A 2-Tuple Linguistic Dynamic OWAWA Aggregation Operator and its application to multi-Attribute decision-making

Yeleny Zulueta-Véliz; Carlos Rafael Rodríguez Rodríguez; Aylin Estrada Velazco

doi:10.14313/jamris-2025-032

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A 2-Tuple Linguistic Dynamic OWAWA Aggregation Operator and its application to multi-Attribute decision-making

Journal of Automation, Mobile Robotics and Intelligent Systems

Volume 19 (2025): Issue 4 (December 2025)

By: Yeleny Zulueta-Véliz , Carlos Rafael Rodríguez Rodríguez and Aylin Estrada Velazco

Open Access

|Dec 2025

Figures & Tables

Non-dynamic 2-tuple linguistic evaluation of alternatives

Table 1.

x_ijk linguistic values for period t₁

e_k	a_i	c₁	c₂	c₃	c₄
e₁	a₁	VP	P	G	M
	a₂	M	EP	M	VP
	a₃	EP	VP	VG	G
	a₄	M	VG	VG	M
e₂	a₁	G	P	M	G
	a₂	P	VP	P	VP
	a₃	EP	EP	EG	P
	a₄	VG	G	M	G
e₃	a₁	VP	VG	VG	P
	a₂	^G	VP	VP	^P
	a₃	VP	M	G	G
	a₄	G	G	M	P

Table 2.

x_ijk linguistic values for period t₂

e_k	a_i	c₁	c₂	c₃	c₄
e₁	a₁	M	G	VG	M
	a₂	P	VG	G	G
	a₃	M	G	VG	G
	a₄	G	VG	G	M
e₂	a₁	G	G	M	G
	a₂	G	M	M	G
	a₃	G	VG	EG	P
	a₄	P	G	P	VG
e₃	a₁	M	M	EG	EG
	a₂	G	M	VP	VG
	a₃	P	G	VG	G
	a₄	M	G	M	M

Table 3.

x_ijk linguistic values for period t₃

e_k	a_i	c₁	c₂	c₃	c₄
e₁	a₁	VP	V	G	M
	a₂	G	G	M	G
	a₃	VP	P	V	G
	a₄	M	G	P	VP
e₂	a₁	P	P	E	G
	a₂	VG	V	G	VG
	a₃	M	V	E	P
	a₄	P	M	M	G
e₃	a₁	VP	V	E	EG
	a₂	G	V	M	VG
	a₃	VP	M	G	G
	a₄	G	P	P	M

Table 4.

${\bar{x}}_{i}$ non-dynamic 2-tuple linguistic evaluation of alternatives for each period.

a_i	t₁	t₂	t₃
a₁	(s₃,0)	(s₄,0)	(s₄,–0.25)
a₂	(s₂,–0.25)	(s₄,–0.50)	(s₄, 0.25)
a₃	(s₃,–0.50)	(s₄,0)	(s₃,0)
a₄	(s₄,–0.25)	(s₄,–0.50)	(s₃,–0.25)

Table 5.

$\overset{⌣}{X} (t_{λ})$ outputs for different ℓ = 0 values in the 2TDOWAWA_V,W

ℓ	a₁	a₂	a₃	a₄
0	(s₄, –.25)	(s₄, –.22)	(s₃, .25)	(s₃,.08)
0.1	(s₄, –.25)	(s₄, –.25)	(s₃, .27)	(s₃, .12)
0.2	(s₄, –.25)	(s₄, –.27)	(s₃, .28)	(s₃, .16)
0.5	(s₄,–.26)	(s₄, –.35)	(s₃,.33)	(s₃.28)
0.8	(s₄,–.27)	(s₄,–.42)	(s₃,.37)	(s₃, .40)
0.9	(s₄,–.27)	(s₄, –.45)	(s₃, .39)	(s₃, .44)
1.0	(s₄,–.27)	(s₄, –.47)	(s₃,.40)	(s₃, .48)
2TDWA	(s₄,–.25)	(s₄,–.22)	(s₃, .25)	(s₃, .08)
2TDOWA	(s₄,-^7)	(s₄, –.47)	(s₃,.40)	(s₃, .48)
2TDWG [23]	(s₄,–.26)	(s₄, –.33)	(s₃, .21)	(s₃,.05)
2TDWHA [23]	(s₄,–.27)	(s₄, –.48)	(s₃,.17)	(s₃,.03)

Table 6.

Dynamic aggregation operators, order and solution obtained

ℓ	Order
0	a₂ ≺ a₁ ≺ a₃ ≺ a₄
0.1	a₁ = a₂ ≺ a₃ ≺ a₄
0.2	a₁ ≺ a₂ ≺ a₃ ≺ a₄
0.5	a₁ ≺ a₂ ≺ a₃ ≺ a₄
0.8	a₁ ≺ a₂ ≺ a₄ ≺ a₃
0.9	a₁ ≺ a₂ ≺ a₄ ≺ a₃
1.0	a₁ ≺ a₂ ≺ a₄ ≺ a₃
2TDWA	a₂ ≺ a₁ ≺ a₃ ≺ a₄
2TDOWA	a₁ ≺ a₂ ≺ a₄ ≺ a₃
2TDWG [23]	a₁ ≺ a₂ ≺ a₃ ≺ a₄
2TDWHA [23]	a₁ ≺ a₂ ≺ a₃ ≺ a₄

Dynamic 2-tuple linguistic evaluation of alternatives using different ℓ values

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DOI: https://doi.org/10.14313/jamris-2025-032 | Journal eISSN: 2080-2145 | Journal ISSN: 1897-8649

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Language: English

Page range: 18 - 25

Submitted on: Apr 14, 2024

Accepted on: Sep 17, 2024

Published on: Dec 24, 2025

Published by: Łukasiewicz Research Network – Industrial Research Institute for Automation and Measurements PIAP

In partnership with: Paradigm Publishing Services

Publication frequency: 4 issues per year

Keywords:

linguistic decision-making,

dynamic decision-making,

2-tuple linguistic model,

aggregation operator

Related subjects:

Computer sciences,

Artificial intelligence,

Engineering,

Electrical engineering,

Control engineering, metrology and testing,

Mechanical engineering,

Fundamentals of mechanical engineering

© 2025 Yeleny Zulueta-Véliz, Carlos Rafael Rodríguez Rodríguez, Aylin Estrada Velazco, published by Łukasiewicz Research Network – Industrial Research Institute for Automation and Measurements PIAP
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 19 (2025): Issue 4 (December 2025)

A 2-Tuple Linguistic Dynamic OWAWA Aggregation Operator and its application to multi-Attribute decision-making

Figures & Tables

Figure 1.

Figure 2.

Table 1.

Table 2.

Table 3.

Table 4.

Table 5.

Table 6.

Figure 3.

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