A FUZZY SCALE APPROACH TO THE THOR ALGORITHM

Elacoste, Ticiane Schivittez; Machado, Catia Maria dos Santos; Longaray, André Andrade; Gomes, Luiz Flavio Autran Monteiro

doi:10.1590/0101-7438.2022.042.00261547

Ticiane Schivittez Elacoste ^**Corresponding author

Federal University of Rio Grande, Graduate Program in Computer Modeling, Av. Itália, km 8, s/n, 96203-900, Rio Grande, RS, Brazil - E-mail: ticiane rg@hotmail.com

https://orcid.org/0000-0003-4359-4251

Catia Maria dos Santos Machado

Federal University of Rio Grande, Graduate Program in Computer Modeling, Av. Itália, km 8, s/n, 96203-900, Rio Grande, RS, Brazil

https://orcid.org/0000-0003-4055-6014

André Andrade Longaray

Federal University of Rio Grande, Graduate Program in Computer Modeling, Av. Itália, km 8, s/n, 96203-900, Rio Grande, RS, Brazil - E-mail: catiamachado.furg@gmail.com

https://orcid.org/0000-0002-2908-9390

Luiz Flavio Autran Monteiro Gomes

Ibmec University Center, Av. Presidente Wilson, 118, 22030-020, Rio de Janeiro, RJ, Brazil - E-mail: luiz.gomes@professores.ibmec.edu.br

https://orcid.org/0000-0002-9413-7811

*Corresponding author

Step 1	Problem identification, formulation, and analysis.
Step 2	Object setting and preferences.
Step 3	Identification of constraints and/or relaxations.
Step 4	Identification of criteria, through cognitive maps, fishbone diagrams, and brainstorming.
Step 5	Weightings of the criteria.
Step 6	Weights of the alternatives.
Step 7	Definition of the disagreement for each criterion.
Step 8	Classification of alternatives based on the definition of the limits p and q. For each criterion Cj criteria, the alternatives a and b are classified as:
	• −q ≤ \|g(a) − g(b)\| ≤ q, a and b will be considered indifferent;
	• q < \|g(a) − g(b)\| ≤ p, a will have weak preference with respect to b, otherwise b will be weakly preferred with respect to a.
	• g(a) − g(b) > p, a will have strong preference with respect to b. Where: g (.) represents the gain in the criterion C _j for the alternative (.)
Step 9	Comparison of the alternatives, following the formalism of the scenarios S1, S2, and S3 presented by equations (1), (2) and (3):
	$S_{1} : \sum_{j = 1}^{n} (w_{j} \| a Q_{j} b + a I_{j} b + a R_{j} b + b Q_{j} a + b P_{j} a)$ (1)
	$S_{2} : \sum_{j = 1}^{n} (w_{j} \| a P_{j} b + a Q_{j} b) > \sum_{j = 1}^{n} (w_{j} \| a I_{j} b + a R_{j} b + b Q_{j} a + b P_{j} a)$ (2)
	$S_{3} : \sum_{j = 1}^{n} (w_{j} \| a P_{j} b + a Q_{j} b + a I_{j} b) > \sum_{j = 1}^{n} (w_{j} \| a R_{j} b + b Q_{j} a + b P_{j} a)$ (3)
	where:
	R: non-comparability
	P: strong preference
	I: indifference
	Q: weak preference
Step 10	Choice of alternatives.
Step 11	Implementation of the alternatives.
Step 12	System feedback.

Authors	Application of fuzzy theory
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Karimi et al. (2018KARIMI M, NIKNAMFAR AH, TAGHI S & NIAKI. 2018. An application of Fuzzy-logic and grey-relational ANP- based SWOT in the ceramic and tile industry. Knowledge- Based Systems, 18: 581-594.)	Fuzzy logic is applied to ANP for the SWOT analysis of a ceramic and tile factory in Iran.
Zhou et al. (2018ZHOU Q, WONG YD, LOH HS & YUEN KF. 2018. A Fuzzy and Bayesian network CREAM model for human reliability analysis- the case of tanker shipping. Safety Science, 105: 149-157.)	They propose a quantitative human reliability analysis (HRA) model based on fuzzy logic theory, Bayesian networks, and the cognitive reliability and error analysis method (CREAM) for tanker transportation industries.
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Value	Fuzzy scale application
0.5	Class 1	(0.5, 1, 1.5)
	Class 2	(2.5, 3, 3.5)
	Class 3	(4.5, 5, 5.5)
	Class 4	(6.5, 7, 7.5)
	Class 5	(8.5, 9, 9.5)
	Class 6	(10.5, 11, 11.5)

Value	Fuzzy scale application
1.0	Class 1	(1, 1, 2)
	Class 2	(1, 2, 3)
	Class 3	(2, 3, 4)
	Class 4	(3, 4, 5)
	Class 5	(4, 5, 6)
	Class 6	(5, 6, 7)

Value	Fuzzy scale application
2.0	Class 1	(1, 1, 3)
	Class 2	(1, 3, 5)
	Class 3	(3, 5, 7)
	Class 4	(5, 7, 9)
	Class 5	(7, 9, 11)
	Class 6	(9, 11, 11)

Alternative / criterion	C1	C2	C3	C4
a1	7	4	5	3
a2	5	3	5,5	7
a3	5	4	5	2
Weights	6	5	4	2

Alternative / criterion	C1	C2	C3	C4
a1	7,007932	4,013865	5,011099	3,018462
a2	5,011099	3,018462	5,510092	7,007932
a3	5,011099	4,013865	5,011099	2,027588
Weights	6,00952	5,011099	4,13865	2,02588

Veto	THOR	THOR + Fuzzy Scale
Disagreement	4	4,013865
p	0,9	0,959745
q	0,9	0,959745

S1	a1	a2	a3	Score
a1	0	0,5	0,5	1
a2	0,5	0	0,5	1
a3	0,5	0,5	0	1

S2	a1	a2	a3	Score
a1	0	0,5	0,5	1
a2	0,5	0	0,5	1
a3	0,5	0,5	0	1

S3	a1	a2	a3	Score
a1	0	0,5	1	1,5
a2	0,5	0	0,5	1
a3	0,52	0,5	0	1,02

S1	a1	a2	a3	Score
a1	0	0,5	0,5	1
a2	0,5	0	0,5	1
a3	0,5	0,5	0	1

S2	a1	a2	a3	Score
a1	0	0,5	0,5	1
a2	0,5	0	0,5	1
a3	0,5	0,5	0	1

S3	a1	a2	a3	Score
a1	0	0,5	1	1,5
a2	0,5	0	0,5	1
a3	0,52895	0,5	0	1,02895

[1] *Corresponding author

Brasil

Brasil

A FUZZY SCALE APPROACH TO THE THOR ALGORITHM

ABSTRACT