Pythagorean m-polar Fuzzy Neutrosophic Metric Spaces

• Published in: Neutrosophic sets and systems Vol. 53; pp. 562 - 579
• Main Authors: Siraj, Atiqa, Naeem, Khalid, Said, Broumi
• Format: Journal Article
• Language: English
• Published: Neutrosophic Sets and Systems 01-01-2023; University of New Mexico
• Subjects: pattern recognition; pythagorean m-polar fuzzy neutrosophic metric spaces; pythagorean m-polar fuzzy neutrosophic set; pythagorean m-polar fuzzy neutrosophic subset
• ISSN: 2331-6055; 2331-608X
• DOI: 10.5281/zenodo.7536088

Neutrosophy deals with the study of neutrosophic logic, set and probability. A Pythagorean m-polar neutrosophic set is indeed an expansion of crisp, fuzzy, intuitionistic fuzzy, neutrosophic and Pythagorean m-polar fuzzy sets. In this paper, we develop the perception of Pythagorean m-polar fuzzy neutrosophic metric space defined over Pythagorean m-polar fuzzy neutrosophic set relying on the classical definition of metric spaces defined on a crisp set. We present some related results and illustrations to perceive the conceptions. We present many examples of metrics which hold true for classical sets but fail to make sense in Pythagorean m-polar fuzzy environment. We also render a practical utility of the proposed metrics in pattern recognition. Keywords: Pythagorean m-polar fuzzy neutrosophic set; Pythagorean m-polar fuzzy neutrosophic subset; Pythagorean m-polar fuzzy neutrosophic metric spaces; Pattern recognition