Q-rung orthopair hesitant fuzzy set (q-ROHFS) is a potent and effective technique for dealing with more general and complex uncertainty. Multiple attribute decision-making (MADM) under complex uncertainty has been a key research issue. However in the existing MADM approaches, the fuzzy entropies involve much higher hesitancy degree loss and the fuzzy measure of attributes can not be determined objectively. Also these existing MADM methods under complex uncertainty have high data redundancy and low computational efficiency. In order to solve these problems, this paper proposes a novel q-rung orthopair hesitant fuzzy information MADM method based on the Choquet integral. Firstly, we give the axiomatic definition of q-rung orthopair hesitant fuzzy entropy (q-ROHFE) by extending dual hesitant fuzzy information entropy and derive the fuzzy entropy construction theorem and the two related q-ROHFE formulas, which greatly reduces the loss of hesitancy degree resulting from the existing fuzzy entropy. Secondly, combined with λfuzzy measure and proposed q-ROHFE, a constrained nonlinear fuzzy measure optimization model for q-rung orthopair hesitant fuzzy decision making is presented, which addresses the difficulty that existing research cannot determine the fuzzy measure of attributes under fuzzy MADM. Thirdly, an improved Choquet integral-based VIKOR approach based on the fuzzy measure computed by the model is developed. Finally, two real-life cases are shown to fully illustrate the suggested approach. Experiment results demonstrate that the proposed fuzzy entropy has much less hesitancy degree loss and the proposed approach significantly increases computational efficiency while reducing data redundancy. And our method has strong adaptability and scalability.

Hesitant Fermatean fuzzy sets (HFFS) can characterize the membership degree (MD) and non-membership degree (NMD) of hesitant fuzzy elements in a broader range, which offers superior fuzzy data processing capabilities for addressing complex uncertainty issues. In this research, first, we present the definition of the hesitant Fermatean fuzzy Bonferroni mean operator (HFFBM). Further, with the basic operations of HFFS in Einstein t-norms, the definition and derivation process of the hesitant Fermatean fuzzy Einstein Bonferroni mean operator (HFFEBM) are given. In addition, considering how weights affect decision-making outcomes, the hesitant Fermatean fuzzy weighted Bonferroni mean (HFFWBM) operator and the hesitant Fermatean fuzzy Einstein weighted Bonferroni mean operator (HFFEWBM) are developed. Then, the properties of the operators are discussed. Based on HFFWBM and HFFEWBM operator, a new multi-attribute decision-making (MADM) approach is provided. Finally, we apply the proposed decision-making approach to the case of a depression diagnostic evaluation for three depressed patients. The three patients' diagnosis results confirmed the proposed method's validity and rationality. Through a series of comparative experiments and analyses, the proposed MADM method is an efficient solution for decision-making issues in the hesitant Fermatean fuzzy environment.

A fuzzy soft set is a mathematical tool used to deal with vagueness and uncertainty. Parameter reduction is an important issue when applying a fuzzy soft set to handle decision making. However, existing methods neglect newly added parameters and have higher computational complexities. In this paper, we propose a new S-Score table-based parameter-reduction approach for fuzzy soft sets. Compared with two existing methods of parameter reduction for a fuzzy soft set, our method takes newly added parameters into account, which brings about greater flexibility and is beneficial to the extension of fuzzy soft sets and a combination of multiple fuzzy soft sets. Additionally, our method accesses fewer elements from the dataset, which results in lower computation compared with the two existing approaches. The experimental results from two applications show the availability and feasibility of our approach.