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On Mixed b-Fuzzy Topological Spaces
Wadei Faris Al-Omeri 한국지능시스템학회 2020 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.20 No.3
This paper describes the construction of a topological space from two different fuzzy topologies using the fuzzy b-q-nbd of a fuzzy point with respect to one topology and the fuzzy b-closure of a fuzzy set with respect to another topology. Additionally, some relationships are established between the two adopted topologies and the resulting mixed topology. Finally, we define countability on mixed fuzzy topological spaces and investigate the various quasi-type properties of such spaces.
Intuitionistic Fuzzy Topology and Intuitionistic Fuzzy Preorder
Sang Min Yun,Seok Jong Lee 한국지능시스템학회 2015 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.15 No.1
This paper is devoted to finding relationship between intuitionistic fuzzy preorders and intuitionistic fuzzy topologies. For any intuitionistic fuzzy preordered space, an intuitionistic fuzzy topology will be constructed. Conversely, for any intuitionistic fuzzy topological space, we obtain an intuitionistic fuzzy preorder on the set. Moreover, we will show that the family of all intuitionistic fuzzy preorders on an underlying set has a very close link to the family of all intuitionistic fuzzy topologies on the set satisfying some extra condition.
On Fuzzy Point Applications of Fuzzy Topological Spaces
Radwan Abu-Gdairi,Arafa A. Nasef,Mostafa A. El-Gayar,Mostafa K. El-Bably 한국지능시스템학회 2023 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.23 No.2
In this study, different kinds of fuzzy point applications in fuzzy topological spaces wereexamined. In addition, the characteristics of fuzzy β-closed sets via the contribution offuzzy points, as well as new separation axioms, were investigated. Besides, some propertiesrelated to the β-closure of such points using the notions of weak and strong fuzzy points wereexamined with illustrated examples. New ideas regarding fuzzy β-upper limit, fuzzy β-lowerlimit, and fuzzy β-limit using the idea of fuzzy points were also discussed. Lastly, the fuzzyβ-continuous convergence on the set of fuzzy β-continuous functions was characterized withthe help of the fuzzy β-upper limit.
민원근(Won Keun Min) 한국지능시스템학회 2010 한국지능시스템학회논문지 Vol.20 No.6
본 논문에서는 smooth topology 와 Chang's fuzzy topology의 개념을 일반화시킨 fuzzy quasi topology의 개념을 소개한다. 그리고 퍼지 준-위상의 일반적인 위상적 성질들을 조사한다. In this paper, we introduce the concept of fuzzy quasi topologies which are generalizations of smooth topologies and Chang's fuzzy topologies, and obtain some basic properties of their structures.
Fuzzy Generalized Topological Spaces
민원근(Won Keun Min) 한국지능시스템학회 2009 한국지능시스템학회논문지 Vol.19 No.3
본 논문에서는 퍼지 일반-위상과 퍼지 일반-위상 공간의 개념을 소개한다. 퍼지 일반 위상은 smooth topology 와 Chang’s fuzzy topology의 일반화된 개념이다. 퍼지 일반-위상의 일반적인 성질과 퍼지 일반 연속, 약 퍼지 일반 연속 함수의 개념과 성질을 조사한다. In this paper, we introduce the concept of fuzzy generalized topologies which are generalizations of smooth topologies and Chang's fuzzy topologies and obtain some basic properties of their structure. Also we introduce and study the concepts of fuzzy generalized continuity and weakly fuzzy generalized continuity.
Intuitionistic Fuzzy Theta-Compact Spaces
엄연석,이석종 한국지능시스템학회 2013 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.13 No.3
In this paper, we introduce certain types of continuous functions and intuitionistic fuzzy -compactness in intuitionistic fuzzy topological spaces. We show that intuitionistic fuzzy -compactness is strictly weaker than intuitionistic fuzzy compactness. Furthermore, we show that if a topological space is intuitionistic fuzzy retopologized, then intuitionistic fuzzy compactness in the new intuitionistic fuzzy topology is equivalent to intuitionistic fuzzy -compactness in the original intuitionistic fuzzy topology. This characterization shows that intuitionistic fuzzy -compactness can be related to an appropriated notion of intuitionistic fuzzy convergence.
Intuitionistic Fuzzy Theta-Compact Spaces
Eom, Yeon Seok,Lee, Seok Jong Korean Institute of Intelligent Systems 2013 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.13 No.3
In this paper, we introduce certain types of continuous functions and intuitionistic fuzzy ${\theta}$-compactness in intuitionistic fuzzy topological spaces. We show that intuitionistic fuzzy ${\theta}$-compactness is strictly weaker than intuitionistic fuzzy compactness. Furthermore, we show that if a topological space is intuitionistic fuzzy retopologized, then intuitionistic fuzzy compactness in the new intuitionistic fuzzy topology is equivalent to intuitionistic fuzzy ${\theta}$-compactness in the original intuitionistic fuzzy topology. This characterization shows that intuitionistic fuzzy ${\theta}$-compactness can be related to an appropriated notion of intuitionistic fuzzy convergence.
Intuitionistic Fuzzy Theta-Compact Spaces
Yeon Seok Eom,Seok Jong Lee 한국지능시스템학회 2013 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.13 No.3
In this paper, we introduce certain types of continuous functions and intuitionistic fuzzy θ-compactness in intuitionistic fuzzy topological spaces. We show that intuitionistic fuzzy θ-compactness is strictly weaker than intuitionistic fuzzy compactness. Furthermore, we show that if a topological space is intuitionistic fuzzy retopologized, then intuitionistic fuzzy compactness in the new intuitionistic fuzzy topology is equivalent to intuitionistic fuzzy θ-compactness in the original intuitionistic fuzzy topology. This characterization shows that intuitionistic fuzzy θ-compactness can be related to an appropriated notion of intuitionistic fuzzy convergence.
Intuitionistic Fuzzy Topology and Intuitionistic Fuzzy Preorder
Yun, Sang Min,Lee, Seok Jong Korean Institute of Intelligent Systems 2015 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.15 No.1
This paper is devoted to finding relationship between intuitionistic fuzzy preorders and intuitionistic fuzzy topologies. For any intuitionistic fuzzy preordered space, an intuitionistic fuzzy topology will be constructed. Conversely, for any intuitionistic fuzzy topological space, we obtain an intuitionistic fuzzy preorder on the set. Moreover, we will show that the family of all intuitionistic fuzzy preorders on an underlying set has a very close link to the family of all intuitionistic fuzzy topologies on the set satisfying some extra condition.
nth Power Root Fuzzy Sets and Its Topology
Tareq M. Al-shami,ariwan Z. Ibrahim,Abdelwaheb Mhemdi,Radwan Abu-Gdairi 한국지능시스템학회 2022 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.22 No.4
One of the most useful expansions of fuzzy sets for coping with information uncertaintiesis the q-rung orthopair fuzzy sets. In such circumstances, in this article, we define a novelextension of fuzzy sets called nth power root fuzzy set (briefly, nPR-fuzzy set) and elucidatetheir relationship with intuitionistic fuzzy sets, SR-fuzzy sets, CR-fuzzy sets and q-rungorthopair fuzzy sets. Then, we provide the necessary set of operations for nPR-fuzzy sets aswell as study their various features. Furthermore, we familiarize the concept of nPR-fuzzytopology and investigate the basic aspects of this topology. In addition, we define separatednPR-fuzzy sets and then present the concept of disconnected nPR-fuzzy sets. Moreover, westudy and characterize nPR-fuzzy continuous maps in great depth. Finally, we establish T0and T1 in nPR-fuzzy topologies and discover the links between them.