Pythagorean Fuzzy Nano Topological Space With (Min-Max Open Set)

Pythagorean fuzzy set, Pythagorean fuzzy topology, Maximal open set, Minimal open set, Fuzzy topological space, Generalized topology, uncertainty modelling.

C.Dilly Rani
Research Scholar, Department of Mathematics,
Annamalai University, Chidambaram.
Assistant Professor, J.J.College of Engineering
and Technology,Tiruchirappalli-600009,
Email id:[email protected]
Orcid ID: 0000-0001-9409-0817

Dr.R.Theivaraman2
Assistant Professor, Department of
Mathematics, SRM Valliammal Engineering
College, Kattankulathur,Chennai603203.
Email id:[email protected]
Orcid ID: 0000-0001-7149-5336

Dr.K.Maheshwaran3
Assistant Professor,Department of
Mathematics, School of Engineering and
Technology, Dhanalakshmi Srinivasan
University, Preambalur,Chennai-621 212.
Email id:[email protected]
Orcid ID: 0000-0001-9546-4657

Dr.K.Suresh4
Associate Professor, Department of
Mathematics, St. Joseph’s College of
Engineering OMR, Chennai-600119.
Email id:[email protected]
Orcid ID: 0000-0002-7768-9577

D.Sujatha5
Assistant Professor, Department of Nautical
Science, Academy of Maritime Education and
Training (AMET) University, Kanathur603112, Chennai.
Email id:[email protected]
Orcid ID: 0009-0006-5677-1260

RM.Valliammai6
Assistant Professor, Department of
Mathematics, K.Ramakrishnan College of
Engineering (Autonomous), Tiruchirappalli621112.
Kattankulathur,Chennai-603 203.
Email id:[email protected]
Orcid ID: 0009-0004-8187-6449

Address for correspondence: C.Dilly Rani,
Research Scholar, Department of Mathematics,
Annamalai University, Chidambaram. Assistant
Professor, J.J.College of Engineering and
Technology,Tiruchirappalli-600009
Email id:[email protected]
Orcid ID: 0000-0001-9409-0817

Received:20-06-2026
Revised:26-07-2026
Accepted:30-07-2026

European Journal of Prosthodontics and Restorative Dentistry (2026) 34 (7s), 1037–1040

Pythagorean Fuzzy Nano Topological Space With (Min-Max Open Set)

Pythagorean fuzzy set, characterized by the condition that the sum of the squares of membership and non-membership degrees does not exceed one, provide a more flexible framework for modeling uncertainty than intuitionistic fuzzy sets. In this paper, we introduce and investigate the concept of maximal open sets in Pythagorean fuzzy topological spaces. Several properties and fundamental are established, and their relationships with Pythagorean fuzzy open and closed sets are examined. Characterizations of maximal and minimal open sets are obtained through inclusion relations and intersection properties. Furthermore, illustrative examples are provided to demonstrate the applicability of the proposed concepts. The developed theory extends classical topological notions to the Pythagorean fuzzy setting and contributes to the study of generalized topological structures under uncertainty. Potential applications of the proposed framework in decision-making, information systems, and intelligent data analysis are also discussed, offering new directions for future research in fuzzy topology and soft computing.

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