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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.
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    Using I-subgroup-based weighted generalized interval t-norms for aggregating basic uncertain information
    (Elsevier, 2024) Yang, Yi; Chen, Zhen-Song; Pedrycz, Witold; Gomez, Marisol; Bustince, Humberto
    In this paper, we present a method of extending t-norms and t-conorms to a given closed subinterval [a, b] in [-infinity,+infinity], which preserves the basic properties of these fuzzy connectives and their one-to-one correspondence with operations in a I-semigroup. Subsequently, the generalized De Morgan triples, weighted generalized interval t-norms and t-conorms are provided to construct the aggregation function for extended basic uncertain information. Eventually, we apply the proposed aggregation function to establish the basic uncertain linguistic information-based aggregation operator.