Fuzzy Hidden Markov Model Using Aggregation Operators

Abstract

The Fuzzy Markov Model (FMM) is a fascinating domain for dealing with ambiguity in real-world scenarios. In type 2 fuzzy set (T2F), it has an uncertainty footprint, and the region circumscribed by the lower and upper interval membership functions is uncertain. In fuzzy sets, Triangular norms (t-norms) are a valuable tool for understanding the conjunction in fuzzy logic and, as a result, determining where fuzzy sets intersect. Norms and conforms in Triangular operations that generalize logical conjunction and disjunction. They also provide a natural explanation for the conjunction and disjunction in mathematical fuzzy logic semantics. Fuzzy Frank Triangular Norms have been used to verify this t-norm as there are many of them the aggregation qualities of Trapezoidal Interval Type-2 numbers (TpIT2FNs) because triangular norm meets the compatibility with Frank norms. Frank triangular norms provide more flexibility and robustness this requires more justification in the information fusion process than other triangular norms. Previous works on not concentrate on Frank's norms. Other Aggregation works on norms that are not flexible to get the solution. Because of that, the Frank norms are used for the hidden Markov model. We've also used them in the Viterbi method with TpIT2FNs for Fuzzy Hidden Markov Model in the staff selection process.