In a typical formulation of decision-making under uncertainty, a decision-maker must choose a single-optimal option among many possible options. However, the problem of selecting a unique and optimal choice has remained a significant challenge to solve. In this article, we propose a new interval-valued intuitionistic fuzzy soft set (IVIFSS) based decision-making approach to address this problem. The proposed approach is based on the choice value and score value of membership/nonmembership degrees. Furthermore, three parameter reduction algorithms are proposed. We apply the proposed approaches on a real application to demonstrate their working and effectiveness. We also compare the proposed approach against the adjustable IVIFSSs approach and show that the proposed approach has lower computation overhead and enable a decision-maker to choose top options to make a proper decision.

Kong et al. introduced the concept of normal parameter reduction in fuzzy soft sets. However, due to entries of fuzzy soft sets belonging to the unit interval [0, 1], it is nearly impossible to obtain the normal parameter reduction of fuzzy soft sets in the real applications. At the same time, this method involves a great amount of computation. In order to solve these problems, in this paper, we propose a distance-based parameter reduction of fuzzy soft set, which has much higher applicability and involves much less computation compared with the method of normal parameter reduction of fuzzy soft sets. Two case studies and twenty synthetic generated datasets show our contributions.

Interval-valued q-rung orthopair fuzzy set (IVq-ROFS) is a powerful tool for dealing with uncertainty. In this paper, we first propose a new method for aggregating multiple IVq-ROFSs, which is easier to understand and implement in the multi-attribute group decision making process compared to current aggregation operators. Secondly, this paper introduces a new fuzzy entropy with parameters based on IVq-ROFS, which is highly flexible due to its adjustable parameters. Based on this, the IVq-ROFS-based attribute weight calculation method is proposed to obtain the objective weights of the attributes, which is more reasonable and objective than the existing methods. Then, for the dimensional differences between the three compromise scores in the original Combined Compromise Solution (CoCoSo) method, the enhanced compromise scores are proposed. These scores are obtained by normalizing the three dependent compromise scores, ensuring that they fall within the same range. Finally, a novel CoCoSo mothed on IVq-ROFS using the proposed fuzzy entropy and enhanced compromise scores is presented. The proposed method is highly adaptable and scalable, not limited to IVq-ROFS. The excellent performance and robustness of the proposed method are verified in sepsis diagnosis applications.

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.