• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.737-748
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• 2009

Using the notion of intuitionistic fuzzy subgroups, its roughness is discussed. With respect to a congruence relation on a group, several properties about the lower and upper approximations of a subset of a group are investigated.

• Bulletin of the Korean Mathematical Society
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• v.33 no.2
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• pp.193-204
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• 1996

Let U and V be nonempty compact subsets of two Hausdorff topological vector spaces. Suppose that a function $J : U \times V \to R$ is such that for each $\upsilon \in V, J(\cdot, \upsilon)$ is lower semi-continuous and convex on U, and for each $ u \in U, J(u, \cdot)$ is upper semi-continuous and concave on V.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.288-295
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• 1998

This paper proposes a new data classification method based on the tolerant rough set that extends the existing equivalent rough set. Similarity measure between two data is described by a distance function of all constituent attributes and they are defined to be tolerant when their similarity measure exceeds a similarity threshold value. The determination of optimal similarity theshold value is very important for the accurate classification. So, we determine it optimally by using the genetic algorithm (GA), where the goal of evolution is to balance two requirements such that (1) some tolerant objects are required to be included in the same class as many as possible. After finding the optimal similarity threshold value, a tolerant set of each object is obtained and the data set is grounded into the lower and upper approximation set depending on the coincidence of their classes. We propose a two-stage classification method that all data are classified by using the lower approxi ation at the first stage and then the non-classified data at the first stage are classified again by using the rough membership functions obtained from the upper approximation set. We apply the proposed classification method to the handwritten numeral character classification. problem and compare its classification performance and learning time with those of the feed forward neural network's back propagation algorithm.

• 전기의세계
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• v.22 no.1
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• pp.28-34
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• 1973

This paper treats with the sub-optimal control problem of noninear systems by approximation method. This method involves the approximation by linearization which provides the sub-optimal solution of non-linear control problems. The result of this work shows that, in the problem in which the controlled plant is characterized by an ordinary differential equation of first order, the solution obtained by this method coincides with the exact solution of problem. In of case of the second or higher order systems, it is proved analytically that this method of linearization produces the sub-optimal solution of the given problem. It is also shown that the sub-optimality of solution by the method can be evaluated by introducing the upper and lower bounded performance indices. Discussion is made on the procedure with some illustrative examples whose performance indices are given in the quadratic forms.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.34 no.2
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• pp.30-34
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• 2011

Variable precision rough set models have been successfully applied to problems whose domains are discrete values. However, there are many situations where discrete data is not available. When it comes to the problems with interval values, no variable precision rough set model has been proposed. In this paper, we propose a variable precision rough set model for interval values in which classification errors are allowed in determining if two intervals are same. To build the model, we define equivalence class, upper approximation, lower approximation, and boundary region. Then, we check if each of 11 characteristics on approximation that works in Pawlak's rough set model is valid for the proposed model or not.

• Journal of computational fluids engineering
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• v.20 no.4
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• pp.109-115
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• 2015

In this study, the Stokes flow in the microchannel is analysed where the semicircular protuberances with constant spacing are attached on the upper and lower walls with staggered arrangement. For the low Reynolds number flow in microchannel, Stokes approximation is used and the periodicity and symmetry of the flow are considered to determine the stream function and pressure distribution in the flow field by using the method of least squared error. As results, the streamline patterns and pressure distributions in the flow field are shown for some specific values of the size and spacing of the protuberances, and shear stress distributions on the surface of semicircular protuberances are plotted. Especially, for an important physical property, the average pressure gradient along the microchannel is obtained and compared with that for the case of in-phase arrangement of the upper and lower protuberances. And, for the small clearance between the protuberances of upper and lower walls or between the protuberances and the opposite wall, the average pressure gradient is derived from the lubrication theory and compared with that of the present study.

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.329-338
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• 2014

In this paper, we study the method of upper and lower solutions and develop the generalized quasilinearization technique for the existence and approximation of solutions to some three-point nonlocal boundary value problems associated with higher order fractional differential equations of the type $$^c{\mathcal{D}}^q_{0+}u(t)+f(t,u(t))=0,\;t{\in}(0,1)$$ $$u^{\prime}(0)={\gamma}u^{\prime}({\eta}),\;u^{\prime\prime}(0)=0,\;u^{\prime\prime\prime}(0)=0,{\ldots},u^{(n-1)}(0)=0,\;u(1)={\delta}u({\eta})$$, where, n-1 < q < n, $n({\geq}3){\in}\mathbb{N}$, 0 < ${\eta},{\gamma},{\delta}$ < 1 and $^c\mathcal{D}^q_{0+}$ is the Caputo fractional derivative of order q. The nonlinear function f is assumed to be continuous.

• Journal of Communications and Networks
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• v.18 no.2
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• pp.182-189
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• 2016

The focus in this paper is on obtaining tight, simple algebraic-form bounds and invertible expressions for the average symbol error probability (ASEP) of M-ary phase shift keying (MPSK) in a class of composite fading channels. We employ the mixture gamma (MG) distribution to approximate the signal-to-noise ratio (SNR) distributions of fading models, which include Nakagami-m, Generalized-K ($K_G$), and Nakagami-lognormal fading as specific examples. Our approach involves using the tight upper and lower bounds that we recently derived on the Gaussian Q-function, which can easily be averaged over the general MG distribution. First, algebraic-form upper bounds are derived on the ASEP of MPSK for M > 2, based on the union upper bound on the symbol error probability (SEP) of MPSK in additive white Gaussian noise (AWGN) given by a single Gaussian Q-function. By comparison with the exact ASEP results obtained by numerical integration, we show that these upper bounds are extremely tight for all SNR values of practical interest. These bounds can be employed as accurate approximations that are invertible for high SNR. For the special case of binary phase shift keying (BPSK) (M = 2), where the exact SEP in the AWGN channel is given as one Gaussian Q-function, upper and lower bounds on the exact ASEP are obtained. The bounds can be made arbitrarily tight by adjusting the parameters in our Gaussian bounds. The average of the upper and lower bounds gives a very accurate approximation of the exact ASEP. Moreover, the arbitrarily accurate approximations for all three of the fading models we consider become invertible for reasonably high SNR.

• PNF and Movement
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• v.4 no.1
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• pp.9-18
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• 2006

Purpose: The purpose of this study was to investigate the effect of Proprioceptive Neuromuscular Facilitation (PNF) applied to the unilateral upper extremity on the muscle activation of contralateral lower extremity. Twenty-two healthy subjects (mean age of 23.7 years) participated in this study. Method : PNF patterns applied on the unilateral upper extremity in all subjects were the flexion/abduction/external rotation and lifting pattern. The hold and appoximation techniques for the irradiation were applied to end range of both patterns. Muscle activations in four patterns were measured in vastus medialis, tibialis anterior, rectus femoris, and gastrocnemius medial muscles of contralateral lower extremity using surface EMG system. Each EMG value in individual muscle was normalized for maximal voluntary contraction. The data were analyzed by one factor analysis of variance with repeated measure test. Result : There were significant differences in the between-subject effect (muscles) and within-subject effect (patterns) in comparison of muscle activation by application of PNF patterns (p<.05). The irradiation led to higher activation in the flexion/abduction/external rotation pattern than that of lifting pattern in all muscles (p<.05). The approximation techniques revealed more activations than these of hold technique in all muscles (p<.05). Conclusion : These results suggest that the application of PNF patterns to the unilateral upper extremity affect on the muscle activation of contralateral lower extremity and increase according to the intensity of resistance. This mechanism of contralateral effect might provide a help to the development of treatment method for the affected side and functional improvement for the patients who have damages of central nervous system or musculoskeletal problems by orthopedic injury.

• Korean Journal of Mathematics
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• v.25 no.1
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• pp.71-85
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• 2017

This paper introduces a novel extension of soft rough fuzzy set so-called modified soft rough fuzzy set model in which new lower and upper approximation operators are presented together their related properties that are also investigated. Eventually it is shown that these new models of approximations are finer than previous ones developed by using soft rough fuzzy sets.