Afrika Matematika https://doi.org/10.1007/s13370-020-00829-7 Generalized fuzzy closed sets in a fuzzy bitopological space via -open sets Birojit Das 1 · Baby Bhattacharya 1 · Jayasree Chakraborty 1 · Binod Chandra Tripathy 1 Received: 27 November 2018 / Accepted: 27 August 2020 © African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2020 Abstract The paper presents the notion of (i , j ) ∗ γ -generalized fuzzy closed set in a fuzzy bitopolog- ical space considering a parallel form of (i , j ) fuzzy γ -open set. We introduce the idea of γ -generalized fuzzy q -neighbourhood of a fuzzy point. Moreover, we study various related properties and cite some interesting results on this set. Also, we show that generalized fuzzy closed sets and γ -generalized fuzzy closed sets are completely independent of each other in the same environment. Furthermore, we introduce the notion of γ -generalized fuzzy con- tinuous function in a fuzzy bitopological space. Finally, we propose a new type of closure operator and establish important results based on this concept. Keywords (i , j ) ∗ γ -generalized fuzzy closed set · (i , j ) ∗ generalized fuzzy continuous function · (i , j ) ∗ γ -generalized fuzzy continuous function · (i , j ) ∗ γ -generalized fuzzy closure operator Mathematics Subject Classification 54E55 · 54A40 1 Introduction After the concept of fuzzy set came into literature, it was applied in various fields of science and important investigations were made accordingly. Different kinds of fuzzy topological spaces were introduced and their properties have been characterized by Tripathy and Ray [1,2], Tripathy and Debnath [3,4]. The study of bitopological space was first introduced and B Baby Bhattacharya babybhatt75@gmail.com Birojit Das dasbirojit@gmail.com Jayasree Chakraborty chakrabortyjayasree1@gmail.com Binod Chandra Tripathy tripathybc@rediffmail.com 1 Department of Mathematics, NIT, Agartala, India 123