Bipolar Ordered Weighted Quasi-Averages and Induced Bipolar Ordered Weighted Averages: BIGOWA and IBIOWA operators

Document Type : Research Paper

Authors

1 Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, Sk-810 05 Bratislava, Slovakia

2 Faculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovića 6, 21000 Novi Sad, Serbia

3 Department of Mathematics and Informatics Faculty of Sciences university of Novi Sad

Abstract

A generalization of bipolar OWA operators, bipolar ordered weighted quasi-averages, based on the bipolar Choquet g-integrals, so called g-BIOWA operators are introduced and investigated. A generalization of induced OWA operators considering non-negative inputs and order-inducing variables, induced bipolar ordered weighted averages are introduced considering real inputs and order-inducing vectors. Their main properties are considered and some illustrative examples are presented.

Keywords

Main Subjects


[1] J. Abbas, R. Mesiar, R. Halaˇs, Bipolar decomposition integrals, International Journal of Approximate Reasoning,
183 (2025), 109439. https://doi.org/10.1016/j.ijar.2025.109439
[2] X. Y. Bai, Y. L. Yang, Fuzzy decision tree algorithm based on feature value’s class contribution level, Iranian Journal
of Fuzzy Systems, 19(4) (2022), 73-88. https://doi.org/10.22111/ijfs.2022.7088
[3] G. Beliakov, Learning weights in the generalized OWA operators, Fuzzy Optimization and Decision Making, 4 (2005),
119-130. https://doi.org/10.1007/s10700-004-5868-3
[4] J. Chachi, A. Kazemifard, A novel extended approach to evaluate criteria weights in MADM problems in fuzzy
framework, Iranian Journal of Fuzzy Systems, 21(4) (2024), 101-122. https://doi.org/10.22111/ijfs.2024.
48112.8479
[5] G. Choquet,Theory of capacities, Annales de l’institut Fourier, (Grenoble), 5 (1954), 131-292.
[6] D. Denneberg, Non-additive measure and integral, Kluwer Academic Publishers, Dordrecht, 1994.
[7] M. Grabisch, Fuzzy integral in multicriteria decision making, Fuzzy Sets and Systems, 69(3) (1995), 279-298.https://doi.org/10.1016/0165-0114(94)00174-6
[8] M. Grabisch, Ch. Labreuche, Bi-capacities I: Definition, M¨obius transform and intersection, Fuzzy Sets and Systems,
151 (2005), 211-236. https://doi.org/10.1016/j.fss.2004.08.012
[9] M. Grabisch, Ch. Labreuche, Bi-capacities II: Choquet integral, Fuzzy Sets and Systems, 151 (2005), 237-259.
https://doi.org/10.1016/j.fss.2004.08.013
[10] M. Grabisch, J. L. Marichal, R. Mesiar, E. Pap, Aggregation functions, Encyclopedia of Mathematics and its
Applications, 127, Cambridge University Press, 2009.
[11] S. Greco, R. Mesiar, F. Rindone, Discrete bipolar universal integrals, Fuzzy Sets and Systems, 252 (2014), 55-
65.https://doi.org/10.1016/j.fss.2014.02.002
[12] S. Greco, F. Rindone, Bipolar fuzzy integrals, Fuzzy Sets and Systems, 220 (2013), 21-33. https://doi.org/10.
1016/j.fss.2012.11.021
[13] L. Jin, Z. S. Chen, J. Y. Zhang, R. R. Yager, R. Mesiar, M. Kalina, H. Bustince, L. Martinez, Bi-polar preference
based weights allocation with incomplete fuzzy relations, Information Sciences, 621 (2023), 308-318. https://doi.
org/10.1016/j.ins.2022.11.097
[14] L. Jin, R. Mesiar, M. Kalina, R. R. Yager, Canonical form of ordered weighted averaging operators, Annals of
Operations Research, 295(2) (2020), 605-631. https://doi.org/10.1007/s10479-020-03802-6
[15] L. Jin, R. Mesiar, A. Stupˇnanov´a, R. R. Yager, M. Kalina, On some construction method and orness measure of
bi-capacities, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 29(1) (2021), 107-117.
https://doi.org/10.1142/S0218488521500069
[16] M. Kalina, Continuous OWA operators, Atlantis Studies in Uncertainty Modelling, vol. 3, Joint Proceedings of the
19th World Congress of the International Fuzzy Systems Association (IFSA), the 12th Conference of the European
Society for Fuzzy Logic and Technology (EUSFLAT), and the 11th International Summer School on Aggregation
Operators (AGOP) (2021), 589-594. https://doi.org/10.2991/asum.k.210827.079
[17] D. Kim, H. Kim, L. C. Jang, Some inequalities for generalized Choquet integrals of triangular fuzzy number-valued
functions and its application, Iranian Journal of Fuzzy Systems, 21(6) (2024), 83-99. https://doi.org/10.22111/
ijfs.2024.48347.8504
[18] J. M. Merig´o, A. M. Gil-Lafuente, The induced generalized OWA operator, Information Sciences, 179 (2009),
729-741. https://doi.org/10.1016/j.ins.2008.11.013
[19] R. Mesiar, Choquet-like integrals, Journal of Mathematical Analysis and Applications, 194 (1995), 477-488. https:
//doi.org/10.1006/jmaa.1995.1312
[20] R. Mesiar, A. Stupˇnanov´a, L. Jin, Bipolar ordered weighted averages: BIOWA operators, Fuzzy Sets and Systems,
433 (2022), 108-121. https://doi.org/10.1016/j.fss.2021.01.010
[21] R. Mesiar, A. Stupˇnanov´a, R. R. Yager, Generalizations of OWA operators, IEEE Transactions on Fuzzy Systems,
23 (2015), 2154-2161. https://doi.org/10.1109/TFUZZ.2015.2406888
[22] B. Mihailovi´c, E. Pap, M. ˇStrboja, A. Simi´cevi´c, A unified approach to the monotone integral-based premium
principles under the CPT theory, Fuzzy Sets and Systems, 398 (2020), 78-97. https://doi.org/10.1016/j.fss.
2020.02.006
[23] B. Mihailovi´c, M. ˇStrboja, M. Todorov, The bipolar Choquet g-integrals, Proceedings of 17th IEEE International
Symposium on Intelligent Systems and Informatics (SISY), Subotica, (2019), 173-178. https://doi.org/10.1109/
SISY47553.2019.9111535
[24] B. Mihailovi´c, M. ˇStrboja, M. Todorov, Jensen type inequality for the bipolar Shilkret, Sugeno and Choquet integrals,
Acta Polytechnica Hungarica, 18(9) (2021), 9-25. https://doi.org/10.12700/APH.18.9.2021.9.2
[25] E. Pap, Null-additive set functions, Kluwer Academic Publishers, Dordrecht-Boston-London, 1995.
[26] M. ˇStrboja, E. Pap, B. Mihailovi´c, Discrete bipolar pseudo-integrals, Information Sciences, 468 (2018), 72-88.
https://doi.org/0.1016/j.ins.2018.07.075
[27] A. Stupˇnanov´a, L. Jin, BIOWA operators. In: Lesot MJ. et al. (eds) Information Processing and Management
of Uncertainty in Knowledge-Based Systems. IPMU 2020. Communications in Computer and Information Science
1238, Springer, Cham, (2020), 419-425. https://doi.org/10.1007/978-3-030-50143-3_32
[28] C. Tan, X. Chen, Induced Choquet ordered averaging operator and its application to group decision making, International Journal of Intelligent Systems, 25 (2010), 59-82. https://doi.org/10.1002/int.20388
[29] Z. Wang, G. J. Klir, Generalized measure theory, Springer, Boston, 2009.
[30] R. R. Yager, On ordered weighted averaging aggregation operators in multi-criteria decision making, IEEE Transactions on Systems, Man, and Cybernetics, 18 (1988), 183-190. https://doi.org/10.1109/21.87068
[31] R. R. Yager, Induced aggregation operators, Fuzzy Sets and Systems, 137 (2003), 59-69. https://doi.org/10.
1016/S0165-0114(02)00432-3
[32] R. R. Yager, Generalized OWA aggregation operators, Fuzzy Optimization and Decision Making, 3 (2004), 93-107.
https://doi.org/10.1023/B:FODM.0000013074.68765.97
[33] R. R. Yager, J. Kacprzyk, The ordered weighted averaging operators: Theory and applications, Kluwer: Norwell,
MA, 1997.