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    Aggregation of Basic Uncertain Information With Two-Step Aggregation Frame
    (Ieee-Inst Electrical Electronics Engineers Inc, 2024) Jin, Lesheng; Chen, Zhen-Song; Pedrycz, Witold; Senapati, Tapan; Yatsalo, Boris; Mesiar, Radko; Beliakov, Gleb
    There exist various categories of uncertain information, and their corresponding methods of aggregation may also vary. At present, there exists a dearth of specifically tailored techniques for aggregating basic uncertain information (BUI). The present study introduces a two-step aggregation frame that is applicable to inputs of both real-valued and BUI-valued inputs. In the process of constructing such a frame, several novel notions and definitions are introduced. These comprise of extended aggregation operators with respect to a finite set and to a collection of subsets of the set, some certainty independent BUI aggregation and some certainty dependent BUI aggregation, BUI merging operators and BUI aggregation operators, BUI-valued min operator, and BUI-valued Sugeno integral. Some corresponding deductions, necessary reasoning and numerical examples are presented.
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    Generalized extended Bonferroni means for isomorphic membership grades
    (Elsevier B.V., 2024) Chen, Zhen Song; Yang, Yi; Jin, LeSheng; Dutta, Bapi; Martínez, Luis; Pedrycz, Witold; Mesiar, Radko; Bustince, Humberto
    The 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.