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In this paper, the notions of regularity and normality of ( L , M ) -fuzzy topological spaces are introduced by using residual implication, where L and M are completely distributive De Morgan algebras. It is shown that ( L , M ) -fuzzy interior operator and ( L , M ) -fuzzy closure operator can be used to characterize regularity and normality. The relationships among separation axioms of an ( L , M ) -fuzzy topological space are discussed. Moreover, it is proved that the four separation axioms are equivalent to one another in an ( L , M ) -fuzzy metric space.

Tamamen ikili değerlendirmeye dayanan bir matematiksel modelleme olan klasik mantıkta her değer için sadece iki durum vardır, 1 sembolünün verildiği ve doğru anlamına gelen ilk durum ile 0 sembolünün verildiği ve yanlış anlamına gelen ikinci durum. Ancak gerçek bundan daha geniştir ve yalnızca 0 ve 1 olmak üzere iki duruma bağlı olmayabilir. Bu nedenle, yaklaşık veya spesifik olmayan bilgileri temsil etme problemini çözmek için genel çerçeveyi sağlayan yeni bir mantığa ihtiyaç duyulmuş. Bulanık mantık adı verilen bu mantık ilk olarak 1965 yılında İranlı bilim adamı Lutfi Zadeh, tarafından ortaya atılmıştır. Bulanık mantık, sıcak, soğuk, ılık, az, çok, gibi deyimler ve belirsiz ifadeler aracılığıyla tümdengelim üzerine kuruludur. Çalışma boyunca, bulanık mantığın klasik mantığın bir genişlemesi olduğu sonucuna varılmıştır. Klasik mantık, üyelik derecesi {0,1} kümesi olduğunda, bulanık mantığın özel bir durumudur, Bulanık mantık sadece kümeler teorisinde değil, yapay zekada, gelişmiş elektronik cihazlarda, endüstriyel kontrolörlerde ve hatta günlük hayatımızda büyük öneme sahiptir. Bu tezde de bulanık küme, bulanık küme türleri ve bunlarla ilgili önemli cebirsel işlemler açıklanacaktır. Sonrasında bulanık topolojik uzay tanımı verilerek bulanık topolojik uzayların toplamları üzerinde, açık kümeler, kaplı kümeler, içi, kapanış, taban, komşuluklar ve süreklilik gibi ifadeler tanımlanacaktır. Tanımlanan bu topolojik toplamlar için elde edilen bazı sonuçlardan bahsedilecektir. In classical logic, which is purely a mathematical modeling based on binary evaluation, there are only two cases for each value, the first case where the symbol 1 is given and means true, and the second case where the symbol 0 is given and means false. But the truth is broader than that and may not depend solely on two states 0 and 1. Therefore, a new logic was needed that provides the general framework to solve the problem of representing approximate or nonspecific information. This logic, called fuzzy logic, was first put forward by Iranian scientist Lutfi Zadeh in 1965. Fuzzy logic is based on deduction through idioms such as hot, cold, warm, less, more, and indefinite expressions. Throughout the study, it is concluded that fuzzy logic is an extension of classical logic. Classical logic is a special case of fuzzy logic, when the membership degree is {0,1} set, Fuzzy logic has great importance not only in set theory, but also in artificial intelligence, advanced electronic devices, industrial controllers and even in our daily life. In this thesis, fuzzy set, fuzzy set types and important algebraic operations related to them will be explained. Then, by giving the definition of fuzzy topological space, we will define open sets, covered sets, interior, closure, base, neighborhoods and continuity on the sums of fuzzy topological spaces. Some of the results obtained for these topological sums will be mentioned.

An L , M -fuzzy topological convergence structure on a set X is a mapping which defines a degree in M for any L -filter (of crisp degree) on X to be convergent to a molecule in L X . By means of L , M -fuzzy topological neighborhood operators, we show that the category of L , M -fuzzy topological convergence spaces is isomorphic to the category of L , M -fuzzy topological spaces. Moreover, two characterizations of L -topological spaces are presented and the relationship with other convergence spaces is concretely constructed.

This paper studies the closure and interior operators in LM-fuzzy topological spaces. The algebraic structures associated with various collections of closed sets and open sets are identified. Further, certain lattices formed by these algebraic structures are obtained and some lattice theoretic properties of the same are investigated. Corresponding to every element in M, the study associates a lattice of monoids which is determined by various types of closed sets and open sets.

The purpose of this paper is to study a new class of fuzzy covering dimension functions, called fuzzy

This paper introduces the [Formula: see text]-fuzzy topology induced by a descending family of [Formula: see text]-topologies on a given set and derives many of its properties.

This paper identifies a De Morgan algebra associated with the families of (r, s)-regular fuzzy open sets and (r, s)-regular fuzzy closed sets in a double fuzzy topological space. The situation under which this De Morgan algebra becomes a Boolean algebra is characterized. Certain other properties of this algebra are also investigated.

The concept of $$q$$ -rung orthopair fuzzy set is the extension of the concept of both intuitionistic fuzzy set and Pythagorean fuzzy set. The aim of this paper is to define the concept of $$q$$ -rung orthopair fuzzy topological space and to study some properties of this concept. For this purpose, firstly the basic definition of $$q$$ -rung orthopair fuzzy topology is introduced and an example is constructed and then the concept of $$q$$ -rung orthopair fuzzy continuity is studied and it is shown that a $$q$$ -rung orthopair fuzzy topology can be established on the domain or range of a function.

The aim of introduce and study the notion of a fuzzy δ-open set (Ω-open set, α− Ω-open set, feebly –open set, α-open set, ƥ-open set, Sp-open set, a-open set) and the relationships between them and fuzzy 𝛿-open set in fuzzy topological space on fuzzy set and some properties, remarks related to them .

In this paper, we introduce a new class of fuzzy sets, namely, fuzzy ψ*-closed sets for fuzzy topological spaces, and some of their properties have been proved. Further, we introduce fuzzy ψ*-continuous, fuzzy ψ*-irresolute functions, and fuzzy ψ*-closed (open) functions, as applications of these fuzzy sets, fuzzy T1/5-spaces, fuzzy $$ {T}_{1/5}^{\psi \ast } $$ T 1 / 5 ψ ∗ -spaces, and fuzzy ψ*T1/5-spaces.

In this paper we introduce two new classes of functions between mixed fuzzy topological spaces, namely fuzzy δ∗-almost continuous and fuzzy δ∗-continuous functions and investigate some of their properties. The description of these two types of functions facilitated by the introduction of generalized open sets, called fuzzy δ-preopen sets, fuzzy δ-precluster point, fuzzy preopen sets, fuzzy δ-pre-q-neighbourhoods.

The main view of this article is the extended version of the fine topological space to the novel kind of space say fine fuzzy topological space which is developed by the notion called collection of quasi coincident of fuzzy sets. In this connection, fine fuzzy closed sets are introduced and studied some features on it. Further, the relationship between fine fuzzy closed sets with certain types of fine fuzzy closed sets are investigated and their converses need not be true are elucidated with necessary examples. Fine fuzzy continuous function is defined as the inverse image of fine fuzzy closed set is fine fuzzy closed and its interrelations with other types of fine fuzzy continuous functions are obtained. The reverse implication need not be true is proven with examples. Finally, the applications of fine fuzzy continuous function are explained by using the composition.

In this paper, we aim to develop a new type of neutrosophic fuzzy set called the star neutrosophic fuzzy set as a generalization to star neutrosophic crisp set defined in by Salama et al.[8], and study some of its properties. Adedd to, we introduce the notion of star neutrosophic fuzzy topological space as a generalization to some topological consepts as star neutrosophic fuzzy closure, and star neutrosophic fuzzy interior. Finally, we extend the concepts of fuzzy topological space, and intuitionistic fuzzy topological space to the case of star neutrosophic fuzzy sets.

The algebraic structures of the families of fuzzy sets that arise out of various notions of openness and closedness in a double fuzzy topological space are investigated. The collection of these families forms a bounded, associative lattice. The zero divisors and zero-divisor graph of this lattice are also identified.

In this paper we study different weak forms of open multifunctionsfrom a fuzzy topological space into a fuzzy $m$-space. Further we study the same from a fuzzy bitopological space into a fuzzy bitopological spaces.