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On pairwise fuzzy almost P-spaces
G. Thangaraj,E. Roseline Gladis 원광대학교 기초자연과학연구소 2022 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.23 No.2
In this paper, the concept of pairwise fuzzy almost P-space is introduced by means of pairwise fuzzy Gδ-sets. Several characterizations of pairwise fuzzy almost P-spaces are obtained. The conditions for the pairwise fuzzy submaximal spaces to become pairwise fuzzy almost P-spaces are established. It is shown that the pairwise fuzzy strongly irresolvable and pairwise fuzzy almost P-spaces are pairwise fuzzy irresolvable spaces. The condition for the pairwise fuzzy almost P-spaces to become pairwise fuzzy σ-second category spaces and pairwise fuzzy weakly Volterra spaces are also established.
On A-somewhat fuzzy continuous functions
G. Thangaraj,S. Senthil 원광대학교 기초자연과학연구소 2022 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.23 No.1
In this paper, a new form of somewhat fuzzy continuity, called A-somewhat fuzzy continuity between fuzzy topological spaces, is introduced. Several characterizations of these functions are obtained and a condition for an fuzzy α-continuous function to become an A-somewhat fuzzy continuous function is established. It is shown that A-somewhat fuzzy continuous function from the fuzzy hyperconnected space into another fuzzy topological space is not an somewhat fuzzy continuous function. The conditions by means of A-somewhat fuzzy continuous functions for the fuzzy hyperconnected and fuzzy strongly irresolvable spaces to become fuzzy Baire spaces, are also obtained.
G. Thangaraj,M. Ponnusamy 원광대학교 기초자연과학연구소 2023 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.25 No.1
In this paper, the notion of fuzzy regular $Oz$-space is introduced by means of fuzzy regular closed sets and fuzzy regular $G_\delta$ sets. It is established that fuzzy regular $Oz$-spaces are fuzzy $Oz$-spaces and fuzzy regular $Oz$ and fuzzy $P$-spaces are fuzzy extremally disconnected spaces and fuzzy Moscow spaces. A condition under which fuzzy regular $Oz$-spaces become weak fuzzy $Oz$-spaces is also established. It is obtained that fuzzy regular $Oz$ and weak fuzzy $P$-spaces become fuzzy pseudo $P$-spaces if fuzzy regular $Oz$ and weak fuzzy $P$-spaces have non-zero fuzzy regular $G_\delta$-sets.
Fuzzy P-sets and fuzzy P'-sets in fuzzy topological spaces
G. Thangaraj,S. Muruganantham 원광대학교 기초자연과학연구소 2022 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.24 No.1
In this paper, the notions of fuzzy P-sets and fuzzy P'-sets in fuzzy topological spaces are introduced and several characterizations of these sets are established. A condition for the existence of fuzzy σ-nowhere dense sets in fuzzy hyperconnected spaces is obtained by means of fuzzy P-sets. The conditions under which fuzzy co-σ-boundary sets and fuzzy closed sets in fuzzy perfectly disconnected spaces become fuzzy P'-sets are established. A condition for fuzzy closed Fσ-sets in fuzzy F'-spaces to become fuzzy P'-sets is also obtained in this paper.
G. Thangaraj,S. Muruganantham 원광대학교 기초자연과학연구소 2023 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.25 No.2
In this paper, the concept of fuzzy F-spaces is introduced and studied. Several characterizations of fuzzy F-spaces are established. It is established that fuzzy F- spaces in which fuzzy $G_{\delta}$-sets are fuzzy open, are fuzzy normal spaces and fuzzy F-spaces in which fuzzy $G_{\delta}$- sets are fuzzy closed, are fuzzy F$'$-spaces. It is established that fuzzy F-spaces are not fuzzy hyperconnected spaces. A condition for fuzzy F$'$-spaces to become fuzzy F-spaces is obtained. The conditions under which fuzzy globally disconnected spaces and fuzzy perfectly disconnected spaces become fuzzy F-spaces are also obtained.
Some remarks on fuzzy open hereditarily irresolvable spaces
G. Thangaraj,L. Vikraman 원광대학교 기초자연과학연구소 2024 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.27 No.2
In this paper, the notion of fuzzy open hereditarily irresolvability of fuzzy topological spaces is characterized by means of fuzzy simply$^{\ast}$-open sets, fuzzy B$^{\ast}$-sets and fuzzy pre-open sets possessing fuzzy Baire property. A condition for fuzzy open hereditarily irresolvable spaces to become fuzzy quasi-submaximal spaces is obtained. Also conditions under which fuzzy D-Baire spaces and fuzzy semi-P-spaces become fuzzy open hereditarily irresolvable spaces are obtained. A condition under which fuzzy open hereditarily irresolvability coincides with fuzzy strong irresolvability of fuzzy topological spaces is obtained.
PAIRWISE FUZZY REGULAR VOLTERRA SPACES
THANGARAJ, G.,CHANDIRAN, V. The Korean Society for Computational and Applied M 2015 Journal of applied mathematics & informatics Vol.33 No.5
In this paper the concepts of pairwise fuzzy regular Volterra spaces and pairwise fuzzy weakly regular Volterra spaces are introduced. Several characterizations of pairwise fuzzy regular Volterra spaces and pair-wise fuzzy weakly regular Volterra spaces are investigated.
Some remarks on fuzzy Baire sets
G. Thangaraj,N. Raji 원광대학교 기초자연과학연구소 2023 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.26 No.2
In this paper, the means by which fuzzy Baire sets are obtained from fuzzy simply$^{\ast}$ open sets in fuzzy hyperconnected spaces are discussed. It is obtained that fuzzy Baire sets in fuzzy fraction dense spaces are not fuzzy dense sets. Also the conditions under which fuzzy Baire sets are generated from fuzzy nowhere dense sets, fuzzy dense and fuzzy open sets in fuzzy fraction dense and fuzzy DG$_\delta$-spaces are obtained. It is established that existence of a fuzzy co-$\sigma$-boundary set in fuzzy weakly Baire spaces ensures the existence of a pair of disjoint fuzzy Baire sets and fuzzy open sets in fuzzy hyperconnected and fuzzy nodef spaces are fuzzy Baire sets.
G. Thangaraj,A. Vinothkumar 원광대학교 기초자연과학연구소 2022 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.23 No.3
In this paper, the notion of fuzzy Moscow space is introduced and studied. It is established that fuzzy extremally disconnected spaces are fuzzy Moscow spaces and fuzzy Moscow and fuzzy P-spaces are fuzzy extremally disconnected spaces. It is obtained that fuzzy Moscow spaces are not fuzzy hyperconnected spaces and not fuzzy superconnected spaces. A condition under which fuzzy Moscow spaces become fuzzy hyperconnected spaces is obtained. It is also established that fuzzy semi-open sets are fuzzy pre-open sets in fuzzy Moscow and fuzzy P-spaces.
Pairwise fuzzy functions and pairwise fuzzy Volterra Spaces
G. Thangaraj,Venkattappan Chandiran 원광대학교 기초자연과학연구소 2017 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.14 No.6
In this paper, by using pairwise fuzzy functions and somewhat pairwise fuzzy functions, a study on the conditions under which a fuzzy bitopological space becomes pairwise fuzzy Volterra and pairwise fuzzy weakly Volterra spaces, has been carried out. Results concerning pairwise fuzzy functions that preserve pairwise fuzzy Volterra and pairwise fuzzy weakly Volterra spaces in the context of images and pre-images are also studied.