• 대한수학회논문집
• /
• 제18권1호
• /
• pp.21-29
• /
• 2003

In this paper, we define the notion of a characteristic fuzzy subgroup which is the analogue of a characteristic group in the ordinary group theory and derive various new ones from a given characteristic fuzzy subgroup.

• 한국수학교육학회지시리즈D:수학교육연구
• /
• 제9권3호
• /
• pp.233-241
• /
• 2005

Mathematics has developed dramatically in today's world and come to be increasingly put into practical use in various fields in society. However, many Japanese students dislike mathematics. We have to study mathematics education with this situation in our mind. When we consider a better educational material, we don't have to consider only within the framework of the current school mathematics. We can expect to find good mathematical materials in fields beyond the school mathematics. In this paper, we study how the inclusion of idea such as 'fuzzy theory' and 'graph theory' influences pupils' approaches to learning mathematics.

• 호남수학학술지
• /
• 제44권3호
• /
• pp.461-472
• /
• 2022

In optimization theory, hypo-convergence is considered as an effective tool by providing the convergence of supremum values under some conditions. This feature makes it different from other types of convergence. Therefore, we have defined the hypo-convergence of a sequence of fuzzy sets due to the increasing interest in fuzzy set theory in recent years. After giving a theoretical framework, we deal with the optimization process by using a sequential characterization of hypo-convergence of sequence of fuzzy sets. Since the maximization process in optimization theory is beyond the presence of hypo-convergence, we give some conditions to satisfy the convergence of supremum values. Furthermore, we show how sequence of fuzzy sets and fuzzy numbers differ in the convergence of the supremum values.

• 한국지능시스템학회:학술대회논문집
• /
• 한국퍼지및지능시스템학회 2002년도 춘계학술대회 및 임시총회
• /
• pp.114-118
• /
• 2002

As a generalization of fuzzy sets, the concept of intuitionistic fuzzy sets was introduced by Atanassov [1]. By using intuitionistic fuzzy sets, we introduce and study the concept of intuitionistic fuzzy filters and define the concept of Hausdorffness on intuitionistic fuzzy filters, which can not be defined in crisp theory of filters, and study their properties for some extent.

• 호남수학학술지
• /
• 제36권3호
• /
• pp.555-568
• /
• 2014

On the basis of the theory of a falling shadow and fuzzy sets, the notion of a falling fuzzy BCI-commutative ideal of a BCI-algebra is introduced. Relations between falling fuzzy BCI-commutative ideals and falling fuzzy ideals are given. Relations between fuzzy BCI-commutative ideals and falling fuzzy BCI-commutative ideals are provided. Characterizations of a falling fuzzy BCI-commutative ideal are established, and conditions for a falling fuzzy (closed) ideal to be a falling fuzzy BCI-commutative ideal are considered.

• 호남수학학술지
• /
• 제26권3호
• /
• pp.309-330
• /
• 2004

In this paper, we apply the concept of intuitionistic fuzzy sets to theory of semigroups. We give some properties of intuitionistic fuzzy ideals and intuitionistic fuzzy bi-ideals, and characterize which is left [right] simple, left [right] duo and a semilattice of left [right] simple semigroups or another type of semigroups in terms of intuitionistic fuzzy ideals and intuitionistic fuzzy bi-ideals.

• 호남수학학술지
• /
• 제36권4호
• /
• pp.813-830
• /
• 2014

The notions of a (Boolean, prime, ultra, good) hesitant fuzzy filter and a hesitant fuzzy MV -filter of an MTL-algebras are introduced, and their relations are investigated. Characterizations of a (Boolean, ultra) hesitant fuzzy filter are discussed. Conditions for a hesitant fuzzy set to be a hesitant fuzzy filter, and for a hesitant fuzzy filter to be a Boolean hesitant fuzzy filter are provided.

• Annals of Fuzzy Mathematics and Informatics
• /
• 제16권3호
• /
• pp.261-284
• /
• 2018

In this paper, we recall the definition of soft set, fuzzy soft set, hesitant fuzzy set and hesitant fuzzy soft set and some of their examples. We define the concept of hesitant fuzzy soft multiset which combines hesitant fuzzy soft set and soft multiset theory. We also define basic terms in hesitant fuzzy soft multiset with relevant examples. Some basic operations such as restricted intersection, extended intersection, union, restricted union, AND-product and OR-product and their properties are given, supported with illustrative examples. We finally establish some important results, including De Morgan's inclusions and laws.

• 호남수학학술지
• /
• 제38권4호
• /
• pp.783-794
• /
• 2016

The notions of hesitant fuzzy left (resp., right, bi-, quasi-) ideals are introduced, and several properties are investigated. Relations between a hesitant fuzzy left (resp., right) ideal,a hesitant fuzzy bi-ideal and a hesitant fuzzy quasi-ideal are discussed. Characterizations of hesitant fuzzy left (resp., right, bi-, quasi-) ideals are considered.

• 대한수학회보
• /
• 제43권3호
• /
• pp.461-470
• /
• 2006

As a continuation of [4], characterizations of fuzzy implicative ideals are given. An extension property for fuzzy implicative ideals is established. We prove that the family of fuzzy implicative ideals is a completely distributive lattice. Using level subsets of a BCk-algebra X with respect to a fuzzy set $\={A}$ in X, we construct a fuzzy implicative ideal of X containing $\={A}$.