• 한국정보과학회논문지:소프트웨어및응용
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• 제28권12호
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• pp.930-937
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• 2001

퍼지숫자의 정렬은 퍼지숫자를 크기 순서로 나열을 하는 것이다. 일반적으로 퍼지숫자의 정렬을 위해서는 퍼지숫자 사이의 비교가 필요한데. 피지숫자가 명확하지 않은 값을 표현하기 때문에. 그 비교 결과 역시 명확하지 않을 수 있다 따라서 그 비교결과를 이용한 정렬결과 역시 명확하지 않을 수 있다 그러나 지금가지 대부분의 연구는 퍼지숫자의 정렬 결과를 하나의 배역로만 명확하게 표현하였다. 본 논문 에서는 이러한 점을 고려하여 퍼지만족함수를 이용한 퍼지숫자 정렬방법을 제안한다. 퍼지만족함수는 두 퍼지숫자를 비교하여 그 대소를 0과 1사이의 퍼지집합으로 표현하는 퍼지비교방법이다. 제안하는 방법은 정렬결과로 단순히 하나의 배열만을 생성하지 않고, 퍼지숫자가 겹쳐서 생길 수 있는, 다른 가능한 정렬결 과들을 생성한다.

• Journal of applied mathematics & informatics
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• 제26권5_6호
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• pp.1169-1183
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• 2008

In this paper, a method to find the weighted possibilistic variance and moments about the mean value of fuzzy numbers via applying a difuzzification using minimizer of the weighted distance between two fuzzy numbers is introduced. In this way, we obtain the nearest weighted point with respect to a fuzzy number, this main result is a new and interesting alternative justification to define of weighted mean of a fuzzy number. Considering this point and the weighted distance quantity, we introduce the weighted possibilistic mean (WPM) value and the weighted possibilistic variance(WPV) of fuzzy numbers. This paper shows that WPM is the nearest weighted point to fuzzy number and the WPV of fuzzy number is preserved more properties of variance in probability theory so that it can simply introduce the possibilistic moments about the mean of fuzzy numbers without problem. The moments of fuzzy numbers play an important role to estimate of parameters, skewness, kurtosis in many of fuzzy times series models.

• Journal of applied mathematics & informatics
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• 제29권3_4호
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• pp.1017-1025
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• 2011

In this paper, we survey various notions and results related to statistical convergence of a sequence of fuzzy numbers, in which statistical convergence for fuzzy numbers was first introduced by Nuray and Savas in 1995. We will go over boundedness, convergence of sequences of fuzzy numbers, statistically convergence and statistically Cauchy sequences of fuzzy numbers, statistical limit and cluster point for sequences of fuzzy numbers, statistical mono-tonicity and boundedness of a sequence of fuzzy numbers and finally statistical limit inferior and limit inferior for the statistically bounded sequences of fuzzy numbers.

• Journal of applied mathematics & informatics
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• 제26권3_4호
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• pp.767-778
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• 2008

Comparison between two or more fuzzy numbers, along with their ranking, is an important subject discussed in scholarly articles. We endeavor in this paper to present a simple yet effective parametric method for comparing fuzzy numbers. This method offer significant advantages over similar methods, in comparing intersected fuzzy numbers, rendering the comparison between fuzzy numbers possible in different decision levels. In the process, each fuzzy number will be given a parametric value in terms of $\alpha$, which is dependent on the related $\alpha$-cuts. We have compared this method to Cheng's centroid point method [5] (The relation of calculating centroid point of a fuzzy number was corrected later on by Wang [12]). The proposed method can be utilized for all types of fuzzy numbers whether normal, abnormal or negative.

• 한국정보과학회논문지:소프트웨어및응용
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• 제27권7호
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• pp.723-730
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• 2000

퍼지숫자는 보통숫자와는 달리 애매모호한 값을 표현하기 때문에, 어느 퍼지숫자가 다른 퍼지숫자보다 큰지 작은지를 명확히 기술하기 어렵다. 따라서, 주어진 퍼지숫자의 집합 내에서, 어느 퍼지숫자가 몇 번째로 큰지, 또는 k번째로 큰 퍼지숫자가 어느 것인지 역시 애매모호할 수밖에 없다. 본 논문에서는 퍼지숫자의 순위와 k번째로 큰 퍼지숫자를 결정하기 위하여 퍼지집합을 이용하는 방법을 제안한다. 제안하는 방법은 퍼지숫자들 사이에 퍼지대소관계가 주어졌다고 가정하며, 이를 이용하여 퍼지숫자의 순위와 k번째 큰 퍼지숫자를 결정한다. 제안하는 방법은 어느 한 퍼지숫자가 취할 수 있는 모든 순위를 퍼지집합으로 표현하며, k번째로 큰 퍼지숫자가 될 수 있는 모든 퍼지숫자들을 퍼지집합으로 표현한다.

• Journal of applied mathematics & informatics
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• 제29권3_4호
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• pp.831-846
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• 2011

There are several methods, in the literature, for finding the fuzzy optimal solution of fully fuzzy transportation problems (transportation problems in which all the parameters are represented by fuzzy numbers). In this paper, the shortcomings of some existing methods are pointed out and to overcome these shortcomings, a new method (based on fuzzy linear programming formulation) is proposed to find the fuzzy optimal solution of unbalanced fuzzy transportation problems with a new representation of trapezoidal fuzzy numbers. The advantages of the proposed method over existing method are discussed. Also, it is shown that it is better to use the proposed representation of trapezoidal fuzzy numbers instead of existing representation of trapezoidal fuzzy numbers for finding the fuzzy optimal solution of fuzzy transportation problems. To illustrate the proposed method a fuzzy transportation problem (FTP) is solved by using the proposed method and the obtained results are discussed. The proposed method is easy to understand and to apply for finding the fuzzy optimal solution of fuzzy transportation problems occurring in real life situations.

• Journal of applied mathematics & informatics
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• 제5권1호
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• pp.153-162
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• 1998

We study limits of sums of fuzzy numbers with different spreads and different shape functions where addition is defined by the sup-t-norm. We show the existence of the limit of the series of fuzzy numbers and prove the uniform continuity of the limit. Finally we investigate a law of large numbers for sequences of fuzzy numbers.

• Journal of applied mathematics & informatics
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• 제6권2호
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• pp.447-454
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• 1999

We study a general law of large numbers for array of mu-tually T related fuzzy numbers where T is an Archimedean t-norm and generalize earlier results of Fuller(1992), Triesch(1993) and Hong (1996).

• 대한수학회논문집
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• 제29권1호
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• pp.187-193
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• 2014

In this paper, we want to represent a method for ranking of two exponential trapezoidal fuzzy numbers. In this study a new Cardinality between exponential trapezoidal fuzzy numbers is proposed. Cardinality in this method is relatively simple and easier in computation and ranks various types of exponential fuzzy numbers. For the validation the results of the proposed approach are compared with different existing approaches.

• Journal of the Korean Statistical Society
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• 제31권1호
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• pp.129-140
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• 2002

In this paper, we obtain a strong law of large numbers for convex tight random elements taking values in the space of fuzzy numbers in R.