertain situation, we have assigned a cost in the form of composite relative degree Fpq instead of and this replaced cost is in the maximization form. In this paper, it has been solved and validated by the two proposed algorithms, a new mathematical formulation of IVIF assignment problem has been presented where the cost has been considered to be an IVIFN and the membership of elements in the set can be explained by positive and negative evidences. To determine the composite relative degree of similarity of IVIFS the concept of similarity measure and the score function is used for validating the solution which is obtained by Composite relative similarity degree method. Further, hypothetical numeric illusion is conducted to clarify the method’s effectiveness and feasibility developed in the study. Finally, conclusion and suggestion for future work are also proposed.
Abstract: Stochastic resonance (SR) is a phenomenon whereby
the signal transmission or signal processing through certain nonlinear
systems can be improved by adding noise. This paper discusses SR in
nonlinear signal detection by a simple test statistic, which can be
computed from multiple noisy data in a binary decision problem based
on a maximum a posteriori probability criterion. The performance of
detection is assessed by the probability of detection error Per . When
the input signal is subthreshold signal, we establish that benefit from
noise can be gained for different noises and confirm further that the
subthreshold SR exists in nonlinear signal detection. The efficacy of
SR is significantly improved and the minimum of Per can
dramatically approach to zero as the sample number increases. These
results show the robustness of SR in signal detection and extend the
applicability of SR in signal processing.
Abstract: Allowing diagonalizability of sign pattern is still an open problem. In this paper, we make a carefully discussion about allowing unitary diagonalizability of two sign pattern. Some sufficient and necessary conditions of allowing unitary diagonalizability are also obtained.
Abstract: The notion of S-fuzzy left h-ideals in a hemiring is introduced and it's basic properties are investigated.We also study the homomorphic image and preimage of S-fuzzy left h-ideal of hemirings.Using a collection of left h-ideals of a hemiring, S-fuzzy left h-ideal of hemirings are established.The notion of a finite-valued S-fuzzy left h-ideal is introduced,and its characterization is given.S-fuzzy relations on hemirings are discussed.The notion of direct product and S-product are introduced and some properties of the direct product and S-product of S-fuzzy left h-ideal of hemiring are also discussed.
Abstract: In this paper the Laplace Decomposition method is developed to solve linear and nonlinear fractional integro- differential equations of Volterra type.The fractional derivative is described in the Caputo sense.The Laplace decomposition method is found to be fast and accurate.Illustrative examples are included to demonstrate the validity and applicability of presented technique and comparasion is made with exacting results.
Abstract: In this paper, the backward Ussor iterative matrix is proposed. The relationship of convergence between the backward Ussor iterative matrix and Jacobi iterative matrix is obtained, which makes the results in the corresponding references be improved and refined.Moreover,numerical examples also illustrate the effectiveness of these conclusions.
Abstract: In this paper, we first introduce the concepts of weakly prime and weakly quasi-prime fuzzy left ideals of an ordered semigroup S. Furthermore, we give some characterizations of weakly prime and weakly quasi-prime fuzzy left ideals of an ordered semigroup S by the ordered fuzzy points and fuzzy subsets of S.