“…In order to ensure the accurate and precise modeling [1][2][3][4] of complex real-world situations, the utilization of robust model structures such as Kripke structures 5,6 , multi-valued Kripke structures 7,8 , fuzzy Kripke structures 9,10 , and possibility Kripke structures [11][12][13][14] is essential. These model structures find applicability across a spectrum of complex domains, encompassing strategic decision-making, cancer metabolism investigation, security protocol verification, artificial intelligence analysis, robotics advancements, control systems optimization, and various other fields [15][16][17][18] . Particularly salient is the role of nondeterministic fuzzy Kripke structures in addressing the complexities inherent to real-world situations marked by uncertainty 19,20 .…”