Artificial intelligence powered agricultural field robots selection problem in spatial planning: applications of ${\mathcal{L}}^{\mathit{p}}$-intuitionistic fuzzy sets

It is a well-known fact that ${\mathcal{L}}^p$-spaces provide a robust and flexible framework for analyzing functions with different types of behavior, uncertainty, and regularity. They are widely applicable in many areas of mathematics, science, and engineering. In this study, we introduced a novel generalization that combines interval intuitionistic fuzzy sets ( $IFS$s), as proposed by Atanassov ^[8], with circular intuitionistic fuzzy sets ( $C$- $IFS$), introduced by Atanassov ^[9], because these classical sets restrict us. This new concept is known as the ${\mathcal{L}}^p$-intuitionistic fuzzy set (value) ( ${\mathcal{L}}^p$- $IFS$( $V$)). The degrees of membership and non-membership in a ${\mathcal{L}}^p$- $IFS$ are depicted by a diamond shape, circle, star shape, and square with its center defined by non-negative real numbers $"\kappa "$ and $"𝓈"$, ensuring that $\kappa +𝓈\le 1$. The structure of a ${\mathcal{L}}^p$- $IFS$ facilitates the representation of information through points on different shapes with respect to $pth$-norm with a designated center and norm $"\mathrm{\aleph }"$, thereby enabling a more precise characterization of the fuzziness inherent in uncertain data. As a result, a ${\mathcal{L}}^p$- $IFS$ empowers decision-makers to evaluate options within a broader and more flexible framework, leading to the possibility of making more nuanced decisions. After establishing the concept of ${\mathcal{L}}^p$- $IFS$, some fundamental operations involving ${\mathcal{L}}^p$- $IFSs$ were outlined. To establish a novel scoring function and an accuracy function that incorporates the decision-makers' attitude ( $\lambda$), the set's optimistic and pessimistic points were defined. When the decision-maker's viewpoint ( $\lambda$) approached 1, the defuzzification of ${\mathcal{L}}^p$- $IFS$ occurred near its optimistic point, while it occurred near its pessimistic point as ( $\lambda$) approached 0. Moreover, a technique for converting a collection of intuitionistic fuzzy values into a ${\mathcal{L}}^p$-intuitionistic fuzzy values ( ${\mathcal{L}}^p$- $IFVs$) was formulated. Additionally, several algebraic operations between ${\mathcal{L}}^p$- $IFV$ using general triangular $𝓉$-norms and triangular $𝓉$-conorms were proposed. To transform input values represented by ${\mathcal{L}}^p$- $IFVs$ into a single output value, specific weighted aggregation operators based on these algebraic methods were introduced. The proposed methodology was applied to a problem concerning the selection of the optimal artificial intelligence (AI) agricultural field robots multi-attribute decision-making ( $MADM$) framework. Finally, a framework was also presented for addressing $MADM$ challenges within a ${\mathcal{L}}^p$-intuitionistic fuzzy context. It is interesting to note that the time complexity of the proposed method and a comparative analysis were evaluated.