Aggregation of partial T-indistinguishability operators: an application to image recognition

Elif Güner; Elif Güner

doi:10.3934/math.2026856

AIMS Mathematics

2026, Volume 11, Issue 7: 21091-21112. doi: 10.3934/math.2026856

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Research article

Aggregation of partial T-indistinguishability operators: an application to image recognition

Elif Güner ^,

Department of Mathematics, Kocaeli University, Umuttepe Campus, Kocaeli 41380, Turkey

Received: 09 May 2026 Revised: 18 June 2026 Accepted: 02 July 2026 Published: 16 July 2026
MSC : 03B52, 47S40

In this paper, we introduce the notion of residual domination, which is a stronger version of the usual concept of domination. Then, we show how a family of partial T-indistinguishability operators can be aggregated into one operator using residual domination. This new idea allows the use of partial T-indistinguishability operators instead of T-indistinguishability operators, thus providing a wider variety of operators when we need to apply them to real-life problems. Additionally, we present a practical application to the image recognition problem by using T-indistinguishability operators and partial T-indistinguishability operators. Finally, we give an illustrative example to explain the proposed technique.
- t-norm,
- residuum operator,
- aggregation operator,
- T-indistinguishability operator,
- similarity,
- image recognition
Citation: Elif Güner. Aggregation of partial T-indistinguishability operators: an application to image recognition[J]. AIMS Mathematics, 2026, 11(7): 21091-21112. doi: 10.3934/math.2026856

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Abstract

In this paper, we introduce the notion of residual domination, which is a stronger version of the usual concept of domination. Then, we show how a family of partial T-indistinguishability operators can be aggregated into one operator using residual domination. This new idea allows the use of partial T-indistinguishability operators instead of T-indistinguishability operators, thus providing a wider variety of operators when we need to apply them to real-life problems. Additionally, we present a practical application to the image recognition problem by using T-indistinguishability operators and partial T-indistinguishability operators. Finally, we give an illustrative example to explain the proposed technique.

References

[1]	E. Trillas, Assaig sobre les relacions d'indistingibilitat, Primer Congrés Catalá de Lógica Matemática, 1982, 51–59.
[2]	T. Calvo Sánchez, P. Fuster-Parra, O. Valero, On the problem of aggregation of partial T-indistinguishability operators, IPMU 2018, 853 (2018), 207–218. https://doi.org/10.1007/978-3-319-91473-2_18 doi: 10.1007/978-3-319-91473-2_18
[3]	J. J. Miñana, O. Valero, Aggregation of indistinguishability fuzzy relations revisited, Mathematics, 9 (2021), 1441. https://doi.org/10.3390/math9121441 doi: 10.3390/math9121441
[4]	J. Recasens, Indistinguishability operators and approximate reasoning, Berlin: Springer, 2010. https://doi.org/10.1007/978-3-642-16222-0_11
[5]	J. J. Minãna, O. Valero, On indistinguishability operators, fuzzy metrics and modular metrics, Axioms, 6 (2017), 34. https://doi.org/10.3390/axioms6040034 doi: 10.3390/axioms6040034
[6]	P. Fuster-Parra, J. Martín, J. Recasens, O. Valero, T-equivalences: the metric behavior revisited, Mathematics, 8 (2020), 495. https://doi.org/10.3390/math8040495 doi: 10.3390/math8040495
[7]	M. R. Khan, K. Ullah, W. Ahmad, F. Pervaiz, Prioritizing ventilator machines in emergency scenarios using multi-criteria decision-making with circular intuitionistic fuzzy set and Dombi operations, Spectr. Decis. Mak. Appl., 2024, 1–19. https://doi.org/10.31181/sdmap41202762 doi: 10.31181/sdmap41202762
[8]	S. Petchimuthu, F. Banu M, C. Mahendiran, T. Premala, Power and energy transformation: multi-criteria decision-making utilizing complex q-rung picture fuzzy generalized power prioritized Yager operators, Spectr. Oper. Res., 2 (2025), 260–299. https://doi.org/10.31181/sor21202525 doi: 10.31181/sor21202525
[9]	S. Petchimuthu, B. Palpandi, K. Rajakumar, F. Banu M, Sustainable urban development: q-rung orthopair fuzzy MCDM with generalized power prioritized Yager aggregation, Spectr. Oper. Res., 3 (2026), 275–309. https://doi.org/10.31181/sor31202649 doi: 10.31181/sor31202649
[10]	M. Elkano, J. A. Sanz, M. Galar, B. Pekala, U. Bentkowska, H. Bustince, Composition of interval-valued fuzzy relations using aggregation functions, Inf. Sci., 369 (2016), 690–703. https://doi.org/10.1016/j.ins.2016.07.048 doi: 10.1016/j.ins.2016.07.048
[11]	Z. Xu, Linguistic aggregation operators: an overview, Berlin: Springer, 2008. https://doi.org/10.1007/978-3-540-73723-0_9
[12]	V. Peneva, I. Popchev, Aggregation of fuzzy preference relations to multicriteria decision making, Fuzzy Optim. Decis. Mak., 6 (2007), 351–365. https://doi.org/10.1007/s10700-007-9018-6 doi: 10.1007/s10700-007-9018-6
[13]	M. M. Bibiloni-Femenias, J. Guerrero, J. J. Miñana, O. Valero, Indistinguishability operators via Yager t-norms and their applications to swarm multi-agent task allocation, Mathematics, 9 (2021), 190. https://doi.org/10.3390/math9020190 doi: 10.3390/math9020190
[14]	J. Guerrero, J. J. Miñana, O. Valero, G. Oliver, Indistinguishability operators applied to task allocation problems in multi-agent systems, Appl. Sci., 7 (2017), 963. https://doi.org/10.3390/app7100963 doi: 10.3390/app7100963
[15]	A. Pradera, E. Trillas, E. Castiñeira, On the aggregation of some classes of fuzzy relations, Berlin: Springer, 2002. https://doi.org/10.1007/978-3-7908-1796-6_10
[16]	S. Saminger, R. Mesiar, U. Bodenhofer, Domination of aggregation operators and preservation of transitivity, Int. J. Uncertain. Fuzz., 10 (2002) 11–35. https://doi.org/10.1142/S0218488502001806 doi: 10.1142/S0218488502001806
[17]	U. Höhle, M-valued sets and sheaves over integral commutative CL-monoids, Dordrecht: Springer Netherlands, 1992. https://doi.org/10.1007/978-94-011-2616-8_3
[18]	E. P. Klement, R. Mesiar, E. Pap, Triangular norms, Dordrecht: Springer Netherlands, 2000. https://doi.org/10.1007/978-94-015-9540-7
[19]	R. Mesiar, E. Pap, Aggregation of infinite sequences, Inf. Sci., 178 (2008), 3557–3564. https://doi.org/10.1016/j.ins.2008.05.020 doi: 10.1016/j.ins.2008.05.020
[20]	H. Aygün, E. Güner, J. J. Miñana, O. Valero, Fuzzy partial metric spaces and fixed point theorems, Mathematics, 10 (2022), 3092. https://doi.org/10.3390/math10173092 doi: 10.3390/math10173092
[21]	M. J. Swain, D. H. Ballard, Color indexing, Int. J. Comput. Vis., 7 (1991), 11–32. https://doi.org/10.1007/BF00130487 doi: 10.1007/BF00130487

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