A 3D Distance Measure for Intuitionistic Fuzzy Sets and its Application in Pattern Recognition and Decision-Making Problems

Anjali Patel, Naveen Kumar and Juthika Mahanta
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Anjali Patel: Department of Mathematics, NIT Silchar, Cachar, Assam 788010, India
Naveen Kumar: Department of Mathematics, NIT Silchar, Cachar, Assam 788010, India
Juthika Mahanta: Department of Mathematics, NIT Silchar, Cachar, Assam 788010, India

New Mathematics and Natural Computation (NMNC), 2023, vol. 19, issue 02, 447-472

Abstract: The distance measure as an information measure helps in processing incomplete and confusing data to arrive at a conclusion by assessing the degree of difference between pairs of variables. Reviewing distance measures for Intuitionistic Fuzzy Sets (IFSs), we have pointed out several drawbacks of the existing measures. To overcome these, this paper presents a new distance measure between IFSs based on the probabilistic divergence measure. Several mathematical properties of the proposed metric are established and validated via numerical examples. This proposed definition is further used to devise several similarity measures. Applicability and consistency of the introduced measures have been corroborated by various examples. In addition to that, rationality of the proposed metric is established by applying it to pattern recognition applications, Multi-Attribute-Decision-Making (MADM) problems and medical & pathological diagnoses. Analysis of the results establishes that the suggested measure overcomes shortcomings associated with existing measures and thereby authenticates the superiority of the proposed measure.

Keywords: Intuitionistic fuzzy set; distance measure; similarity measure; decision-making; pattern recognition; pathological diagnosis (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S1793005723500163

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