Exploration of pre-open sets in a fuzzy bitopological space via operation approach

Satabdi  Ray; Birojit Das; Baby Bhattacharya; Omer Kisi

doi:10.5269/bspm.66079

Satabdi Ray
Birojit Das
Baby Bhattacharya
Omer Kisi

Abstract

In this article, we propose an operation $(i,j)^*_\gamma$ on the set of all $(i,j)^*$-fuzzy pre-open set in a given fuzzy bitopological space $(X,\tau_i,\tau_j )$. Using the newly introduced operation, we initiate the $(i,j)^*_\gamma$-fuzzy preopen set and characterize it upto some extent. Also, we explore $(i,j)^*$-fuzzy pre-open set in the light of minimality. Finally, we study locally finiteness of a fuzzy bitopological space via $(i,j)^*_\gamma$-fuzzy open set.

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References

Andrijevic, D., Semi-preopen sets, Math. Vesnik., 24-32, (1986).

Andrijevic, D., On the Topology Generated by Pre-open Sets, Math. Vesnik, 39, 367-376, (1987).

Asaad, B. A., Ahmed, N., Operation on semi generalized open sets with its separation axioms, Int. J. Pure Appl. Math., 118(3), 701-711, (2018).

Carpintero, C., Rajesh, N., Roses, E., Operation approaches on b-open sets and applications, Bol. Soc. Paran. Mat., 20(1), 21-33, (2012).

Das, B.,Saha, A.K., Bhattacharya, B., On Infi-topological Spaces, The Journal of Fuzzy Mathematics, 25(2), 437-448, 2017.

Das, B., Bhattacharya, B., On fuzzy γµ-open sets in generalized fuzzy topological spaces, Proyecciones Journal of Mathematics, 41(3), 733 - 749 (2022).

Das, B., Bhattacharya, B., Chakraborty, J., Tripathy, B. C., Generalized fuzzy closed sets in a fuzzy bitopological space via γ-open sets, Afrika Matematika, 32(2), 1-13, (2021).

Das, B., Chakraborty, J., Paul, G., Bhattacharya, B., A new approach for some applications of generalized fuzzy closed sets, Computational and Applied Mathematics, 40(2), 1-14, (2021).

Das, B., Chakraborty, J., Bhattacharya, B., A new type of generalized closed set via γ-open set in a fuzzy bitopological space, Proyecciones Journal of Mathematics, 38(3), 511-536, (2019).

Das, B., Bhattacharya, B., On (i, j) generalized fuzzy γ-closed Set in fuzzy bitopological spaces, Soft Computing for Problem Solving: SocProS 2017, 1, 661-673, 2018.

Fathi, H. K., Khalaf M. A., Operations on bitopological spaces, Fasciculi Mathematici, 45, 47-57, (2010).

Ghour, S. A., Some generalizations of minimal fuzzy open sets, Acta Mathematica Universitatis Comenianae, 75(1), 107-117, (2006).

Hussain, S., On generalized open sets, Hacettepe Journal of Mathematics and Statistics, 47(6), 1438-1446, (2018).

Kandil, A, Nouh, A. A., El-Sheikh, S. A., On fuzzy bitopological spaces, Fuzzy Sets and Systems, 74, 353-363, (1995).

Kasahara, S., Operation-compact spaces, Mathematica Japonica, 24, 97-105, (1979).

Levine, N., Generalized closed sets in topology, Rend. Circ. Math. Palerno, 2, 89–96, (1970)

Mashhour, A. S., EI-Monsef, M. E., EI-Deep, S. N., On Precontinuous and Weak Continuous Mappings, Proc., Math. Phys., Soc., 53, 47-53, (1982).

Nakaoka, F., Oda, N., Some applications of minimal open sets, Int. J. Math. Math. Sci., 27(8), 471-476, (2001).

Njastad, O., On some classes of nearly open sets, Pacific J. Math., 15, 961-970, (1965).

Ogata, H., Remarks on some operation-separation axioms, Bull. Fukuoka Univ. Ed. Part III, 40, 41-43, (1991).

Ogata, H., Operations on topological spaces and associated topology, Math. Japon., 36, 175-184, (1991).

Ray, S., Das, B., Bhattacharya, B., Kisi, O., Granados, C., Application of Operation approach in fuzzy bitopological spaces, Soft Computing,(in press), 2024

Roy, B., Applications of operations on minimal generalized open sets, Afrika Matematika , 29, 1097-1104, (2018).

Roy, B., Sen, R., On maximal µ-open and minimal µ-closed sets via generalized topology, Acta Math. Hung., 136, 233-239, (2012).

Tahiliani, S., Operation approach to β-open sets and applications, Math. Comm., 16, 577-591, (2011)