Multi-polar Q-hesitant Fuzzy Soft Implicative and Positive Implicative Ideals in BCK/BCI-algebras.

This paper focuses on exploring restricted mathematical concepts within the domain of BCK/BCI-algebras, specifically delving into the intricate realm of Multi-polar Q-hesitant fuzzy soft implicative and positive implicative ideals. BCK and BCI-algebras are pivotal structures in mathematical logic and algebraic systems, finding widespread applications in fields like computer science and artificial intelligence. Our contribution lies in the introduction and thorough investigation of the innovative notions of multi-polar Q-hesitant fuzzy soft implicative and positive implicative ideals, uniquely tailored for BCK/BCI-algebras. These ideals exhibit exceptional flexibility in managing uncertain and hesitant information, serving as potent tools for modeling and solvingreal-world problems characterized by imprecise or incomplete data. This study rigorously defines and explores the foundational properties of multi-polar Q-hesitant fuzzy soft implicative ideals, underscoring their relevance and applicability within BCK/BCI-algebras. Additionally, we present the concept of positive implicative ideals, establishing their interconnectedness with multi-polar Q-hesitant fuzzy soft implicative ideals. Our investigation delves into these ideals’ algebraic and logical facets, offering valuable insights into their mutual interactions and significance within the context of BCK/BCI-algebras. To facilitate practical implementation, we develop algorithms and methodologies for identifying and characterizing multi-polar Q-hesitant fuzzy soft implicative and positive implicative ideals. These computational tools enable efficient decision-making in scenariosinvolving uncertainty. Through illustrative examples and case studies, we showcase the potential of these ideals in handling complex, uncertain information, demonstrating their efficacy in aiding problem-solving processes. This research contributes significantly to advancing BCK/BCI-algebra theory by introducing innovative mathematical structures that bridge the gap between fuzzy logic, soft computing, and implicative ideals. The proposed multi-polar Q-hesitant fuzzy soft implicativeand positive implicative ideals open new avenues for addressing real-world problems characterized by imprecision and uncertainty. As such, they represent a valuable addition to the field of algebraic structures and their applications.