• 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.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2008.04a
• /
• pp.311-312
• /
• 2008

Fuzzy logic is introduced by Zadeh in 1965. It has been continuously developed by many mathematicians and knowledge engineers all over the world. A lot of papers concerning with the history of mathematics and the mathematical education related with fuzzy logic, but there is no paper concerning with Zadeh. In this article, we investigate his life and papers about fuzzy logic. We also compare two-valued logic, three-valued logic, fuzzy logic, intuisionistic logic and intuitionistic fuzzy sets. Finally we discuss about the expression of intuitionistic fuzzy sets.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.17 no.4
• /
• pp.455-459
• /
• 2007

Interval-valued fuzzy sets were suggested for the first time by Gorzafczany(1983) and Turksen(1986). Based on this, Zeng and Li(2006) introduced concepts of similarity measure and entropy on interval-valued fuzzy sets which are different from Bustince and Burillo(1996). In this paper, by using Choquet integral with respect to a fuzzy measure, we introduce distance measure and similarity measure defined by Choquet integral on interval-valued fuzzy sets and discuss some properties of them. Choquet integral is a generalization concept of Lebesgue inetgral, because the two definitions of Choquet integral and Lebesgue integral are equal if a fuzzy measure is a classical measure.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2007.11a
• /
• pp.195-198
• /
• 2007

In this paper, we consider Lebesgue-type theorems in non-additive measure theory and then investigate interval-valued Choquet integrals and interval-valued fuzzy integral with respect to a additive monotone set function. Furthermore, we discuss the equivalence among the Lebesgue's theorems, the monotone convergence theorems of interval-valued fuzzy integrals with respect to a monotone set function and find some sufficient condition that the monotone convergence theorem of interval-valued Choquet integrals with respect to a monotone set function holds.

• Journal of applied mathematics & informatics
• /
• v.6 no.2
• /
• pp.417-432
• /
• 1999

This paper describes a fuzzy system designed to support production planning in an industrial unit producing cardboard boxes. In this industrial unit orders for n boxes of width w, length l, height h, made of q layers of type k paper for delivery in t units of time are produced. In the production of such orders apart from meeting the orders specifications it is usually tried to minimize the margin trim loss the number of machine setups and the holding cost of the finished orders. Considering the dynamism of production systems that are influenced by such factors as market demand fluctuations changes in commercial priorities raw material availability and pro-ducation capabilities we solve this multi-objective problem by fuzzy set theory.

• East Asian mathematical journal
• /
• v.32 no.3
• /
• pp.413-423
• /
• 2016

In this paper, we consider the functional equation f(x + 2y) - 3f(x + y) + 3f(x) - f(x - y) - 3f(y) + 3f(-y) = 0 and prove the generalized Hyers-Ulam stability for it when the target space is a fuzzy Banach space. The usual method to obtain the stability for mixed type functional equation is to split the cases according to whether the involving mappings are odd or even. In this paper, we show that the stability of a quadratic-cubic mapping can be obtained without distinguishing the two cases.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.2 no.1
• /
• pp.3-16
• /
• 1992

In this paper, we establish the conceptes of compactifications of a L-fuzzy topological space and a order relation in these compactifications. This order is a preorder. The existemce problem and the uniqueness problem of the largest compactifications are closely related to the mapping extension problem. We give out the largest compactifications and show the non-uniqueness of the largest compactifications in the preorder for a kind of spaces. Moreover, under some natural assumptions of separation axioms, we prove that the preorder is just a partial order, thus it ensures the uniqueness of the largest compactification. In addition. the related discussion involves the special properties of fuzzy product space, the latter seems to be independent interesting.

• The Pure and Applied Mathematics
• /
• v.11 no.2
• /
• pp.127-132
• /
• 2004

$H_v$-rings first were introduced by Vougiouklis in 1990. The largest class of algebraic systems satisfying ring-like axioms is the $H_v$-ring. Let R be an $H_v$-ring and ${\gamma}_R$ the smallest equivalence relation on R such that the quotient $R/{\gamma}_R$, the set of all equivalence classes, is a ring. In this case $R/{\gamma}_R$ is called the fundamental ring. In this short communication, we study the fundamental rings with respect to the product of two fuzzy subsets.

• The Pure and Applied Mathematics
• /
• v.23 no.2
• /
• pp.163-179
• /
• 2016

Let $M_1f(x,y):=\frac{3}{4}f(x+y)-\frac{1}{4}f(-x-y)+\frac{1}{4}(x-y)+\frac{1}{4}f(y-x)-f(x)-f(y)$, $M_2f(x,y):=2f(\frac{x+y}{2})+f(\frac{x-y}{2})+f(\frac{y-x}{2})-f(x)-f(y)$ Using the direct method, we prove the Hyers-Ulam stability of the additive-quadratic ρ-functional inequalities (0.1) $N(M_1f(x,y)-{\rho}M_2f(x,y),t){\geq}\frac{t}{t+{\varphi}(x,y)}$ and (0.2) $N(M_2f(x,y)-{\rho}M_1f(x,y),t){\geq}\frac{t}{t+{\varphi}(x,y)}$ in fuzzy Banach spaces, where ρ is a fixed real number with ρ ≠ 1.

• Journal of the Chungcheong Mathematical Society
• /
• v.24 no.2
• /
• pp.273-286
• /
• 2011

Using the fixed point method, we prove the Hyers-Ulam stability of the following quadratic functional equations $${cf\left({\displaystyle\sum_{i=1}^n\;xi}\right)+{\displaystyle\sum_{i=2}^nf}{\left(\displaystyle\sum_{i=1}^n\;x_i-(n+c-1)x_j\right)}\\ {=(n+c-1)\;\left(f(x_1)+c{\displaystyle\sum_{i=2}^n\;f(x_i)}+{\displaystyle\sum_{i in fuzzy Banach spaces.