The paper reports a study on the air quality over Kolkata, India during the transition period from post-monsoon to winter. A fuzzy binary relation based approach is implemented to O3, N O2 and P M2 5 and the overall air quality index (AQI). Individual pollutants have been converted to fuzzy sets based on their concentrations as elements of the universe of discourse with appropriate fuzzy membership functions defined on them. AQI has been divided into categories based on the recommendations of the Central Pollution Control Board (CPCB), Govt of India. After defining the fuzzy relations, the fuzzy composite relations have been derived to construct fuzzy membership matrices based on the composite binary fuzzy relations. Afterwards, the membership grades of the matrices for the composite fuzzy binary relations have been studied and N O2 along with O3 have been consideblack as having highly significant influence on the overall AQI over the polluted study zone during the transition from post-monsoon to winter. © 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.