Both computational and experimental methods are used to identify and describe genes within DNA sequences. Experimental methods such as cDNA cloning, RNA-Seq, and CRISPR/Cas9 evaluate gene expression and function directly, whereas computational approaches such as ab initio prediction, homology-based methods, and machine learning predict gene locations using DNA sequence features and comparisons. By measuring sequence similarity or divergence, distance measures are essential to these procedures and support gene grouping, phylogenetic analysis, comparative genomics, and sequence alignment. This paper aims to explore some distance measures (DMs) such as Hamming distance measure, Zhang distance measure, Normalized Hamming distance measure, and Zeeshan distance measure under the environment of complex fuzzy sets (CFSs). We studied some basic properties of complex fuzzy distance measures (CFDMs). Moreover, we employed CFDMs to extract pertinent features from gene that provides uncertainty and ambiguous data. We proposed an innovative digital signal processing method for gene identification using CFDMs. We developed an algorithm utilizing CFDMs to identify a healthy gene out of several affected genes. To demonstrate the effectiveness and advancements of the proposed work, a comparison with various current methodologies was also conducted.

A complex fuzzy distance measure (CFDM) is a way to quantify the dissimilarity or similarity between two complex fuzzy sets (CFSs). This measure often considers both the membership values and the degree of overlap between sets to compute the distance. However, CFDMs are not capable of capturing the hesitancy or uncertainty inherent in real-life problems. To overcome this difficulty, we present generalized notions of some existing distance measures (DMs), such as Zhang DM and Zeeshan DM within the framework of CFSs. The newly defined DMs are said to be complex fuzzy generalized Zhang Hesitance DM (CFGZHDM), complex fuzzy generalized weighted Zhang Hesitance DM (CFGWZHDM), complex fuzzy generalized Zeeshan Hesitance DM (CFGZHDM), and complex fuzzy generalized weighted Zeeshan Hesitance DM (CFGWZHDM). Several new set-theoretic operations and fundamental mathematical results are formally defined and developed. These are built upon the framework of the proposed decision-making models to strengthen their applicability and theoretical foundation. We utilized the proposed generalized CFDMs in applications to decision-making problems. We proposed a new decision-making algorithm that offers a flexible and nuanced approach to selecting exemplary students by considering the fuzzy and overlapping nature of attributes and allowing for uncertainty in the selection process. Furthermore, a comparative analysis is conducted between the proposed models, evaluating their performance and effectiveness about several existing fuzzy models. This comparison aims to highlight the strengths, differences, and potential advantages of the newly proposed models over conventional methods. Moreover, the newly defined decision-making approaches illustrate clear improvements over existing techniques. While traditional techniques fail to provide meaningful ranking values, our proposed approaches produce non-zero scores such as 0.13, 0.30, and 0.10, leading to a valid ordering of alternatives. When weighted information is considered, the effectiveness is further enhanced, yielding higher score values (0.80, 0.85, and 0.81) and more stable rankings.