Chen, Zhen SongYang, YiJin, LeShengDutta, BapiMartínez, LuisPedrycz, WitoldMesiar, RadkoBustince, Humberto2025-04-182025-04-182024Chen, Z. S., Yang, Y., Jin, L., Dutta, B., Martínez, L., Pedrycz, W., ... & Bustince, H. (2024). Generalized extended Bonferroni means for isomorphic membership grades. Fuzzy Sets and Systems, 488, 109009.01650114http://dx.doi.org/10.1016/j.fss.2024.109009https://hdl.handle.net/20.500.12713/6978The generalized extended Bonferroni mean (GEBM) is a powerful tool for modeling the complex process of aggregating information, whether it is homogeneously or heterogeneously connected, within a composite aggregation structure. It maintains several favorable characteristics and effectively captures the diverse and interconnected nature of expert opinions or criteria, which is commonly observed in various decision-making contexts. This research expands upon the existing GEBM framework by applying it to the specific domains of q-rung orthopair fuzzy sets (q-ROFSs) and extended q-rung orthopair fuzzy sets (Eq-ROFSs). Furthermore, it examines the transformation processes among different variants of GEBMs. To facilitate the development of generalized aggregation functions, the de Morgan triplets for q-ROFSs and Eq-ROFSs are established. By introducing an isomorphism, the transformation relationship between the aggregation functions for q-ROFSs and Eq-ROFSs is analyzed. Based on this foundation, the Bonferroni mean de Morgan triplet-based GEBMs for q-ROFSs and Eq-ROFSs are proposed, and the keeping-order relations for these proposed GEBMs are discussed. Finally, several special cases of the GEBMs for q-ROFSs and Eq-ROFSs are obtained, and several relevant theorems are verified. © 2024 Elsevier B.V.eninfo:eu-repo/semantics/closedAccessAggregation FunctionDe Morgan TripletExtended Bonferroni MeanGeneralized Extended Bonferroni MeanQ-rung Orthopair Membership GradesArticle488WOS:0012952904000012-s2.0-85193489497Q110.1016/j.fss.2024.109009Q1