Nonlinear distance measures under the framework of Pythagorean fuzzy sets with applications in problems of pattern recognition, medical diagnosis, and COVID-19 medicine selection

Dutta, Palash; Borah, Gourangajit; Gohain, Brindaban; Chutia, Rituparna

doi:10.1186/s43088-023-00375-8

Beni-Suef University Journal of Basic and Applied Sciences

Table 8 Effect of the parameters \(p\) and \(\lambda\) on the ranking order for the medical diagnosis problem

From: Nonlinear distance measures under the framework of Pythagorean fuzzy sets with applications in problems of pattern recognition, medical diagnosis, and COVID-19 medicine selection

Values of \(p\) and \(\lambda\)	Generalized chordal distance										Non-archimedean chordal distance
Values of \(p\) and \(\lambda\)	\(\left( {P_{1} ,Q} \right)\)	\(\left( {P_{2} ,Q} \right)\)	\(\left( {P_{3} ,Q} \right)\)	\(\left( {P_{4} ,Q} \right)\)	\(\left( {P_{5} ,Q} \right)\)	\(\left( {P_{1} ,Q} \right)\)	\(\left( {P_{2} ,Q} \right)\)	\(\left( {P_{3} ,Q} \right)\)	\(\left( {P_{4} ,Q} \right)\)	\(\left( {P_{5} ,Q} \right)\)	Non-archimedean chordal distance
p = 1	\(\lambda = 0\)	0.0912	0.5321	0.6036	0.3418	0.3477	0.1950	0.6602	0.6821	0.4408	0.5606
	\(\lambda = 0.4\)						0.1502	0.6345	0.6404	0.4166	0.5105
	\(\lambda = 0.6\)						0.0921	0.3973	0.4051	0.2677	0.2954
	\(\lambda = 0.8\)						0.0601	0.2668	0.2724	0.1740	0.1904
	\(\lambda = 1\)						0.0371	0.1738	0.1801	0.1115	0.1238
Ranking		\(P_{1} < P_{4} < P_{5} < P_{2} < P_{3}\)					\(P_{1} < P_{4} < P_{5} < P_{2} < P_{3}\)
p = 2	\(\lambda = 0\)	0.2924	0.7636	0.8522	0.5426	0.6009	0.2943	0.7256	0.7450	0.5002	0.6309
	\(\lambda = 0.4\)						0.2713	0.7030	0.7110	0.4812	0.5801
	\(\lambda = 0.6\)						0.1567	0.6404	0.6654	0.4463	0.4902
	\(\lambda = 0.8\)						0.1001	0.4325	0.4526	0.2846	0.3131
	\(\lambda = 1\)						0.0622	0.2813	0.3007	0.1821	0.2018
Ranking		\(P_{1} < P_{4} < P_{5} < P_{2} < P_{3}\)					\(P_{1} < P_{4} < P_{5} < P_{2} < P_{3}\)
p = 5	\(\lambda = 0\)	0.3113	0.7785	0.8694	0.5649	0.6216	0.4601	0.9328	0.9855	0.7031	0.7530
	\(\lambda = 0.4\)						0.4244	0.8840	0.9003	0.7865	0.7308
	\(\lambda = 0.6\)						0.2175	0.6807	0.7215	0.5602	0.5976
	\(\lambda = 0.8\)						0.1404	0.6506	0.6955	0.4438	0.5052
	\(\lambda = 1\)						0.0901	0.4202	0.4618	0.2834	0.3228
Ranking		\(P_{1} < P_{4} < P_{5} < P_{2} < P_{3}\)					\(P_{1} < P_{4} < P_{5} < P_{2} < P_{3}\)
p = 10	\(\lambda = 0\)	0.3258	0.7813	0.8698	0.5682	0.6289	0.5322	0.9416	0.9601	0.7842	0.8001
	\(\lambda = 0.4\)						0.5103	0.8621	0.9315	0.6501	0.7751
	\(\lambda = 0.6\)						0.2514	0.8409	0.9168	0.5952	0.6925
	\(\lambda = 0.8\)						0.1626	0.8024	0.8908	0.5620	0.6645
	\(\lambda = 1\)						0.1036	0.5137	0.5872	0.3601	0.4244
Ranking		\(P_{1} < P_{4} < P_{5} < P_{2} < P_{3}\)					\(P_{1} < P_{4} < P_{5} < P_{2} < P_{3}\)
p = 50	\(\lambda = 0\)	0.3474	0.8085	0.8767	0.5727	0.6378	0.6205	0.8178	0.8520	0.6575	0.7063
	\(\lambda = 0.4\)						0.5974	0.7924	0.8367	0.6220	0.7605
	\(\lambda = 0.6\)						0.3109	0.7306	0.8134	0.5109	0.6025
	\(\lambda = 0.8\)						0.2041	0.6655	0.7804	0.4838	0.5853
	\(\lambda = 1\)						0.1308	0.6510	0.7673	0.4644	0.5578
Ranking		\(P_{1} < P_{4} < P_{5} < P_{2} < P_{3}\)					\(P_{1} < P_{4} < P_{5} < P_{2} < P_{3}\)

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