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NORMAL FUZZY PROBABILITY FOR GENERALIZED QUADRATIC FUZZY SETS
김창일,윤용식 충청수학회 2012 충청수학회지 Vol.25 No.2
A generalized quadratic fuzzy set is a generalization of a quadratic fuzzy number. Zadeh dees the probability of the fuzzy event using the probability. We dee the normal fuzzy prob-ability on R using the normal distribution. And we calculate the normal fuzzy probability for generalized quadratic fuzzy sets.
Dolomite 로 부터 고토인안비료 제조의 기초적 연구
김창은 한국화학공학회 1972 Korean Chemical Engineering Research(HWAHAK KONGHA Vol.10 No.1
This investigation was carried out to produce a high quality magnesium compounded fertilizer by initially dissolving calcined dolomite in sea water to form the intermediate Mg(OH)₂ precipitate, and reacting this intermediate with phosphoric acid and ammonia thereafter. The experimental results were obtained as follows; 1) The optimum calcination temperature of dolomite was about 950℃ for 30 minutes operation and in the displacement of the calcined dolomite in sea water, the optimum mole ratio of calcium hydroxide to magnesium chloride is 1:1.2 for 4 hours of the dissolution time. 2) The high yield of the magnesium compounded fertilizer was obtained, when the precipitate was reacted with 20% phosphoric acid and neutralized with 28% ammonium hydroxide thereby obtaining the alkalinity of the solution to pH 9. 3) By the results of X-ray diffraction and chemical analysis, the major component of the product was magnesium ammonium phosphate at the above condition and the fertilizing effect was also good.
A FIXED POINT APPROACH TO THE STABILITY OF ADDITIVE-QUADRATIC FUNCTIONAL EQUATIONS IN MODULAR SPACES
김창일,박세원 충청수학회 2015 충청수학회지 Vol.28 No.2
In this paper, we prove the generalized Hyers-Ulam stability for the following additive-quadratic functional equation f(2x + y) + f(2x y) = f(x + y) + f(x y) + 4f(x) + 2f( x) in modular spaces by using a xed point theorem for modular spaces.
The canonical form of involutary fuzzy matrices
김창일,박세원 충청수학회 2014 충청수학회지 Vol.27 No.4
We study special types of matrices. The involutary fuzzy matrices are important in various applications and have many interesting properties. Using the graphical method, we have the zero patterns of involutary fuzzy matrix, that is, involutary Boolean matrices. And we give the construction of all involutary fuzzy matrices for some dimensions and suggest the canonical form of involutary fuzzy matrix.
Minimal quasi-F covers of some extension
김창일,정갑헌 충청수학회 2013 충청수학회지 Vol.26 No.2
Observing that every Tychonoff space X has an extension kX which is a weakly LindelÄof space and the minimal quasi-F cover QF(kX) of kX is a weakly LindelÄof, we show that ΦkX :QF(kX) → kX is a z#-irreducible map and that QF(βX)=βQF(kX). Using these, we prove that QF(kX) = kQF(X) if and only if ΦkX : kQF(X) → kX is an onto map and βQF(X) =QF(βX).
Zadeh's extension principle for 2-dimensional triangular fuzzy numbers
김창일,윤용식 한국지능시스템학회 2015 한국지능시스템학회논문지 Vol.25 No.2
A triangular fuzzy number is one of the most popular fuzzy numbers. Many results for the extended algebraic operations between two triangular fuzzy numbers are well-known. We generalize the triangular fuzzy numbers on to . By defining parametric operations between two regions valued -cuts, we get the parametric operations for two triangular fuzzy numbers defined on R2.
Approximately quintic mappings in non-Archimedean 2-normed spaces by fixed point theorem
김창일,Kap Hun Jung 한국전산응용수학회 2015 Journal of applied mathematics & informatics Vol.33 No.3
In this paper, using the fixed point method, we investigate the generalized Hyers-Ulam stability of the system of quintic functional equation \begin{equation*} \left \{ \begin{array}{ll} f(x_1+x_2,y)+f(x_1-x_2,y)=2f(x_1,y)+2f(x_2,y) \\ f(x,2y_1+y_2)+f(x,2y_1-y_2) = f(x,y_1-2y_2) +f(x,y_1+y_2)\\ - f(x,y_1-y_2)+15f(x,y_1) + 6f(x,y_2). \end{array} \right. \end{equation*} in non-Archimedean 2-Banach spaces.
STABILITY OF A CUBIC FUNCTIONAL EQUATION IN 2-NORMED SPACES
김창일,정갑헌 한국전산응용수학회 2014 Journal of applied mathematics & informatics Vol.32 No.5
In this paper, we prove the generalized Hyers-Ulam stability of the following cubic funtional equation f(2x + y) + f(2x −y) = 2f(x + 2y) −4f(x + y) + 18f(x) −12f(y) by the direct method in 2-normed spaces.
김창일 충청수학회 2013 충청수학회지 Vol.26 No.1
We show that if X is a space such that βQF(X) = QF(βX) and each stable Z(X)#-ultra¯lter has the countable intersection property, then there is a homeomorphism hX : υQF(X) →QF(υX) with rX = ΦυX ο hX. Moreover, if βQF(X) = QF(βX)and υE(X) = E(υX) or υ∧(X) = ∧(υX), then υQF(X) = QF(υX).