• Journal of applied mathematics & informatics
• /
• 제39권5_6호
• /
• pp.743-749
• /
• 2021

The purpose of this article is to study few properties of fuzzy mean open and fuzzy mean closed sets in fuzzy topological spaces. Further, the idea of fuzzy mean clopen set is introduced. It is observed that a fuzzy mean clopen set is both fuzzy mean open and fuzzy mean closed but the converse is not true.

• 호남수학학술지
• /
• 제32권2호
• /
• pp.307-331
• /
• 2010

The notion of intuitionistic fuzzy semi-pre interior (semi-pre closure) is introduced, and several related properties are investigated. Characterizations of an intuitionistic fuzzy regular open set, an intuitionistic fuzzy semi-open set and an intuitionistic fuzzy ${\gamma}$-open set are provided. A method to make an intuitionistic fuzzy regular open set (resp. intuitionistic fuzzy regular closed set) is established. A relation between an intuitionistic fuzzy ${\gamma}$-open set and an intuitionistic fuzzy semi-preopen set is considered. A condition for an intuitionistic fuzzy set to be an intuitionistic fuzzy ${\gamma}$-open set is discussed.

• Journal of applied mathematics & informatics
• /
• 제39권3_4호
• /
• pp.251-257
• /
• 2021

This article is devoted to introduce the notion of fuzzy cleanly covered fuzzy topological spaces; in addition two strong fuzzy separation axioms are studied. By means of fuzzy maximal open sets some properties of fuzzy cleanly covered fuzzy topological spaces are obtained and also by means of fuzzy maximal closed sets few identical results of a fuzzy topological spaces are investigated. Through fuzzy minimal open and fuzzy maximal closed sets, two strong fuzzy separation axioms are discussed.

• East Asian mathematical journal
• /
• 제27권3호
• /
• pp.261-271
• /
• 2011

In this paper, fuzzy ${\alpha}^*$-set, fuzzy C-set, fuzzy AB-set, fuzzy t-set, fuzzy B-set, etc., are introduced in the sense of Sostak [12] and Ramadan [9]. By using these sets, a decomposition of fuzzy continuity and complete fuzzy continuity are provided. Characterization of smooth fuzzy extremally disconnected spaces is also obtained in this connection.

• 한국정보과학회논문지:소프트웨어및응용
• /
• 제27권7호
• /
• pp.723-730
• /
• 2000

퍼지숫자는 보통숫자와는 달리 애매모호한 값을 표현하기 때문에, 어느 퍼지숫자가 다른 퍼지숫자보다 큰지 작은지를 명확히 기술하기 어렵다. 따라서, 주어진 퍼지숫자의 집합 내에서, 어느 퍼지숫자가 몇 번째로 큰지, 또는 k번째로 큰 퍼지숫자가 어느 것인지 역시 애매모호할 수밖에 없다. 본 논문에서는 퍼지숫자의 순위와 k번째로 큰 퍼지숫자를 결정하기 위하여 퍼지집합을 이용하는 방법을 제안한다. 제안하는 방법은 퍼지숫자들 사이에 퍼지대소관계가 주어졌다고 가정하며, 이를 이용하여 퍼지숫자의 순위와 k번째 큰 퍼지숫자를 결정한다. 제안하는 방법은 어느 한 퍼지숫자가 취할 수 있는 모든 순위를 퍼지집합으로 표현하며, k번째로 큰 퍼지숫자가 될 수 있는 모든 퍼지숫자들을 퍼지집합으로 표현한다.

• Korean Journal of Mathematics
• /
• 제17권4호
• /
• pp.361-374
• /
• 2009

We characterize a fuzzy partial order relation using its level set, find sufficient conditions for the image of a fuzzy partial order relation to be a fuzzy partial order relation, and find sufficient conditions for the inverse image of a fuzzy partial order relation to be a fuzzy partial order relation. Also we define a fuzzy lattice as fuzzy relations, characterize a fuzzy lattice using its level set, show that a fuzzy totally ordered set is a distributive fuzzy lattice, and show that the direct product of two fuzzy lattices is a fuzzy lattice.

• Journal of Applied and Pure Mathematics
• /
• 제4권1_2호
• /
• pp.79-84
• /
• 2022

We have observed that there exist certain fuzzy topological spaces with no fuzzy minimal open sets. This observation motivates us to investigate fuzzy topological spaces with neither fuzzy minimal open sets nor fuzzy maximal open sets. We have observed if such fuzzy topological spaces exist and if it is connected are not fuzzy cut-point spaces. We also study and characterize certain properties of fuzzy mean open sets in fuzzy T₁-connected fuzzy topological spaces.

• 호남수학학술지
• /
• 제36권3호
• /
• pp.623-635
• /
• 2014

Classications of (${\alpha},{\beta}$)-fuzzy subalgebras of BCK/BCI-algebras are discussed. Relations between (${\in},{\in}{\vee}q$)-fuzzy subalgebras and ($q,{\in}{\vee}q$)-fuzzy subalgebras are established. Given special sets, so called t-q-set and t-${\in}{\vee}q$-set, conditions for the t-q-set and t-${\in}{\vee}q$-set to be subalgebras are considered. The notions of $({\in},q)^{max}$-fuzzy subalgebra, $(q,{\in})^{max}$-fuzzy subalgebra and $(q,{\in}{\vee}q)^{max}$-fuzzy subalgebra are introduced. Conditions for a fuzzy set to be an $({\in},q)^{max}$-fuzzy subalgebra, a $(q,{\in})^{max}$-fuzzy subalgebra and a $(q,{\in}{\vee}q)^{max}$-fuzzy subalgebra are considered.

• 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.

• Journal of applied mathematics & informatics
• /
• 제7권1호
• /
• pp.335-346
• /
• 2000

This paper discusses the relation of fuzzy sets satisfying some types of fuzzy covering properties. We give some characterizations of such fuzzy sets and investigate a few properties.