Codes over Lattice-Valued Intuitionistic Fuzzy Set Type-3 with Application to the Complex DNA Analysis

Abstract

In this article codes over lattice valued intuitionistic fuzzy set type-3 (LIFS-3) are defined. Binary block codes and linear codes are constructed over LIFS-3. Hamming distance and related properties of these newly established codes are examined. The research findings are applied to genetic codes. The set $L$ of sixty-four codons is converted into a lattice and then codes are created over the set $S$ of twenty amino acids by defining membership and nonmembership functions from the set of twenty amino acids to the sixty-four codon set. Comparison of codes over $L$ -fuzzy set and LIFS-3 conducted in terms of hamming distance for codon system that ensures the efficiency of newly established codes.