FUZZY TOPSIS Application in Materials Analysis for Economic Production of Cashew Juice Extractor

Figures & data

Table 1. Fuzzy linguistic terms and corresponding TFN for each criterion and alternatives [26,27].

Importance	Abbreviation	TFN
Very low/very poor	VL	1,1,3
Low/poor	L	1,3,5
Medium/fair	M	3,5,7
High/good	H	5,7,9
Very high/very good	VH	7,9,9

Table 2. Decision-maker 1 (DM1).

	Criteria
Alternatives	C1	C2	C3	C4
Alloy steel (A1)	VH	H	H	VH
Galvanised steel (A2)	H	H	M	VL
Stainless steel (A3)	L	L	VH	VH
Mild steel (A4)	M	H	L	L

Table 3. Decision-maker 2 (DM2).

	Criteria
Alternatives	C1	C2	C3	C3
A1	H	VH	H	VH
A2	H	M	H	L
A3	VL	L	VH	VH
A4	L	H	M	M

Table 4. Decision-maker 3 (DM3).

	Criteria
Alternatives	C1	C2	C3	C4
A1	VH	VH	H	VH
A2	H	H	H	VL
A3	VL	L	H	VH
A4	L	H	L	M

Table 5. Fuzzy number representation for DM1.

Alternatives	C1			C2			C3			C4
A1	7	9	9	5	7	9	5	7	9	7	9	9
A2	5	7	9	5	7	9	3	5	7	1	1	3
A3	1	3	5	1	3	5	7	9	9	7	9	9
A4	3	5	7	5	7	9	1	3	5	1	3	5

Table 6. Fuzzy number representation for DM2.

Alternatives	C1			C2			C3			C4
A1	5	7	9	7	9	9	5	7	9	7	9	9
A2	5	7	9	3	5	9	5	7	9	1	3	5
A3	1	1	3	1	3	5	7	9	9	7	9	9
A4	1	3	5	5	7	9	3	5	7	3	5	7

Table 7. Fuzzy number representation for DM3.

Alternatives	C1			C2			C3			C4
A1	7	9	9	7	9	9	5	7	9	7	9	9
A2	5	7	9	5	7	9	5	7	9	1	1	3
A3	1	1	3	1	3	5	5	7	9	7	9	9
A4	1	3	5	5	7	9	1	3	5	3	5	7

Table 8. Decision criteria rating.

Decision criteria	Linguistic rating	Fuzzy number
Yield strength	H	5,7,9
Thermal conductivity	M	3,5,7
Corrosion resistance	H	5,7,9
Cost	VH	7,9,9

Table 9. Combined group decision matrix.

Alternatives	C1			C2			C3			C4
A1	5	8.3333	9	5	8.3333	9	5	7	9	7	9	9
A2	5	7	9	3	6.3333	9	3	6.3333	9	1	1.6667	5
A3	1	1.6667	5	1	3	5	5	8.3333	9	7	9	9
A4	1	3.6667	7	5	7	9	1	3.6667	7	1	4.3333	7

Table 10. Normalised fuzzy decision matrix based on group decision-making.

Alternatives	C1			C2			C3			C4
A1	0.5556	0.9259	1.0000	0.5556	0.9259	1.0000	0.5556	0.7778	1.0000	0.1429	0.1111	0.1111
A2	0.5556	0.7778	1.0000	0.3333	0.7037	1.0000	0.3333	0.7037	1.0000	1.0000	0.6000	0.2000
A3	0.1111	0.1852	0.5556	0.1111	0.3333	0.5556	0.5556	0.9259	1.0000	0.1429	0.1111	0.1111
A4	0.1111	0.4074	0.7778	0.5556	0.7778	1.0000	0.1111	0.4074	0.7778	1.0000	0.2308	0.1429

Table 11. Weighted normalised fuzzy decision matrix based on group decision-making.

Alternatives	C1			C2			C3			C4
A1	2.7778	6.4815	9.0000	1.6667	4.6296	7.0000	2.7778	5.4444	9.0000	1.0000	1.0000	1.0000
A2	2.7778	5.4444	9.0000	1.0000	3.5185	7.0000	1.6667	4.9259	9.0000	7.0000	5.4000	1.8000
A3	0.5556	1.2963	5.0000	0.3333	1.6667	3.8889	2.7778	6.4815	9.0000	1.0000	1.0000	1.0000
A4	0.5556	2.8519	7.0000	1.6667	3.8889	7.0000	0.5556	2.8519	7.0000	7.0000	2.0769	1.2857

Table 12. Fuzzy positive ideal solution $A^{+}$ and negative ideal solution $A^{-}$ based on group decision-making.

A^+	2.7778	6.4815	9.0000	1.6667	4.6296	7.0000	2.7778	6.4815	9.0000	7.0000	5.4000	1.8000
A^−	0.5556	1.2963	5.0000	0.3333	1.6667	3.8889	0.5556	2.8519	7.0000	1.0000	1.0000	1.0000

Table 13. Distance of each alternative from A⁺ based on group decision-making.

Alternatives	C1	C2	C3	C4
A1	0.0000	0.0000	0.5987	5.6569
A2	0.5987	1.1759	1.6826	0.0000
A3	2.5337	3.9000	0.0000	3.6389
A4	5.1753	0.9623	2.8698	1.1547

Table 14. Distance of each alternative from A⁻ based on group decision-making.

Alternatives	C1	C2	C3	C4
A1	6.6732	4.3647	3.5168	0.0000
A2	5.9037	3.6409	2.9518	5.6569
A3	0.0000	0.0000	4.3382	0.0000
A4	2.1924	3.9000	0.0000	3.6389

Figure 1. Alternatives, CC_i values, and corresponding rank based on group decision-making.

Table 15. CC_i and corresponding alternatives ranking based on group decision-making.

Alternatives	$Y_i^{+}$	$Y_i^{-}$	(CCi)	Rank
A1	6.2556	14.5547	0.6994	2
A2	3.4573	18.1533	0.8400	1
A3	10.0726	4.3382	0.3010	4
A4	10.1620	9.7312	0.4892	3

Figure 2. Ranking of different methods based on group decision-making.

Table 16. Ranking of different methods based on group decision-making.

Alternatives	FUZZY TOPSIS	FUZZY MOORA	FUZZY SAW
A1	2	1	2
A2	1	2	1
A3	4	4	4
A4	3	3	3

Figure 3. Alternatives, CC_i values, and corresponding rank.

Table 17. Normalised decision matrix.

Alternatives	C1			C2			C3			C4
A1	0.7778	1.0000	1.0000	0.5556	0.7778	1.0000	0.5556	0.7778	1.0000	0.1429	0.1111	0.1111
A2	0.5556	0.7778	1.0000	0.5556	0.7778	1.0000	0.3333	0.5556	0.7778	1.0000	1.0000	0.3333
A3	0.1111	0.3333	0.5556	0.1111	0.3333	0.5556	0.7778	1.0000	1.0000	0.1429	0.1111	0.1111
A4	0.3333	0.5556	0.7778	0.5556	0.7778	1.0000	0.1111	0.3333	0.5556	1.0000	0.3333	0.2000

Table 18. Weighted normalised matrix.

Alternatives	C1			C2			C3			C4
A1	3.8889	7.0000	9.0000	1.6667	3.8889	7.0000	2.7778	5.4444	9.0000	1.0000	1.0000	1.0000
A2	2.7778	5.4444	9.0000	1.6667	3.8889	7.0000	1.6667	3.8889	7.0000	7.0000	9.0000	3.0000
A3	0.5556	2.3333	5.0000	0.3333	1.6667	3.8889	3.8889	7.0000	9.0000	1.0000	1.0000	1.0000
A4	1.6667	3.8889	7.0000	1.6667	3.8889	7.0000	0.5556	2.3333	5.0000	7.0000	3.0000	1.8000

Table 19. Fuzzy positive ideal solution $A^{+}$ and negative ideal solution $A^{-}$_.

A^+	3.8889	7.0000	9.0000	1.6667	3.8889	7.0000	3.8889	7.0000	9.0000	7.0000	9.0000	3.0000
A^−	0.5556	2.3333	5.0000	0.3333	1.6667	3.8889	0.5556	2.3333	5.0000	1.0000	1.0000	1.0000

Table 20. Distance of each alternative from A⁺.

Alternatives	C1	C2	C3	C4
A1	0.0000	0.0000	1.1036	5.8875
A2	1.1036	0.0000	2.4910	0.0000
A3	4.0367	2.3376	0.0000	5.8875
A4	2.4910	0.0000	4.0367	3.5325

Table 21. Distance of each alternative from A⁻.

Alternatives	C1	C2	C3	C4
A1	4.0367	2.3376	3.1945	0.0000
A2	3.1945	2.3376	1.5972	5.8875
A3	0.0000	0.0000	4.0367	0.0000
A4	1.5972	2.3376	0.0000	3.6804

Table 22. CC_i and corresponding alternatives ranking.

Alternatives	Y^+	Y^−	CCi	Rank
A1	6.9912	9.5688	0.577826	2
A2	3.5946	13.0169	0.783606	1
A3	12.2618	4.0367	0.247671	4
A4	10.0602	7.6153	0.430838	3

Table 23. Ranking of the proposed method in comparison with other methods.

Alternatives	FUZZY TOPSIS	FUZZY MOORA	FUZZY SAW
A1	2	1	2
A2	1	2	1
A3	4	4	4
A4	3	3	3

Figure 4. Ranking of different methods.

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