Foundations of (m, n; L)-SuperHyperFuzzy Sets

Uncertainty modeling plays a crucial role in decision-making across diverse domains [1], and numerous mathematical frameworks have been proposed to capture various aspects of imprecision. These include Fuzzy Sets [2], Rough Sets [3,4], Vague Sets [5,6], Intuitionistic Fuzzy Sets [7,8], Hesitant Fuzzy Sets [9,10], Neutrosophic Sets [11,12], and Plithogenic Sets [13,14]. Among these developments, Hyperfuzzy Sets [15,16] and their recursive generalizations, SuperHyperfuzzy Sets [17], extend the classical notion by assigning setvalued membership degrees at multiple hierarchical levels. In this paper, we formally define the concept of (𝑚, 𝑛; 𝐿)–SuperHyperFuzzy Sets and investigate their relationships with related structures, including SuperHyperFuzzy Sets, SuperHyperNeutrosophic Sets, and SuperHyperPlithogenic Sets. An (𝑚, 𝑛; 𝐿)–SuperHyperFuzzy Set maps nonempty 𝑚-level subsets of a base set to nonempty families of 𝑛-level degree-sets valued in a complete commutative residuated lattice 𝐿, supporting 𝑡-norm/𝑡-conorm aggregation.