Evaluation of Investment Opportunities With Interval-Valued Fuzzy Topsis Method

Naiyer Mohammadi Lanbaran; Ercan Celik; Muhammed Yiğider

Otwarty dostęp

Evaluation of Investment Opportunities With Interval-Valued Fuzzy Topsis Method

Naiyer Mohammadi Lanbaran

Ercan Celik

oraz

Muhammed Yiğider

| 10 kwi 2020

Applied Mathematics and Nonlinear Sciences

Tom 5 (2020): Zeszyt 1 (January 2020)

O artykule

Poprzedni artykuł

Następny artykuł

Zacytuj

Udostępnij

Data publikacji: 10 kwi 2020

Zakres stron: 461 - 474

Otrzymano: 29 maj 2019

Przyjęty: 13 cze 2019

DOI: https://doi.org/10.2478/amns.2020.1.00044

Słowa kluczowe
Multi-Criteria decision making, Fuzzy logic theory, Interval-Valued Fuzzy TOPSIS Analysis, Euclid distance, Shannon Entropy

© 2020 Naiyer Mohammadi Lanbaran et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

j.amns.2020.1.00044.tab.013.w2aab3b7e2756b1b6b1ab1b3b6b3b6Aa

10	4.83	5.5	10	4.83	10	9.83	10	10	5.5	9.83	5.5	10
$c_{1}^{+}$ c_1^ +	$a_{2}^{-}$ a_2^ -	$a_{3}^{-}$ a_3^ -	$C_{4}^{+}$ C_4^ +	$a_{5}^{-}$ a_5^ -	$C_{6}^{+}$ C_6^ +	$C_{7}^{+}$ C_7^ +	$C_{8}^{+}$ C_8^ +	$C_{9}^{+}$ C_9^ +	$a_{10}^{-}$ a_{10}^ -	$C_{11}^{+}$ C_{11}^ +	$a_{12}^{-}$ a_{12}^ -	$C_{13}^{+}$ C_{13}^ +

Desired options for investment

Code	Title
A1	Project 1
A2	Project 2
A3	Project 3
A4	Project 4

Definition of linguistic variables for the importance of each criterion

Very low (VL)	[(0,0);0;(0.1,0.15)]
Low (L)	[(0,0.05);0.1;(0.25,0.35)]
Medium low (ML)	[(0,0.15);0.3;(0.45,0.55)]
Medium (M)	[(0.25,0.35),0.5,(0.65,0.75)]
Medium high (MH)	[(0.45,0.55),0.7,(0,8,0.95)]
High (H)	[(0.55,0.75),0.9,(0.95,1)]
Very high (VH)	[(0.85,0.95),1,(1,1)]

Decision matrix according to linguistic variables

	C11	C12	C13	C14	C15	C21	C22	C23	C24	C25	C26	C31	C32
A1	MG	P	MP	G	MP	MG	MG	M	M	MP	M	MP	MG
A2	VG	VP	P	MG	VP	G	G	G	G	P	MG	P	VG
A3	P	M	M	MP	P	M	MP	P	VP	MP	MP	M	M
A4	M	MP	MP	MG	P	MG	M	P	MG	MP	MG	MP	M

Interval fuzzy value of linguistic variables

[(3.83,4.83);6.33;(7.5,8.83)]	VP
[(4.5,5.5);6.67;(7.67,8.33)]	P
[(5.17,6.17);7.33;(8.17,9)]	MP
[(6.17,7.5);8.67;(,9.179.83)]	M
[(7.17,8.17);9;(9.33,9.83)]	MG
[(7.5,8.83);9.67;(9.83,10)]	G
[(8.5,9.5);10;(10,10)]	VG

Normalize Decision Matrix

	C11	C12	C13	C14	C15

A1	[(0.72,0.82);0.9;(0.93,0.98)]	[(0.88,1.07);0.72;(0.58,0.63)]	[(0.89,1.06);0.75;(0.61,0.67)]	[(0.75,0.88);0.97;(0.98,1)]	[(0.78,0.93);0.66;(0.54,0.59)]
A2	[(0.85,0.95);1;(1,1)]	[(1,1.3);0.76;(0.55,0.64)]	[(1,1.22);0.82;(0.62,0.72)]	[(0.72,0.82);0.9;(0.93,0.98)]	[(1,1.3);0.76;(0.55,0.64)]
A3	[(0.45,0.55);0.67;(0.77,0.83)]	[(0.64,0.78);0.56;(0.49,0.53)]	[(0.73,0.89);0.63;(0.56,0.6)]	[(0.52,0.62);0.7;(0.82,0.9)]	[(0.88,1.07);0.72;(0.58,0.63)]
A4	[(0.62,0.75);0.73;(0.82,0.9)]	[(0.78,0.93);0.66;(0.54,0.59)]	[(0.89,1.06);0.75;(0.61,0.67)]	[(0.72,0.82);0.9;(0.93,0.98)]	[(0.88,1.07);0.72;(0.58,0.63)]

	C21	C22	C23	C24	C25

A1	[(0.72,0.82);0.9;(0.93,0.98)]	[(0.73,0.83);0.92;(0.95,0.95)]	[(0.62,0.75);0.73;(0.82,0.9)]	[(0.62,0.75);0.73;(0.82,0.9)]	[(0.89,1.06);0.75;(0.61,0.67)]
A2	[(0.85,0.95);1;(1,1)]	[(0.63,0.76);0.88;(0.93,1)]	[(0.85,0.95);1;(1,1)]	[(0.75,0.88);0.97;(0.98,1)]	[(1,1.22);0.82;(0.62,0.72)]
A3	[(0.62,0.75);0.73;(0.82,0.9)]	[(0.53,0.63);0.75;(0.83,0.92)]	[(0.45,0.55);0.67;(0.77,0.83)]	[(0.38,0.48);0.63;(0.75,0.88)]	[(0.89,1.06);0.75;(0.61,0.67)]
A4	[(0.72,0.82);0.9;(0.93,0.98)]	[(0.63,0.76);0.88;(0.93,1)]	[(0.45,0.55);0.67;(0.77,0.83)]	[(0.72,0.82);0.9;(0.93,0.98)]	[(0.89,1.06);0.75;(0.61,0.67)]

	C26	C31	C32

A1	[(0.63,0.76);0.88;(0.93,1)]	[(0.89,1.06);0.75;(0.61,0.67)]	[(0.72,0.82);0.9;(0.93,0.98)]
A2	[(0.73,0.83);0.92;(0.95,0.95)]	[(1,1.22);0.82;(0.62,0.72)]	[(0.85,0.95);1;(1,1)]
A3	[(0.53,0.63);0.75;(0.83,0.92)]	[(0.73,0.89);0.63;(0.56,0.6)]	[(0.62,0.75);0.73;(0.82,0.9)]
A4	[(0.73,0.83);0.92;(0.95,0.95)]	[(0.89,1.06);0.75;(0.61,0.67)]	[(0.62,0.75);0.73;(0.82,0.9)]

The final ranking of Options

	RC1	RC2	RC*	RANK
A1	0.428572	0.353983	0.391278	2
A2	0.462286	0.602653	0.532469	1
A3	0.373306	0.30307	0.338188	4
A4	0.415433	0.357171	0.386302	3

Weight values of criteria

[(0.85,0.95);1;(1,1)]	VH
[(0.55,0.75);0.9;(0.95,1)]	H
[(0.45,0.55);0.7;(0.8,0.95)]	MH
[(0.25,0.35);0.5;(0.65,0.75)]	M
[(0,0.15);0.3;(0.45,0.55)]	ML
[(0,0.05);0.1;(0.25,0.35)]	L
[(0,0);0;(0.1,0.15)]	VL

Distance of alternatives from ideal alternatives

A1	$D_{11}^{+}$ D_{11}^ +	$D_{12}^{+}$ D_{12}^ +	$D_{11}^{-}$ D_{11}^ -	$D_{12}^{-}$ D_{12}^ -	A2	$D_{11}^{+}$ D_{11}^ +	$D_{12}^{+}$ D_{12}^ +	$D_{11}^{-}$ D_{11}^ -	$D_{12}^{-}$ D_{12}^ -
C11	0.234521	0.14	0.826035	0.890468	C11	0.161658	0.057735	0.916224	0.967815
C12	0.443471	0.31459	0.564329	0.697472	C12	0.422414	0.278328	0.587452	0.781537
C13	0.424264	0.288039	0.588473	0.719097	C13	0.382187	0.225389	0.631981	0.798415
C14	0.892562	0.851293	0.153406	0.209921	C14	0.898332	0.853483	0.142595	0.204369
C15	0.585947	0.491155	0.415933	0.511631	C15	0.528205	0.3879	0.475044	0.624873
C21	0.898146	0.851293	0.142595	0.209921	C21	0.889288	0.843603	0.155456	0.212132
C22	0.783156	0.712928	0.296254	0.312463	C22	0.792465	0.716984	0.28519	0.356931
C23	0.665833	0.591608	0.384448	0.471487	C23	0.576368	0.503786	0.48874	0.554196
C24	0.816497	0.742092	0.248529	0.321714	C24	0.778396	0.698451	0.304248	0.366742
C25	0.791623	0.776745	0.034641	0.057735	C25	0.980408	0.964728	0.034641	0.063509
C26	0.627163	0.549363	0.439394	0.525674	C26	0.607838	0.541541	0.457675	0.516333
C31	0.67082	0.585064	0.342929	0.420833	C31	0.485833	0.543016	0.665357	0.463537
C32	0.789515	0.710868	0.288271	0.355387	C32	0.772981	0.690917	0.31225	0.37063
Sum	8.623517	7.605039	4.725234	5.703802	Sum	8.276371	7.305862	5.456853	6.281021

Weight of criterias

C11	VH	C21	L	C31	M
C12	H	C22	ML	C32	ML
C13	H	C23	M
C14	L	C24	ML
C15	MH	C25	VL
		C26	M

Weighted normalize fuzzy decision matrix

	C11	C12	C13	C14	C15

A1	[(0.61,0.78);0.9;(0.93,0.98)]	[(0.48,0.80);0.65;(0.55,0.63)]	[(0.49,0.8);0.68;(0.58,0.67)]	[(0,0.04);0.09;(0.25,0.35)]	[(0.35,0.51);0.46;(0.43,0.56)]
A2	[(0.72,0.9);1;(1,1)]	[(0.55,0.98);0.68;(0.52,0.64)]	[(0.55,0.92);0.74;(0.59,0.72)]	[(0,0.04);0.09;(0.23,0.34)]	[(0.45,0.72);0.53;(0.44,0.61)]
A3	[(0.38,0.52);0.67;(0.77,0.83)]	[(0.35,0.59);0.50;(0.47,0.53)]	[(0.40,0.67);0.57;(0.53,0.6)]	[(0,0.03);0.07;(0.21,0.32)]	[(0.4,0.6);0.5;(0.46,0.6)]
A4	[(0.53,0.71);0.73;(0.82,0.9)]	[(0.43,0.70);0.59;(0.51,0.59)]	[(0.49,0.8);0.68;(0.58,0.67)]	[(0,0.04);0.09;(0.23,0.34)]	[(0.4,0.6);0.5;(0.46,0.6)]

	C21	C22	C23	C24	C25

A1	[(0,0.04);0.09;(0.23,0.35)]	[(0,0.12);0.28;(0.43,0.52)]	[(0.16,0.26);0.37;(0.53,0.68)]	[(0,0.11);0.22;(0.37,0.5)]	[(0,0);0;(0.06,0.1)]
A2	[(0,0.05);0.1;(0.25,0.35)]	[(0,0.11);0.26;(0.42,0.55)]	[(0.21,0.33);0.5;(0.65,0.75)]	[(0,0.13);0.29;(0.44,0.55)]	[(0,0);0;(0.06,0.11)]
A3	[(0,0.04);0.07;(0.21,0.32)]	[(0,0.08);0.23;(0.37,0.51)]	[(0.11,0.19);0.34;(0.5,0.62)]	[(0,0.07);0.19;(0.34,0.48)]	[(0,0);0;(0.06,0.1)]
A4	[(0,0.04);0.09;(0.23,0.34)]	[(0,0.11);0.26;(0.42,0.55)]	[(0.11,0.19);0.34;(0.5,0.62)]	[(0,0.12);0.27;(0.42,0.54)]	[(0,0);0;(0.06,0.1)]

	C26	C31	C32

A1	[(0.16,0.27);0.44;(0.6,0.75)]	[(0.22,0.37);0.38;(0.4,0.5)]	[(0,0.12);0.27;(0.42,0.54)]
A2	[(0.18,0.29);0.46;(0.62,0.71)]	[(1,0.43);0.41;(0.4,0.54)]	[(0,0.14);0.3;(0.45,0.55)]
A3	[(0.13,0.22);0.38;(0.54,0.69)]	[(0.18,0.31);0.32;(0.36,0.45)]	[(0,0.11);0.22;(0.37,0.5)]
A4	[(0.18,0.29);0.46;(0.62,0.71)]	[(0.22,0.37);0.38;(0.4,0.5)]	[(0,0.11);0.22;(0.37,0.5)]

Interval valued fuzzy decision matrix

	C11	C12	C13	C14	C15
A1	[(7.17,8.17);9;(9.33,9.83)]	[(4.5,5.5);6.67;(7.67,8.33)]	[(5.17,6.17);7.33;(8.17,9)]	[(7.5,8.83);9.67;(9.83,10)]	[(5.17,6.17);7.33;(8.17,9)]
A2	[(8.5,9.5);10;(10,10)]	[(3.83,4.83);6.33;(7.5,8.83)]	[(4.5,5.5);6.67;(7.67,8.33)]	[(7.17,8.17);9;(9.33,9.83)]	[(3.83,4.83);6.33;(7.5,8.83)]
A3	[(4.5,5.5);6.67;(7.67,8.33)]	[(6.17,7.5);8.67;(,9.179.83)]	[(6.17,7.5);8.67;(,9.179.83)]	[(5.17,6.17);7.33;(8.17,9)]	[(4.5,5.5);6.67;(7.67,8.33)]
A4	[(6.17,7.5);8.67;(,9.179.83)]	[(5.17,6.17);7.33;(8.17,9)]	[(5.17,6.17);7.33;(8.17,9)]	[(7.17,8.17);9;(9.33,9.83)]	[(4.5,5.5);6.67;(7.67,8.33)]
	C21	C22	C23	C24	C25
A1	[(7.17,8.17);9;(9.33,9.83)]	[(7.17,8.17);9;(9.33,9.83)]	[(6.17,7.5);8.67;(,9.179.83)]	[(6.17,7.5);8.67;(,9.179.83)]	[(5.17,6.17);7.33;(8.17,9)]
A2	[(8.5,9.5);10;(10,10)]	[(6.17,7.5);8.67;(,9.179.83)]	[(8.5,9.5);10;(10,10)]	[(7.5,8.83);9.67;(9.83,10)]	[(4.5,5.5);6.67;(7.67,8.33)]
A3	[(6.17,7.5);8.67;(,9.179.83)]	[(5.17,6.17);7.33;(8.17,9)]	[(4.5,5.5);6.67;(7.67,8.33)]	[(3.83,4.83);6.33;(7.5,8.83)]	[(5.17,6.17);7.33;(8.17,9)]
A4	[(7.17,8.17);9;(9.33,9.83)]	[(6.17,7.5);8.67;(,9.179.83)]	[(4.5,5.5);6.67;(7.67,8.33)]	[(7.17,8.17);9;(9.33,9.83)]	[(5.17,6.17);7.33;(8.17,9)]
	C26	C31	C32
A1	[(6.17,7.5);8.67;(,9.179.83)]	[(5.17,6.17);7.33;(8.17,9)]	[(7.17,8.17);9;(9.33,9.83)]
A2	[(7.17,8.17);9;(9.33,9.83)]	[(4.5,5.5);6.67;(7.67,8.33)]	[(8.5,9.5);10;(10,10)]
A3	[(5.17,6.17);7.33;(8.17,9)]	[(6.17,7.5);8.67;(,9.179.83)]	[(6.17,7.5);8.67;(,9.179.83)]
A4	[(7.17,8.17);9;(9.33,9.83)]	[(5.17,6.17);7.33;(8.17,9)]	[(6.17,7.5);8.67;(,9.179.83)]

The hierarchy of criteria and sub-criteria

	C1-Industrial efficiency		C2-Compliance withcompany’sstrategy		C3-Industrial experience
C11	Increasing demand for industrial products (P)	C21	Ability to attract foreign investors (P)	C31	Receivables in the subordinate (C)
C12	Alternative Products (C)	C22	Entrepreneurship (P)	C32	Implementation process of industrial projects (P)
C13	government intervention in product pricing (P)	C23	Technology transfer Capacity (P)
C14	Current value of the industry on the exchange (P)	C24	Ability to reduce dependency on foreign products (P)
C15	Average process for the delivery of industrial projects (C)	C25	Amount of dependency on foreign raw material (C)
		C26	Exportamount (P)

Definition of linguistic variables for the ratings

Very Poor (VP)	[(0,0);0;(1,1.5)]
Poor (P)	[(0,0.5);1;(2.5,3.5)]
Moderately Poor (MP)	[(0,1.5);3;(4.5,5.5)]
Fair (F)	[(2.5,3.5),5,(6.5,7.5)]
Moderately Good (MG)	[(4.5,5.5),7,(8.9.5)]
Good (G)	[(5.5,7.5),9,(9.5,10)]
Very Good (VG)	[(8.5,9.5),10,(10,10)]

eISSN:: 2444-8656
Język:: Angielski

Częstotliwość wydawania:: Volume Open
Dziedziny czasopisma:: Life Sciences, other, Mathematics, Applied Mathematics, General Mathematics, Physics

Kanał RSS czasopisma

Evaluation of Investment Opportunities With Interval-Valued Fuzzy Topsis Method

Data publikacji: 10 kwi 2020

Zakres stron: 461 - 474

Otrzymano: 29 maj 2019

Przyjęty: 13 cze 2019

DOI: https://doi.org/10.2478/amns.2020.1.00044

Słowa kluczowe
Multi-Criteria decision making, Fuzzy logic theory, Interval-Valued Fuzzy TOPSIS Analysis, Euclid distance, Shannon Entropy

© 2020 Naiyer Mohammadi Lanbaran et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

Fig. 2

j.amns.2020.1.00044.tab.013.w2aab3b7e2756b1b6b1ab1b3b6b3b6Aa

Desired options for investment

Definition of linguistic variables for the importance of each criterion

Decision matrix according to linguistic variables

Interval fuzzy value of linguistic variables

Normalize Decision Matrix

The final ranking of Options

Weight values of criteria

Distance of alternatives from ideal alternatives

Weight of criterias

Weighted normalize fuzzy decision matrix

Interval valued fuzzy decision matrix

The hierarchy of criteria and sub-criteria

Definition of linguistic variables for the ratings

	C11	C12	C13	C14	C15	C21	C22	C23	C24	C25	C26	C31	C32
A1	MG	P	MP	G	MP	MG	MG	M	M	MP	M	MP	MG
A2	VG	VP	P	MG	VP	G	G	G	G	P	MG	P	VG
A3	P	M	M	MP	P	M	MP	P	VP	MP	MP	M	M
A4	M	MP	MP	MG	P	MG	M	P	MG	MP	MG	MP	M

	C11	C12	C13	C14	C15	C21	C22	C23	C24	C25	C26	C31	C32
A1	MG	P	MP	G	MP	MG	MG	M	M	MP	M	MP	MG
A2	VG	VP	P	MG	VP	G	G	G	G	P	MG	P	VG
A3	P	M	M	MP	P	M	MP	P	VP	MP	MP	M	M
A4	M	MP	MP	MG	P	MG	M	P	MG	MP	MG	MP	M

Evaluation of Investment Opportunities With Interval-Valued Fuzzy Topsis Method

Data publikacji: 10 kwi 2020

Zakres stron: 461 - 474

Otrzymano: 29 maj 2019

Przyjęty: 13 cze 2019

DOI: https://doi.org/10.2478/amns.2020.1.00044

Słowa kluczoweMulti-Criteria decision making, Fuzzy logic theory, Interval-Valued Fuzzy TOPSIS Analysis, Euclid distance, Shannon Entropy

© 2020 Naiyer Mohammadi Lanbaran et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

Fig. 2

j.amns.2020.1.00044.tab.013.w2aab3b7e2756b1b6b1ab1b3b6b3b6Aa

Desired options for investment

Definition of linguistic variables for the importance of each criterion

Decision matrix according to linguistic variables

Interval fuzzy value of linguistic variables

Normalize Decision Matrix

The final ranking of Options

Weight values of criteria

Distance of alternatives from ideal alternatives

Weight of criterias

Weighted normalize fuzzy decision matrix

Interval valued fuzzy decision matrix

The hierarchy of criteria and sub-criteria

Definition of linguistic variables for the ratings

Słowa kluczowe
Multi-Criteria decision making, Fuzzy logic theory, Interval-Valued Fuzzy TOPSIS Analysis, Euclid distance, Shannon Entropy

	C11	C12	C13	C14	C15	C21	C22	C23	C24	C25	C26	C31	C32
A1	MG	P	MP	G	MP	MG	MG	M	M	MP	M	MP	MG
A2	VG	VP	P	MG	VP	G	G	G	G	P	MG	P	VG
A3	P	M	M	MP	P	M	MP	P	VP	MP	MP	M	M
A4	M	MP	MP	MG	P	MG	M	P	MG	MP	MG	MP	M