Any non-empty set with four topologies is called a Quad topological space. Let be a non-empty universal set. A fuzzy set *λ* : *X* → [0:1] is a mapping from *X* into the unit interval *I = *[0,1], for all x € *X* The purpose of this paper is to define the concept of fuzzy q-open set and fuzzy q-b open sets in fuzzy quad topological space .We describe some of the basic operations on fuzzy q-open sets and fuzzy q-b open sets. Furthermore, we discuss the properties of fuzzy q- continuous function and fuzzy q-b continuous function. we introduce the concept of fuzzy q-gb open sets and study fuzzy q-separation axioms and fuzzy q-b separation axioms in fuzzy quad topological space.

**Author(s) Details:**

**Ranu Sharma,
**Department of Applied Mathematics and Computational Science, SGSITS, Indore, India.

**Bhagyashri A. Deole,**

Department of Applied Mathematics and Computational Science, SGSITS, Indore, India.

**Smita Verma,**

Department of Applied Mathematics and Computational Science, SGSITS, Indore, India.

**Please see the link here: ****https://stm.bookpi.org/RAMRCS-V10/article/view/6271**