• Title/Summary/Keyword: Korean mathematics

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SOME NOTES ON STRONG LAW OF LARGE NUMBERS FOR BANACH SPACE VALUED FUZZY RANDOM VARIABLES

  • Kim, Joo-Mok;Kim, Yun Kyong
    • Korean Journal of Mathematics
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    • v.21 no.4
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    • pp.383-399
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    • 2013
  • In this paper, we establish two types of strong law of large numbers for fuzzy random variables taking values on the space of normal and upper-semicontinuous fuzzy sets with compact support in a separable Banach space. The first result is SLLN for strong-compactly uniformly integrable fuzzy random variables, and the other is the case of that the averages of its expectations converges.

SHIFTING AND MODULATION FOR FOURIER-FEYNMAN TRANSFORM OF FUNCTIONALS IN A GENERALIZED FRESNEL CLASS

  • Kim, Byoung Soo
    • Korean Journal of Mathematics
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    • v.25 no.3
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    • pp.335-347
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    • 2017
  • Time shifting and frequency shifting proprerties for the Fourier-Feynman transform of functionals in a generalized Fresnel class ${\mathcal{F}}_{A_1,A_2}$ are given. We discuss scaling and modulation proprerties for the Fourier-Feynman transform. These properties help us to obtain Fourier-Feynman transforms of new functionals from the Fourier-Feynman transforms of old functionals which we know their Fourier-Feynman transforms.

ON THE INITIAL SEED OF THE RANDOM NUMBER GENERATORS

  • Kim, Tae-Soo;Yang, Young-Kyun
    • Korean Journal of Mathematics
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    • v.14 no.1
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    • pp.85-93
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    • 2006
  • A good arithmetic random number generator should possess full period, uniformity and independence, etc. To obtain the excellent random number generator, many researchers have found good parameters. Also an initial seed is the important factor in random number generator. But, there is no theoretical guideline for using the initial seeds. Therefore, random number generator is usually used with the arbitrary initial seed. Through the empirical tests, we show that the choice of the initial values for the seed is important to generate good random numbers.

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ON C-INTEGRAL OF BANACH-VALUED FUNCTIONS

  • Ye, Guoju;Zhao, Dafang
    • Korean Journal of Mathematics
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    • v.14 no.2
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    • pp.169-183
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    • 2006
  • In this paper, we define and study the C-integral and the strong C-integral of functions mapping an interval [a,b] into a Banach space X. We prove that the C-integral and the strong C-integral are equivalent if and only if the Banach space is finite dimensional, We also consider the property of primitives corresponding to Banach-valued functions with respect to the C-integral and the strong C-integral.

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On Fuzzy Irresolute Functions

  • Ekici, Erdal;Park, Jin-Han
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.5 no.2
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    • pp.164-168
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    • 2005
  • As a generalization of the notions of fuzzy $\alpha-irresolute$, fuzzy preirresolute, fuzzy irresolute and fuzzy $\beta-irresolute$ functions, we introduce the notion of fuzzy $\beta\alpha-continuous$ functions and investigate the relationships between fuzzy $\beta\alpha-continuous$ functions and fuzzy separation axioms.

γ-Connectedness in fuzzy topological spaces

  • Hanafy, I.M.
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.3 no.2
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    • pp.258-261
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    • 2003
  • The aim of this paper is to introduce the concept $\gamma$-connectedness in fuzzy topological spaces. We also investigate some interre lations between this types of fuzzy connectedness together with the preservation properties under some types of fuzzy continuity. A comparison between some types of connectedness in fuzzy topological spaces is of interest.

INTUITIONISTIC FUZZY FUNCTIONS

  • Hanafy, I.M.
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.3 no.2
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    • pp.200-205
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    • 2003
  • In this paper, we generally introduce some of the terminology of Yalvac [10] and Azad [4] in intuitionistic fuzzy topological spaces. In addition to the fundamental concepts of intuitionistic fuzzy sets, we emphasize the usefulness of the concepts of intuitionistic fuzzy points intuitionistic fuzzy elementhood. Mainly, this paper is devoted to the study of intuitionistic fuzzy topological spaces with specific attention to the weaker forms of fuzzy continuity.

A Note on Possibilistic Correlation

  • Hong, Dug-Hun
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.9 no.1
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    • pp.1-3
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    • 2009
  • Recently, Carlsson, Full\acute{e}$r and Majlender [1] presented the concept of possibilitic correlation representing an average degree of interaction between marginal distribution of a joint possibility distribution as compared to their respective dispersions. They also formulated the weak and strong forms of the possibilistic Cauchy-Schwarz inequality. In this paper, we define a new probability measure. Then the weak and strong forms of the Cauchy-Schwarz inequality are immediate consequence of probabilistic Cauchy-Schwarz inequality with respect to the new probability measure.

Some Properties on Intuitionistic Fuzzy Metric Space

  • Park, Jong-Seo;Kwun, Young-Chel;Park, Jin-Han
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.10 no.2
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    • pp.152-156
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    • 2010
  • We define some terminologies on intuitionistic fuzzy metric space and prove that the topology generated by any intuitionistic fuzzy metric space is metrizable. Also, we show that if the intuitionistic fuzzy metric space is complete, then the generated topology is completely metrizable, a Baire space, and that an intuitionistic fuzzy metric space is precompact if and only if every sequence has a Cauchy subsequence.