• Title, Summary, Keyword: fuzzy numbers

### A Ranking Method for Fuzzy Numbers based on Fuzzy Comparisons (퍼지 비교 기반 퍼지 숫자의 등급과 방법)

• Lee, Jee-Hyong;Lee, Kwang-Hyung
• Journal of KIISE:Software and Applications
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• v.28 no.12
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• pp.930-937
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• 2001
• For ranking fuzzy numbers, comparisons between numbers are necessary However, the comparison results can be vague since fuzzy numbers represent vague numeric values. Thus, ranking results of fuzzy numbers which are based on comparisons between fuzzy numbers, could also be vague. This means that there could be several possible ranking sequences of fuzzy numbers. There have been proposed many ranking methods for fuzzy numbers. However, most of them generate only ranking sequence. In this paper, we present a ranking method for fuzzy numbers using the fuzzy satisfaction function, Our method generates several possible ranking sequences of the given fuzzy numbers using the fuzzy satisfaction function.

### WEIGHTED POSSIBILISTIC VARIANCE AND MOMENTS OF FUZZY NUMBERS

• Pasha, E.;Asady, B.;Saeidifar, A.
• Journal of applied mathematics & informatics
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• v.26 no.5_6
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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.

### OVERVIEWS ON LIMIT CONCEPTS OF A SEQUENCE OF FUZZY NUMBERS I

• Kwon, Joong-Sung;Shim, Hong-Tae
• Journal of applied mathematics & informatics
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• v.29 no.3_4
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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.

### A Fuzzy Set based Method for Determining the Ranks of Fuzzy Numbers (퍼지집합을 이용한 퍼지숫자의 순위 결정 방법)

• Lee, Jee-Hyong;Lee, Kwang-Hyung
• Journal of KIISE:Software and Applications
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• v.27 no.7
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• pp.723-730
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• 2000
• Fuzzy numbers represent fuzzy numeric values. However, it is difficult to clearly determine whether one fuzzy number is larger or smaller than other fuzzy numbers. Thus it is also difficult to determine the rank which a fuzzy number takes, or to select the k-th largest fuzzy number in a given set of fuzzy numbers. In this paper, we propose a fuzzy set based method to determine the rank of a fuzzy number and the k-th largest fuzzy number. The proposed method uses a given fuzzy greater-than relation which is defined on a set of fuzzy numbers. Our method describes the rank of a fuzzy number with a fuzzy set of ranks that the fuzzy number can take, and the k-th largest fuzzy number with a fuzzy set of fuzzy numbers which can be k-th ranked.

### A NEW APPROACH FOR RANKING FUZZY NUMBERS BASED ON $\alpha$-CUTS

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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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.

### APPLICATION OF LINEAR PROGRAMMING FOR SOLVING FUZZY TRANSPORTATION PROBLEMS

• Kumar, Amit;Kaur, Amarpreet
• Journal of applied mathematics & informatics
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• v.29 no.3_4
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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.

### RANKING EXPONENTIAL TRAPEZOIDAL FUZZY NUMBERS WITH CARDINALITY

• Rezvani, Salim
• Communications of the Korean Mathematical Society
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• v.29 no.1
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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.

### A Note on Statistically Monotonic and Bounded Sequences of Fuzzy Numbers

• Hong, Dug-Hun;Kim, Kyung-Tae
• Journal of the Korean Data and Information Science Society
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• v.17 no.2
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• pp.657-659
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• 2006
• This note gives a counterexample showing that a main theorem of Aytal and Pehliven's (Information Sciences 176 (2006) 734-744) result on statically monotonic and bounded sequences of fuzzy numbers is not valid.

### Strong Law of Large Numbers for Tight Fuzzy Random Variables

• Joo, Sang Yeol
• Journal of the Korean Statistical Society
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• v.31 no.1
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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.

### Weak laws of large numbers for weighted sums of Banach space valued fuzzy random variables

• Kim, Yun Kyong
• International Journal of Fuzzy Logic and Intelligent Systems
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• v.13 no.3
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• pp.215-223
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• 2013
• In this paper, we present some results on weak laws of large numbers for weighted sums of fuzzy random variables taking values in the space of normal and upper-semicontinuous fuzzy sets with compact support in a separable real Banach space. First, we give weak laws of large numbers for weighted sums of strong-compactly uniformly integrable fuzzy random variables. Then, we consider the case that the weighted averages of expectations of fuzzy random variables converge. Finally, weak laws of large numbers for weighted sums of strongly tight or identically distributed fuzzy random variables are obtained as corollaries.