Open Maps via δ-open Sets in Pythagorean Fuzzy Topological Spaces and its Applications

In this paper, we introduce the concept of Pythagorean fuzzy (resp. , , or )-open mappings are introduced and their properties are discussed. In current scenario people with symptom of Covid-19 like fever, cough, sneezing, sore throat, loss of taste and smell etc., were panic about the disease, and the diagnosis of Covid-19 takes many hours and people cannot go for the test frequently. Some other diseases like flu, pneumonia, cold etc., also has the same symptoms. Each patients has unique experience of that particular symptom and some time they may not experience that symptom even though they were affected by the Covid-19. Also, in this paper we tried to diagnosis Covid-19 with the help of picture fuzzy sets which helps to record all symptoms in précised manner. Introduction: This paper introduces the concept of Pythagorean fuzzy open mappings and their relevance to COVID-19 symptom diagnosis. Due to the overlapping symptoms of COVID-19 with other illnesses, a Pythagorean fuzzy set approach is utilized to more accurately capture and analyze symptom patterns. Objectives: The objective is to develop a precise mapping model that utilizes Pythagorean fuzzy sets to differentiate between COVID-19 symptoms and other similar conditions, aiming to improve diagnostic speed and accuracy. Methods: The method involves formulating fuzzy sets based on COVID-19 symptoms, computing distances (Hamming, Euclidean) between patients' symptoms and ideal symptom patterns, and identifying cases with higher COVID-19 risk. Results: The approach successfully identifies patients with symptoms closest to COVID-19 indicators, offering a more systematic and timely diagnosis. Results suggest that this fuzzy set model can enhance early detection and intervention for affected individuals Conclusions: In this paper, Some new notions of strongly Pythagorean fuzzy open (closed) maps called Pythagorean fuzzy -open and Pythagorean fuzzy -closed maps are introduced and discussed their relationship between their near mappings with examples. Also, we have tried to diagnosis Covid-19 with the help of Pythagorean fuzzy sets which helps to record all symptoms in précised manner. In future, researchers can extend this model to other extensions of fuzzy sets such as rough sets and utilize the interdependency among the various evaluation criteria for better judgement.