• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.1
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• pp.20-29
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• 2009

In this paper, by using the definition of fuzzy equivalence relations introduced by Dib and Youssef, we obtain fuzzy analogues of many results concerning ordinary equivalence relations. Moreover, we investigate fuzzy analogues of many results concerning relationships between ordinary equivalence relations and ordinary functions. In particular, we obtain the fuzzy-canonical decomposition of a fuzzy function.

• Journal of the Korean Institute of Intelligent Systems
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• v.18 no.1
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• pp.32-40
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• 2008

Fuzzy rules are very useful and efficient to describe classification rules especially when the attribute values are continuous and fuzzy in nature. However, it is generally difficult to determine membership functions for generating efficient fuzzy classification rules. In this paper, we propose a method of automatic generation of efficient fuzzy classification rules using evolutionary algorithm. In our method we generate a set of initial membership functions for evolutionary algorithm by supervised clustering the training data set and we evolve the set of initial membership functions in order to generate fuzzy classification rules taking into consideration both classification accuracy and rule comprehensibility. To reduce time to evaluate an individual we also propose an evolutionary algorithm with data partition evaluation in which the training data set is partitioned into a number of subsets and individuals are evaluated using a randomly selected subset of data at a time instead of the whole training data set. We experimented our algorithm with the UCI learning data sets, the experiment results showed that our method was more efficient at average compared with the existing algorithms. For the evolutionary algorithm with data partition evaluation, we experimented with our method over the intrusion detection data of KDD'99 Cup, and confirmed that evaluation time was reduced by about 70%. Compared with the KDD'99 Cup winner, the accuracy was increased by 1.54% while the cost was reduced by 20.8%.

• Communications of the Korean Mathematical Society
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• v.10 no.4
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• pp.789-795
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• 1995

For nonintegrable weight $-\rho$, some weight multiplicities of the irreducible module $L(-\rho)$ over $A^{(1)}_{(1)}$ affine Lie algebras are expressed in terms of the colored partition functions. Also we find the multiplicity of $L(-\rho)$ in ther Verma module $M(-\rho)$ for any affine Lie algebras.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.7 no.4
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• pp.151-158
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• 2014

In this paper, we introduce an inference system using hard scatter partition method and model the nonlinear process. To do this, we use the hard scatter partition method that partition the input space in the scatter form with the value of the membership degree of 0 or 1. The proposed method is implemented by C-Means clustering algorithm. and is used for the initial center values by means of binary split. by applying the LBG algorithm to compensate for shortcomings in the sensitive initial center value. Hard-scatter-partitioned input space forms the rules in the rule-based system modeling. The premise parameters of the rules are determined by membership matrix by means of C-Means clustering algorithm. The consequence part of the rules is expressed in the form of polynomial functions and the coefficient parameters of each rule are determined by the standard least-squares method. The data widely used in nonlinear process is used to model the nonlinear process and evaluate the characteristics of nonlinear process.

• Bulletin of the Korean Mathematical Society
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• v.43 no.1
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• pp.189-212
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• 2006

Let $F^{\alpha}G$ be a twisted group algebra with basis ${{\mu}g|g\;{\in}\;G}$ and $P\;=\;{C_g|g\;{\in}\;G}$ be a partition of G. A projective class algebra associated with P is a subalgebra of $F^{\alpha}G$ generated by all class sums $\sum\limits{_{x{\in}C_g}}\;{\mu}_x$. A main object of the paper is to find interrelationships of projective class algebras in $F^{\alpha}G$ and in $F^{\alpha}H$ for H < G. And the a-spherical function will play an important role for the purpose. We find functional properties of a-spherical functions and investigate roles of $\alpha-spherical$ functions as characters of projective class algebras.

• Journal of Communications and Networks
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• v.17 no.3
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• pp.286-295
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• 2015

Avionic databuses fulfill a critical function in the connection and communication of aircraft components and functions such as flight-control, navigation, and monitoring. Ethernet-based avionic databuses have become the mainstream for large aircraft owning to their advantages of full-duplex communication with high bandwidth, low latency, low packet-loss, and low cost. As a new generation aviation network communication standard, avionics full-duplex switched ethernet (AFDX) adopted concepts from the telecom standard, asynchronous transfer mode (ATM). In this technology, the switches are the key devices influencing the overall performance. This paper reviews the avionic databus with emphasis on the switch architecture classifications. Based on a comparison, analysis, and discussion of the different switch architectures, we propose a new avionic switch design based on a time-division switch fabric for high flexibility and scalability. This also merges the design concept of space-partition switch fabric to achieve reliability and predictability. The new switch architecture, called space partitioned shared memory switch (SPSMS), isolates the memory space for each output port. This can reduce the competition for resources and avoid conflicts, decrease the packet forwarding latency through the switch, and reduce the packet loss rate. A simulation of the architecture with optimized network engineering tools (OPNET) confirms the efficiency and significant performance improvement over a classic shared memory switch, in terms of overall packet latency, queuing delay, and queue size.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1857-1868
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• 2016

We consider a natural generalization of $h_2(n)$, denoted $h_m(n)$, which is the number of partitions of n into parts which are power of $m{\geq}2$ wherein each power of m is allowed to be used as a part at most m times. In this note, we approach in three different ways using the recurrences, the matrix and the tree to calculate the value of $h_m(n)$.

• Journal of the Korean Society for information Management
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• v.16 no.4
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• pp.75-94
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• 1999

Indexing is a prerequisite function for the information retrieval system in order to retrieve the information of the documents effectively which are saved in database. As a digital data increases in accordance with the development of a computer, the numbers of literatures to be saved in database have also been increased in a large volume. To retrieve such documents of large volume, a lot of system resources and processing time will be required. In this paper, we suggest a advanced indexing method using text partition. This method can retrieve the documents of large volume in short processing time. We applied this suggested indexing method to real information retrieval system, and proved its excellent functions through the demonstration.

• Journal of the Korean Mathematical Society
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• v.51 no.5
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• pp.987-1028
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• 2014

In a recent systematic study, C. Sandon and F. Zanello offered 30 conjectured identities for partitions. As a consequence of their study of partition identities arising from Ramanujan's formulas for multipliers in the theory of modular equations, the present authors in an earlier paper proved three of these conjectures. In this paper, we provide proofs for the remaining 27 conjectures of Sandon and Zanello. Most of our proofs depend upon known modular equations and formulas of Ramanujan for theta functions, while for the remainder of our proofs it was necessary to derive new modular equations and to employ the process of duplication to extend Ramanujan's catalogue of theta function formulas.

• Bulletin of the Korean Chemical Society
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• v.34 no.3
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• pp.743-748
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• 2013

The temperature dependence of the partition coefficients of a neuropeptide, substance P (SP), in isotropic acidic bicelles was investigated by using a pulsed field gradient nuclear magnetic resonance diffusion technique. The addition of negatively charged dimyristoylphosphatidylserine to the neutral bicelle changed the SP partitioning a little, which implies that the hydrophobic interaction between the hydrophobic residues of SP and the acyl chains of lipid molecules is the major interaction while the electrostatic interaction is minor in SP binding in a lipid membrane. From the temperature dependence of the partition coefficients, thermodynamic functions were calculated. The partitioning of SP into the acidic bicelles is enthalpy-driven, as it is for small unilamellar vesicles and dodecylphosphocholine micelles, while peptide partitioning into a large unilamellar vesicle is entropy-driven. This may mean that the size of lipid membranes is a more important factor for peptide binding than the surface curvature and surface charge density.