Integrating Cognitive Decision-Making and Production Workflowswith HyperFuzzy Trace and HyperFuzzy Front-End

Abstract

Fuzzy sets model vagueness by assigning each element a membership degree in the interval [0, 1]. Hyperfuzzy
sets generalize this notion by mapping each element to a nonempty subset of [0, 1], thereby accommodating
both uncertainty and variability in membership degrees. An (m, n)-superhyperfuzzy set further extends
these frameworks by assigning to each nonempty member of the m-th and n-th iterated powersets a
nonempty family of subsets of [0, 1], enabling hierarchical and nested imprecision. These generalized
fuzzy models have found applications in decision-making and many other domains. Meanwhile, the
theories of Fuzzy Trace—retaining both verbatim and gist representations of information—and Fuzzy
Front-Ends—using graded membership functions to evaluate and aggregate multiple criteria for soft
go/no-go decisions—play a crucial role in information processing and innovation screening. However,
corresponding concepts built upon hyperfuzzy and superhyperfuzzy structures have not yet been explored.
To bridge this gap, we introduce extensions of Fuzzy Trace and Fuzzy Front-Ends based on hyperfuzzy and
(m, n)-superhyperfuzzy sets. We present their formal definitions, examine basic properties, and illustrate
them with examples. By doing so, we open the door to applying Fuzzy Trace and Fuzzy Front-End
methodologies in contexts characterized by hierarchical uncertainty.