Some interval-valued spherical fuzzy Frank Choquet integral operators in multicriteria decision making

In real-life decision-making, expressing uncertainty, impreciseness, and hesitancy accurately is essential. Interval-valued spherical fuzzy sets (IVSFS) offer a suitable framework as an extension of interval-valued intuitionistic fuzzy sets, interval-valued picture fuzzy sets, and spherical fuzzy sets, allowing for interval-valued membership grades rather than exact values. This enhanced expressiveness enables more effective modeling of real-life decision-making problems by introducing suitable aggregation operators. In this paper, we propose the interval-valued spherical fuzzy Frank Choquet integral (IVSFFCI) and the interval-valued spherical fuzzy Frank geometric Choquet integral (IVSFFGCI) operators. These operators effectively capture the interaction among the criteria in real-life decision-making problems, overcoming the limitations of traditional methods. The IVSFFCI and IVSFFGCI operators utilize Frank’s t-norm and t-conorm, providing flexibility and robustness during the aggregation process. By considering the interrelation among the criteria, they exceed existing operators, making them the ideal choice for real-life decision-making situations. We develop a multicriteria decision-making (MCDM) method using the proposed operators that effectively deal with correlated criteria in real-life decision-making problems. To demonstrate the efficacy of the proposed method, an illustrative example relating to a financial body’s investment partner selection from four potential alternatives, based on criteria such as financial strength, mercantile expertise, entrepreneurial competencies, and risk management, is presented. The proposed method encapsulates immense potential across industries, promoting informed and data-driven decision-making processes.