• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.12a
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• pp.1-4
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• 2002

There have been several tipical methods being used to measure the fuzziness (entropy) of fuzzy sets. Pedrycz is the original motivation of this paper. This paper studies the entropy variation on the fuzzy numbers with arithmetic operations(addition, subtraction, multiplication) and the relationship between entropy and information energy. It is shown that through the arithmetic operations, the entropy of the resultant fuzzy number has the arithmetic relation with the entropy of each original fuzzy number. Moreover, the information energy variation on the fuzzy numbers is also discussed. The results generalize earlier results of Pedrycz [FSS 64(1994) 21-30] and Wang and Chiu [FSS 103(1999) 443-455].

• Korean Journal of Mathematics
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• v.9 no.2
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• pp.83-98
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• 2001

We characterize ($r,w$)-nuclear operators acting from a Banach space whose dual has weak type $q$ into a Banach space of weak type $p$ by the asymptotic behaviour of their entropy numbers.

• Journal of the Korean Institute of Intelligent Systems
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• v.15 no.6
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• pp.754-758
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• 2005

There have been several tipical methods being used tomeasure the fuzziness (entropy) of fuzzy sets. Pedrycz is the original motivation of this paper. Recently, Wang and Chiu [FSS103(1999) 443-455] and Pedrycz [FSS 64(1994) 21-30] showed the relationship(addition, subtraction, multiplication) between the entropies of the resultant fuzzy number and the original fuzzy numbers of same type. In this paper, using Lebesgue-Stieltjes integral, we generalize results of Wang and Chiu [FSS 103(1999) 443-455] concerning entropy arithmetic operations without the condition of same types of fuzzy numbers. And using this results and trade-off relationship between information energy and entropy, we study more properties of information energy of fuzzy numbers.

• The Pure and Applied Mathematics
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• v.23 no.3
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• pp.205-221
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• 2016

We formulate the additive entropy of a natural number in terms of the additive partition function, and show that its multiplicative entropy is directly related to the multiplicative partition function. We give a practical formula for the multiplicative entropy of natural numbers with two prime factors. We use this formula to analyze the comparative density of additive and multiplicative entropy, prove that this density converges to zero as the number tends to infinity, and empirically observe this asymptotic behavior.

• Proceedings of the KIEE Conference
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• 1999.07g
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• pp.2876-2878
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• 1999

There have been several tipical methods being used to measure the fuzziness (entropy) of fuzzy sets. Pedrycz is the original motivation of this paper. This paper studies the entropy variation on the fuzzy numbers with arithmetic operations(addition, subtraction, multiplication). It is shown that through the arithmetic operations, the entropy of the resultant fuzzy number has the arithmetic relation with the entropy of each original fuzzy number. This paper generalize earlier results of Pedrycz [FSS 64(1994) 21-30] and Wang and Chiu [FSS 103(1999) 443-455].

• Proceedings of the IEEK Conference
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• 1998.10a
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• pp.863-866
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• 1998

In this paper, we proposes Moving Picture Compression reducing bit numbers within the block by probability in 3D-DCT considered of temporal axis. From Delta Modification theory for frequency components, bit numbers within the block(4$\times$4) were properly compressed by using the Probability Entropy. At the result for the proposed algorithm, we could find that the values of PSNR for resolution and the compression rate were better than existing methods.

• International Journal of Computer Science & Network Security
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• v.24 no.4
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• pp.77-86
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• 2024

Using random numbers to represent uncertainty and unpredictability is essential in many industries. This is crucial in disciplines like computer science, cryptography, and statistics where the use of randomness helps to guarantee the security and dependability of systems and procedures. In computer science, random number generation is used to generate passwords, keys, and other security tokens as well as to add randomness to algorithms and simulations. According to recent research, the hardware random number generators used in billions of Internet of Things devices do not produce enough entropy. This article describes how raw data gathered by IoT system sensors can be used to generate random numbers for cryptography systems and also examines the results of these random numbers. The results obtained have been validated by successfully passing the FIPS 140-1 and NIST 800-22 test suites.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.12 no.4
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• pp.707-715
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• 2008

This paper proposes an algorithm for efficient compression gray-level images by entropy encoder. The issue of the proposed method is to replace original data of gray-level images with particular ranked data. For this, first, before encoding a stream of gray-level values in an image, the proposed method counts co-occurrence frequencies for neighboring pixel values. Then, it replaces each pay value with particularly ranked numbers based on the investigated co-occurrence frequencies. Finally, the ranked numbers are transmitted to an entropy encoder. The proposed method improves the performance of existing entropy coding by transforming original gray-level values into rank based images using statistical co-occurrence frequencies of gray-level images. The simulation results, using gray-level images with 8-bits, show that the proposed method can reduce bit rate by up to 37.85% compared to existing conventional entropy coders.

• Journal of Information Processing Systems
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• v.20 no.3
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• pp.285-295
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• 2024

Driven by the vague assessment big data, a product service system (PSS) evaluation method is developed based on a hybrid model of multi-weight combination and improved TOPSIS by relative entropy. The index values of PSS alternatives are solved by the integration of the stakeholders' vague assessment comments presented in the form of trapezoidal fuzzy numbers. Multi-weight combination method is proposed for index weight solving of PSS evaluation decision-making. An improved TOPSIS by relative entropy (RE) is presented to overcome the shortcomings of traditional TOPSIS and related modified TOPSIS and then PSS alternatives are evaluated. A PSS evaluation case in a printer company is given to test and verify the proposed model. The RE closeness of seven PSS alternatives are 0.3940, 0.5147, 0.7913, 0.3719, 0.2403, 0.4959, and 0.6332 and the one with the highest RE closeness is selected as the best alternative. The results of comparison examples show that the presented model can compensate for the shortcomings of existing traditional methods.

• Bulletin of the Korean Mathematical Society
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• v.35 no.1
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• pp.173-187
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• 1998

Several aspects of pseudorandom number generators are investigated from the viewpoint of ergodic theory. An algorithm of generating pseudorandom numbers proposed and shown to behave reasonably well.