• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.10a
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• pp.9-15
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• 1998

In this paper, we introduce new results of law large numbers for mutually T-related fuzzy numbers, when T is Archimedean t-norm and spreads are random variables, and generalize earlier result of Fullr[FSS 45(1992) 299-303].

• Journal of the Korean Data and Information Science Society
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• v.16 no.4
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• pp.1141-1145
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• 2005

In this note, we show that Theorem 2.1[Kybernetika, 28(1992) 45-49], a result of a functional relationship between the membership function of LR fuzzy numbers of T-sum and T-product, remains valid for convex additive generator and concave shape functions L and R with simple proof. We also consider the case for 0-symmetric R fuzzy numbers.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2002.09a
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• pp.13.1-13
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• 2002

• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.55-60
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• 2014

In this paper, we will obtain Marcinkiewicz's type limit laws for fuzzy random sets as follows : Let {$X_n{\mid}n{\geq}1$} be a sequence of independent identically distributed fuzzy random sets and $E{\parallel}X_i{\parallel}^r_{{\rho_p}}$ < ${\infty}$ with $1{\leq}r{\leq}2$. Then the following are equivalent: $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ a.s. in the metric ${\rho}_p$ if and only if $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ in probability in the metric ${\rho}_p$ if and only if $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ in $L_1$ if and only if $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ in $L_r$ where $S_n={\Sigma}^n_{i=1}\;X_i$.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1419-1430
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• 2010

Since Goetschel and Voxman [5] proposed a linear order on fuzzy numbers, several authors studied the concept of semicontinuity and convexity of fuzzy mappings defined through the order. Since the order is only defined for fuzzy numbers on $\mathbb{R}$, it is natural to find a new order for normal fuzzy sets on $\mathbb{R}^n$ in order to study the concept of semicontinuity and convexity of fuzzy mappings on normal fuzzy sets. In this paper, we introduce a new order "${\preceq}_s$ for normal fuzzy sets on $\mathbb{R}^n$ with respect to the support function. We define the semicontinuity and convexity of fuzzy mappings with this order. Some issues which are related with semicontinuity and convexity of fuzzy mappings will be discussed.

• Proceedings of the KIEE Conference
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• 1993.07a
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• pp.489-491
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• 1993

Many optimization problem or multiple attribute, multiple alternative decision making problem may have fuzzy evaluation factors. In this case, fuzzy number operation technique is needed to evaluate and compare object functions which become fuzzy sets. Generally, fuzzy number operations can be defined by extension principle of fuzzy set theory, but it is tedious to do fuzzy number operations by using extension principle when the membership functions are defined by complex functions. Many fast methods which approximate the membership functions such as triangle, trapezoidal, or L-R type functions are proposed. In this paper, a fast fuzzy number operation method is proposed which do not simplify the membership functions of fuzzy numbers.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.517-521
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• 1998

DEA(data envelopment analysis) is a non-parametric technique for measuring and evaluating the relative efficiencies of a set of entities with common crisp inputs and outputs. In fact, in a real evaluation problem input and output data of entities often flucturate. These fluctuating data can be represented as linguistic variables characterized by fuzzy numbers. Based on a fundamental CCR model, a fuzzy DEA model is proposed to deal with fuzzy input and output data, Furthermore, a model that extends a fuzzy DEA to a more general case is also proposed with considering the relation between DEA and RA (regression analysis) . the crisp efficiency in CCR modelis extended to an L-R fuzzy number in fuzzy DEA problems to reflect some uncertainty in real evaluation problems.

• Korean Journal of Mathematics
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• v.29 no.1
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• pp.137-167
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• 2021

Spherical fuzzy set (SFS) is also one of the fundamental concepts for address more uncertainties in decision problems than the existing structures of fuzzy sets, and thus its implementation was more substantial. The well-known sine trigonometric function maintains the periodicity and symmetry of the origin in nature and thus satisfies the expectations of the experts over the multi parameters. Taking this feature and the significance of the SFSs into the consideration, the main objective of the article is to describe some reliable sine trigonometric laws (ST L) for SFSs. Associated with these laws, we develop new average and geometric aggregation operators to aggregate the Spherical fuzzy numbers (SFNs). Then, we presented a group decision- making (DM) strategy to address the multi-attribute group decision making (MAGDM) problem using the developed aggregation operators. In order to verify the value of the defined operators, a MAGDM strategy is provided along with an application for the selection of laptop. Moreover, a comparative study is also performed to present the effectiveness of the developed approach.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.13 no.22
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• pp.51-57
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• 1990

A new interactive multiobjective decision making technique, which is called the fuzzy sequential proxy optimization technique, has been proposed. This technique is the revised version the sequential proxy optimization technique that the decision-maker's marginal rates of substitution is interpreted as type of L-R fuzzy numbers. It used to the square of normalized scalar product as the doptimalilry condition. However, this technique ignores the imprecise nature of a decision-maker's judgement of marginal rates of substitution. Also, it have a shortcoming that can be only applied over three objective functions. In this paper, considering the imprecise nature of a decision-maker's judgement, we presents an interactive fuzzy decision-making method on the basis of the decision-maker's MRS presented through the use of five types of membership functions including non-linear functions. FORTRAN programs that run in conversational mode are developed to implement man-machine interactive procedure.

• Journal of Navigation and Port Research
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• v.37 no.5
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• pp.493-498
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• 2013

This paper is aimed to priority evaluation of preliminary cases for IMO -IMS(International Maritime Organization- Information Management System) using fuzzy TOPSIS(Technique for Order Performance by Similarity to Ideal Solution) and AHP(Analytic Hierarchy Process). To this solve, therefore, this paper extract 24 preliminary cases and select 4 major preliminary alternative cases after analysing the structure of its alternative cases using FSM(Fuzzy Structure Modeling). Also, the weights of evaluation factors determine using AHP which able to keep the consistency when decision-makers assess. In AHP method, but, the numbers of paired comparison incerase as much as the numbers of the comparison items increase and because this evaluation have the many of vagueness, the decision of final ranking is used to fuzzy TOPSIS method which is included TOPSIS and Fuzzy Set Theory. The result are developed as order as Management of IMO Convention Information, Delivery of IMO Convention Information, Total IMO Database, Knowledge Hub of IMO Convention Information in IMO-IMS.