• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.7 no.1
• /
• pp.85-89
• /
• 2007

Many authors considered the computational aspect of sup-min convolution when applied to weighted average operations. They used a computational algorithm based on a-cut representation of fuzzy sets, nonlinear programming implementation of the extension principle, and interval analysis. It is well known that $T_W$(the weakest t-norm)-based addition and multiplication preserve the shape of L-R type fuzzy numbers. In this paper, we consider the computational aspect of the extension principle by the use of $T_W$ when the principle is applied to fuzzy weighted average operations. We give the exact solution for the case where variables and coefficients are L-L fuzzy numbers without programming or the aid of computer resources.

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

• Journal of the Korean Data and Information Science Society
• /
• v.14 no.1
• /
• pp.93-101
• /
• 2003

Computation with fuzzy numbers is a prospective branch of a fuzzy set theory regarding the data processing applications. In this paper we consider an open problem about distributivity of fuzzy quantities based on the extension principle suggested by Mare (1997). Indeed, we show that the distributivity on the class of fuzzy numbers holds and min-norm is the only continuous t-norm which holds the distributivity under t-norm based fuzzy arithmetic operations.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.13 no.2
• /
• pp.231-236
• /
• 2003

Recently, Oussalah 〔Fuzzy Sets and Systems 128(2002) 247-260〕 investigated some theoretical results about some invariance properties concerning the relationships between the defuzzification outcomes and the arithmetic of fuzzy numbers. But, in this note we introduce some explicit calculations of the resulting fuzzy set or possibility distribution when the matter is the determination of the defuzzified value pertaining to the result of some manipulation of fuzzy quantities under t-norm based fuzzy arithmetic operations.

• 한국데이터정보과학회:학술대회논문집
• /
• 2006.11a
• /
• pp.81-95
• /
• 2006

The usual arithmetic operations on real numbers can be extended to arithmetical operations on fuzzy intervals by means of Zadeh's extension principle based on a t-norm T. A t-norm is called consistent with respect to a class of fuzzy intervals for some arithmetic operation if this arithmetic operation is closed for this class. It is important to know which t-norms are consistent with a particular type of fuzzy intervals. Recently Dombi and Gyorbiro proved that addition is closed if the Dombi t-norm is used with two bell-shaped fuzzy intervals. A result proved by Mesiar on a strict t-norm based shape preserving additions of LR-fuzzy intervals with unbounded support is recalled. As applications, we define a broader class of bell-shaped fuzzy intervals. Then we study t-norms which are consistent with these particular types of fuzzy intervals. Dombi and Gyorbiro's results are special cases of the results described in this paper.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.17 no.6
• /
• pp.804-806
• /
• 2007

The usual arithmetic operations on real numbers can be extended to arithmetical operations on fuzzy intervals by means of Zadeh's extension principle based on a t-norm T. Dombi and Gyorbiro proved that addition is closed if the Dombi t-norm is used with two bell-shaped fuzzy intervals. Recently, Hong [Fuzzy Sets and Systems 158(2007) 739-746] defined a broader class of bell-shaped fuzzy intervals. Then he study t-norms which are consistent with these particular types of fuzzy intervals as applications of a result proved by Mesiar on a strict f-norm based shape preserving additions of LR-fuzzy intervals with unbounded support. In this note, we give a direct proof of the main results of Hong.

• 제어로봇시스템학회:학술대회논문집
• /
• 1996.10a
• /
• pp.28-31
• /
• 1996

A bag is a set-like entity which can contain repeated elements. Fuzzy bags have been studied by Yager, who defined their basic relations and operations. However, his definitions of the basic relations and operations are inconsistent with the corresponding relations and operations for ordinary fuzzy sets. The present paper presents new basic relations and operations of fuzzy bags using a grade sequence for each element of the universal set. Moreover the .alpha.-cut, t-norms, the extension principle, and the composition of fuzzy bag relations are described.

• Journal of the Korean Data and Information Science Society
• /
• v.14 no.1
• /
• pp.131-141
• /
• 2003

In this paper, we prove that multi-variate fuzzy polynomials are universal approximators for multi-variate fuzzy functions which are the extension principle of continuous real-valued function under $T_W-based$ fuzzy arithmetic operations for a distance measure that Buckley et al.(1999) used. We also consider a class of fuzzy polynomial regression model. A mixed non-linear programming approach is used to derive the satisfying solution.

• Journal of Korean Elementary Science Education
• /
• v.39 no.1
• /
• pp.26-39
• /
• 2020

Visual Representation Competence Taxonomy (VRC-T) was developed in previous study(Yoon, 2018) to provide a framework conducive to assess visual representation competence and to devise appropriate educational activities for it. This study is an extension of the previous study. It aimed to explore the usefulness of VRC-T and revise it by analyzing the patterns of visual representation use in science lessons. The researcher collected lesson plans on shadow principle from 11 pre-service and 13 in-service elementary teachers and conducted individual interviews regarding what visual representations they considered and how they tried to use them in science lessons. VRC-T was used as an analytical framework to examine the types and cognitive processes of visual representations. As a result, new categories were added and the revised VRC-T was completed (VRC-TR). It was also found that both pre- and in-service teachers mainly focused on 'interpreting' the 'descriptive representation' while designing their lesson plans. Additionally, in-service teachers showed more limited use of visual representations compared to pre-service teachers. In-service teachers largely relied on the national science textbooks, while pre-service teachers reflected their own learning experiences in their teacher-training program. These results showed that teachers' use of visual representations heavily relied on their prior learning and teaching experiences. The VRC-TR presented in this study and examples of class activities in each category can be helpful for teachers and researchers who want to use visual representations more effectively.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.8 no.3
• /
• pp.170-174
• /
• 2008

The measurement of performance of a process considering both the location and the dispersion of information about the process is referred to as the process capacity indices (PCIs) of interest, $C_{pk}$. This information is presented by the mean and standard deviation of the producing process. Linguistic variables are used to express the evaluation of the quality of a product. Consequently, $C_{pk}$ is defined with fuzzy numbers. Lee [Eur. J. Oper. Res. 129(2001) 683-688] constructed the definition of the $C_{pk}$ index estimation presented by fuzzy numbers and approximated its membership function using the "min" - norm based Zadeh's extension principle of fuzzy sets. However, Lee's result was shown to be invalid by Hong [Eur. J. Oper. Res. 158(2004) 529-532]. It is well known that $T_w$ (the weakest t-norm)-based addition and multiplication preserve the shape of L-R fuzzy numbers. In this paper, we allow that the fuzzy numbers are of L-R type. The object of the present study is to propose a new method to calculate the $C_{pk}$ index under $T_w-based$ fuzzy arithmetic operations.