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 9 Effect of the parameters \(p\) and \(\lambda\) on the ranking order for the medicine selection 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 \(\lambda\)		\(\left( {M_{1} ,M^{*} } \right)\)	\(\left( {M_{2} ,M^{*} } \right)\)	\(\left( {M_{3} ,M^{*} } \right)\)	\(\left( {M_{4} ,M^{*} } \right)\)	\(\left( {M_{5} ,M^{*} } \right)\)	\(\left( {M_{6} ,M^{*} } \right)\)	\(\left( {M_{1} ,M^{*} } \right)\)	\(\left( {M_{2} ,M^{*} } \right)\)	\(\left( {M_{3} ,M^{*} } \right)\)	\(\left( {M_{4} ,M^{*} } \right)\)	\(\left( {M_{5} ,M^{*} } \right)\)	\(\left( {M_{6} ,M^{*} } \right)\)
p = 1	\(\lambda = 0\)	0.3062	0.2912	0.2952	0.2683	0.0811	0.2559	0.9063	0.8209	0.8447	0.7830	0.6962	0.7254
	\(\lambda = 0.4\)							0.7062	0.6700	0.6998	0.6202	0.2142	0.6175
	\(\lambda = 0.6\)							0.4620	0.4342	0.4391	0.3999	0.1301	0.3726
	\(\lambda = 0.8\)							0.2942	0.2747	0.2902	0.2624	0.0748	0.2326
	\(\lambda = 1\)							0.1999	0.1864	0.1941	0.1796	0.0563	0.1690
Ranking		\(M_{5} < M_{6} < M_{4} < M_{2} < M_{3} < M_{1}\)						\(M_{5} < M_{6} < M_{4} < M_{2} < M_{3} < M_{1}\)
p = 2	\(\lambda = 0\)	0.3280	0.3049	0.3089	0.2985	0.1246	0.2757	0.9113	0.8261	0.8516	0.7848	0.7278	0.7349
	\(\lambda = 0.4\)							0.7171	0.6836	0.7025	0.6219	0.4831	0.6197
	\(\lambda = 0.6\)							0.4798	0.4431	0.4479	0.4080	0.2695	0.3729
	\(\lambda = 0.8\)							0.4128	0.3978	0.4015	0.3942	0.1671	0.3749
	\(\lambda = 1\)							0.2006	0.1882	0.1950	0.1831	0.1169	0.1744
Ranking		\(M_{5} < M_{6} < M_{4} < M_{2} < M_{3} < M_{1}\)						\(M_{5} < M_{6} < M_{4} < M_{2} < M_{3} < M_{1}\)
p = 5	\(\lambda = 0\)	0.3303	0.3180	0.3294	0.3099	0.1470	0.2958	0.9137	0.8338	0.8690	0.7936	0.7587	0.7609
	\(\lambda = 0.4\)							0.7256	0.6934	0.7104	0.6297	0.5643	0.6272
	\(\lambda = 0.6\)							0.4868	0.4455	0.4537	0.4087	0.2888	0.3838
	\(\lambda = 0.8\)							0.4198	0.4072	0.4145	0.4008	0.1989	0.3804
	\(\lambda = 1\)							0.2044	0.1936	0.1958	0.1839	0.1379	0.1799
Ranking		\(M_{5} < M_{6} < M_{4} < M_{2} < M_{3} < M_{1}\)						\(M_{5} < M_{6} < M_{4} < M_{2} < M_{3} < M_{1}\)
p = 10	\(\lambda = 0\)	0.3522	0.3313	0.3368	0.3195	0.1630	0.3015	0.9236	0.8392	0.8772	0.8008	0.7735	0.7767
	\(\lambda = 0.4\)							0.7373	0.7056	0.7123	0.6393	0.5790	0.6325
	\(\lambda = 0.6\)							0.4877	0.4590	0.4690	0.4164	0.2921	0.3996
	\(\lambda = 0.8\)							0.4269	0.4152	0.4273	0.4100	0.2145	0.3989
	\(\lambda = 1\)							0.2120	0.1976	0.1963	0.1897	0.1672	0.1841
Ranking		\(M_{5} < M_{6} < M_{4} < M_{2} < M_{3} < M_{1}\)						\(M_{5} < M_{6} < M_{4} < M_{2} < M_{3} < M_{1}\)
p = 50	\(\lambda = 0\)	0.3809	0.3539	0.3658	0.3339	0.1940	0.3222	0.9557	0.8989	0.9172	0.8567	0.8300	0.8448
	\(\lambda = 0.4\)							0.7519	0.7196	0.7456	0.6598	0.6198	0.6346
	\(\lambda = 0.6\)							0.4907	0.4629	0.4761	0.4331	0.3071	0.4123
	\(\lambda = 0.8\)							0.4305	0.4247	0.4370	0.4298	0.2489	0.4067
	\(\lambda = 1\)							0.2464	0.2323	0.2361	0.2256	0.1847	0.2198
Ranking		\(M_{5} < M_{6} < M_{4} < M_{2} < M_{3} < M_{1}\)						\(M_{5} < M_{6} < M_{4} < M_{2} < M_{3} < M_{1}\)

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