• 한국지능시스템학회논문지
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• 제17권7호
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• pp.970-976
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• 2007

본 연구에서는 퍼지 추론 메커니즘에 기반 한 다항식 네트워크 패턴 분류기(Polynomial Network Pattern Classifier; PNC)를 설계하고 Particle Swarm Optimization 알고리즘을 이용하여 PNC 파라미터, 즉, 학습률, 모멘텀 계수, FCM 클러스터링의 퍼지화 계수(fuzzification Coefficient)를 최적화한다. 제안된 PNC 구조는 FCM 클러스터링에 기반한 분할 함수를 활성 함수로 사용하며, 다항식 함수로 구성된 연결가중치를 사용함으로서 기존 신경회로망 분류기의 선형적인 특성을 개선한다. PNC 구조는 언어적 해석관점에서 "If-then"의 퍼지 규칙으로 표현되며 퍼지 추론 메커니즘에 의해 구동된다. 즉 조건부, 결론부, 추론부 세 가지의 기능적 모듈로 나뉘어 네트워크 구조가 형성된다. 조건부는 FCM 클러스터링을 사용하여 입력 공간을 분할하고, 결론부는 분할된 로컬 영역을 다항식 함수로 표현한다. 마지막으로, 네트워크의 최종출력은 추론부의 퍼지추론에 의한다. 제안된 PNC는 다항식 기반 구조의 퍼지 추론 특성으로 인해 출력 공간상에 비선형 판별 함수(nonlinear discernment function)가 생성되어 분류기로서의 성능을 높인다.

• 충청수학회지
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• 제25권4호
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• pp.771-777
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• 2012

We give a result on the density of certain additive arithmetic functions which count the number of restricted irreducible polynomials on the polynomial ring.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2005년도 ICCAS
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• pp.1505-1509
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• 2005

This paper introduces a new architecture of genetically optimized self-organizing fuzzy polynomial neural networks by means of information granulation. The conventional SOFPNNs developed so far are based on mechanisms of self-organization and evolutionary optimization. The augmented genetically optimized SOFPNN using Information Granulation (namely IG_gSOFPNN) results in a structurally and parametrically optimized model and comes with a higher level of flexibility in comparison to the one we encounter in the conventional FPNN. With the aid of the information granulation, we determine the initial location (apexes) of membership functions and initial values of polynomial function being used in the premised and consequence part of the fuzzy rules respectively. The GA-based design procedure being applied at each layer of genetically optimized self-organizing fuzzy polynomial neural networks leads to the selection of preferred nodes with specific local characteristics (such as the number of input variables, the order of the polynomial, a collection of the specific subset of input variables, and the number of membership function) available within the network. To evaluate the performance of the IG_gSOFPNN, the model is experimented with using gas furnace process data. A comparative analysis shows that the proposed IG_gSOFPNN is model with higher accuracy as well as more superb predictive capability than intelligent models presented previously.

• 한국정보처리학회논문지
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• 제6권9호
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• pp.2431-2441
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• 1999

우리는 등식으로 표현된 많은 정보들을 다룬다. 이러한 정보에 관한 가장 근본적인 문제중의 하나는 '어떤 주어진 등식이 한 가지 방법이다. Rewrite system은 주어진 항(term)에 rewrite 규칙(rule)들을 적용하여 단순화한다. 따라서 어떤 항이라도 단순화 과정이 무한히 계속되지 않아야 함은 rewrite system의 중요한 성질이다. Rewrite system의 이러한 종료(termination) 여부를 결정하는 방법들 중 하나가 다항식 순서(polynomial ordering)이다. 이 방법은 rewrite system의 함수기호에 적절한 다항식을 대응시켜주는 방법이다. 그러나, 주어진 rewrite system이 종료함을 보이는 다항식 순서를 자동적으로 생성하는 방법은 알려져 있지 않다. 본 논문에서는 유전자 알고리즘을 사용하여, 다항식을 자동으로 생성하는 방법을 제시한다.

• Journal of Electrical Engineering and Technology
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• 제3권1호
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• pp.108-114
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• 2008

Polynomial networks have been known to have excellent properties as classifiers and universal approximators to the optimal Bayes classifier. In this paper, the use of polynomial neural networks is proposed for efficient implementation of the polynomial-based classifiers. The polynomial neural network is a trainable device consisting of some rules and three processes. The three processes are assumption, effect, and fuzzy inference. The assumption process is driven by fuzzy c-means and the effect processes deals with a polynomial function. A learning algorithm for the polynomial neural network is developed and its performance is compared with that of previous studies.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2006년도 심포지엄 논문집 정보 및 제어부문
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• pp.270-272
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• 2006

In this paper, we discuss optimal design of Fuzzy Polynomial Neural Networks by means of Genetic Algorithms(GAs) using symbolic coding for non-linear data. One of the major subject of genetic algorithms is representation of chromosomes. The proposed model optimized by the means genetic algorithms which used symbolic code to represent chromosomes. The proposed gFPNN used a triangle and a Gaussian-like membership function in premise part of rules and design the consequent structure by constant and regression polynomial (linear, quadratic and modified quadratic) function between input and output variables. The performance of the proposed model is quantified through experimentation that exploits standard data already used in fuzzy modeling. These results reveal superiority of the proposed networks over the existing fuzzy and neural models.

• 대한수학회보
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• 제29권2호
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• pp.277-283
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• 1992

Let GF(q) be a finite field with q elements where q=p$^{n}$ for a prime number p and a positive integer n. Consider an arbitrary function .phi. from GF(q) into GF(q). By using the Largrange's Interpolation formula for the given function .phi., .phi. can be represented by a polynomial which is congruent (mod x$^{q}$ -x) to a unique polynomial over GF(q) with the degree < q. In [3], Wells characterized all polynomial over a finite field which commute with translations. Mullen [2] generalized the characterization to linear polynomials over the finite fields, i.e., he characterized all polynomials f(x) over GF(q) for which deg(f) < q and f(bx+a)=b.f(x) + a for fixed elements a and b of GF(q) with a.neq.0. From those papers, a natural question (though difficult to answer to ask is: what are the explicit form of f(x) with zero terms\ulcorner In this paper we obtain the exact form (together with zero terms) of a polynomial f(x) over GF(q) for which satisfies deg(f) < p$^{2}$ and (1) f(x+a)=f(x)+c for the fixed nonzero elements a and c in GF(q).

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2005년도 춘계학술대회 학술발표 논문집 제15권 제1호
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• pp.297-300
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• 2005

In this study, we proposed genetically optimized self-organizing fuzzy polynomial neural network based on information granulation and evolutionary algorithm (gdSOFPNN), develop a comprehensive design methodology involving mechanisms of genetic optimization. The proposed gdSOFPNN gives rise to a structural Iy and parametrically optimized network through an optimal parameters design available within FPN (viz. the number of input variables, the order of the polynomial, input variables, the number of membership functions, and the apexes of membership function). Here, with the aid of the information granulation, we determine the initial location (apexes) of membership functions and initial values of polynomial function being used in the premised and consequence part of the fuzzy rules respectively. The performance of the proposed gdSOFPNN is quantified through experimentation that exploits standard data already used in fuzzy modeling.

• Korean Journal of Mathematics
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• 제27권2호
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• pp.417-423
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• 2019

In the paper, by virtue of the $Fa{\grave{a}}$ di Bruno formula, properties of the Bell polynomials of the second kind, and the Lah inversion formula, the author simplifies coefficients in a family of ordinary differential equations related to the generating function of the Mittag-Leffler polynomials.

• 대한수학회보
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• 제55권3호
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• pp.937-956
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• 2018

This article gives the foundations of the colored Jones polynomial for singular knots. We extend Masbum and Vogel's algorithm [26] to compute the colored Jones polynomial for any singular knot. We also introduce the tail of the colored Jones polynomial of singular knots and use its stability properties to prove a false theta function identity that goes back to Ramanujan.