• Bulletin of the Korean Mathematical Society
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• v.57 no.3
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• pp.569-581
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• 2020

In this paper, we introduce the new general concept of usual expansiveness which is called "positively weak measure expansiveness" and study the basic properties of positively weak measure expansive C¹-differentiable maps on a compact smooth manifold M. And we prove that the following theorems. (1) Let 𝓟𝓦𝓔 be the set of all positively weak measure expansive differentiable maps of M. Denote by int(𝓟𝓦𝓔) is a C¹-interior of 𝓟𝓦𝓔. f ∈ int(𝓟𝓦𝓔) if and only if f is expanding. (2) For C¹-generic f ∈ C¹ (M), f is positively weak measure-expansive if and only if f is expanding.

• Journal of the Korean Society of Marine Environment & Safety
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• v.2 no.1
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• pp.97-106
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• 1996

One of the main problems in evaluating complex objects, such as an ill-defined system, is how to treat ambiguous aspect of the evaluation. Due to the Complexity and ambiguity of the objects, many types of evaluation attributes should be identified based on the rational dsision. One of these attributes is an analytical hierarchy process (AHP). the weight of evaluation attribtes in AHP however comes from the probability measure based on the additivity. Therefore, it is notapplicable to the objects which have the property of non-additivity. In the previous studies by other researchers they intriduced the Hierarchical Fuzzy Integral method or mergd AHP and fuzzy measure for the analysis of the overlaps among the evaluation objects. But, they need more anlyses in terms of transformation of the probability measure into fuzzy measure which fits for the additivity and overlapping coefficient which affects to the fuzzy measure. Considering these matters, this paper deals that, ⅰ) clarifying the relation between the fuzzy and probability measure adopted in AHP, ii) calculating directly the family of fuzzy measure from the overlapping coefficient and probability measure. A simple algorithm for the calculation of fuzzy measures and set family of those from the above results is also proposed. Finally, the effectiveness of the algorithm developed by applying this to the problems for estimation of safety in ship berthing and for evaluation of ports in competition is verified. This implied that the new algoritnm gives better description of the system evaluation.

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.673-683
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• 2000

We define the centered-net covering and the centered-net parking measure and then show that the regular sets induced by the two centered measures are equal for $C{\frac}{\delta}{R}$ almost everywhere.

• Journal of the Korean Data and Information Science Society
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• v.15 no.4
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• pp.957-963
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• 2004

A new agreement measure for multivariate interval data by different sets of raters is proposed. The proposed approach builds on Um's multivariate extension of Cohen's kappa. The proposed measure is compared with corresponding earlier measures based on Berry and Mielke's approach and Janson and Olsson approach, respectively. Application of the proposed measure is exemplified using hypothetical data set.

• Journal of the Korean Mathematical Society
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• v.43 no.3
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• pp.461-489
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• 2006

In this article, we establish the existence theorem for measure-valued Dyson series and show that it satisfies the Volterra-type integral equation. Furthermore, we prove the stability theorems for measure-valued Dyson series.

• Journal of the Ergonomics Society of Korea
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• v.19 no.2
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• pp.33-45
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• 2000

Present study was performed to compare different types of teleoperation performance measures. A modified Cooper-Harper rating scale and a distance measure were newly introduced and compared to two traditional measures, the error rate and time-to-completion. Participants performed a simulated telerobotic task with varying visual display interfaces. The results of correlation analyses revealed that the modified Cooper-Harper ratings had a close association with the error rate measure. The distance measure also appeared to be a consistent performance measure, which accounted for both the error rate and time-to-completion. A further analysis, however, showed that the effectiveness of each performance measure varied with the level of task difficulty. The results imply that the choice of performance measure should be made based on the task difficulty as well as the particular task being studied. The results revealed here also have implication for performance measures of various display and control systems including aircraft navigation displays and tactical displays.

• The Mathematical Education
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• v.50 no.3
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• pp.355-365
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• 2011

The purpose of this study is to provide mathematical knowledge for supporting the didactical knowledge on circular measure and radian in the high school curriculum. We show that circular measure related to arcs can be mathematically justified as an angular measure and radian is a well defined concept to be able to reconcile the values of trigonometric functions and ones of circular functions, which are real variable functions. Radian has two-fold intrinsic attributes of angular measure and arc measure on the unit circle, in particular, the latter property plays a very important role in simplifying the trigonometric derivatives. To improve students's low academic achievement in trigonometry section, the useful advantage and the background over the introduction of radian should be preferentially taught and recognized to students. We suggest some teaching plans to practice in the class of elementary and middle school for enhancing teachers' and students' understanding of radian.

• Speech Sciences
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• v.7 no.2
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• pp.85-95
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• 2000

In this paper, the H1*-H2* measure is introduced and exact procedures for obtaining the H1*-H2* value are fully specified, The H1*-H2* measure (a corrected difference in dB between the first and second harmonics) has been devised to provide an acoustic correlate of the phonation mode of a vowel following a consonant. With this measure, we can investigate the phonation mode of a vowel that is free from the F1 amplitude perturbation effect caused by the preceding consonant, which is especially salient at the voicing onset position of the vowel. For identical research purposes, on the other hand, the H1-H2 measure (the observed difference in dB between the first and second harmonic) has been employed in many previous studies. This paper compares these two measures by illustrating experimental results of exploring post-release phonation modes of vowels following the different manner classes of stop consonants in Korean $\square$i.e., the tense, lenis, and aspirated stops.

• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.5
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• pp.642-647
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• 2004

The relations of fuzzy entropy, distance measure, and similarity measure are discussed in this paper. For the purpose of reliable signal selection, the fuzzy entropy is proposed by a distance measure. Properness of the proposed entropy is verified by the definition of the entropy measure. Fourier and Wavelet transform are applied to the stator current signal to obtain the fault features of an induction motor. Membership functions for 3-phase currents are obtained by the Bootstrap method and Central Limit Theorem. Finally, the proposed entropy is applied to measure the fault signal of an induction machine, and the fuzzy entropy values of phase currents are illustrated.

• Nuclear Engineering and Technology
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• v.35 no.1
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• pp.80-90
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• 2003

According to related studies, it was revealed that the procedural deviation plays a significant role in initiating accidents or incidents. This means that, to maximize safety, it is indispensable to be able to answer the question of “why the operators deviate from procedures\ulcorner” In this study, the SC (step complexity) measure is introduced to investigate its applicability for studying the procedural deviation, since it was shown that the change of the operators' performance is strongly correlated with the change of SC scores. This means that the SC measure could play an important role for researches related to the procedural deviation, since it is strongly believed that complicated procedures would affect both the operator' performance and the possibility of the procedural deviation. Thus, to ensure this expectation, the meaning of the SC measure is investigated through brief explanations including the necessity, theoretical basis and verification activities of the SC measure. As a result, it is confirmed that the SC measure can be used to explain the change of the operators' performance due to the task complexity implied by procedures. In addition, it seems that the SC measure nay be useful for various purposes, particularly for scrutinizing the relationship between the procedural deviation and complicated procedures.