Sequence comparison is an essential part of modern molecular biology research. In this study, we estimated the parameters of Markov chain by considering the frequencies of occurrence of the all possible amino acid pairs from each alignment-free protein sequence. These estimated Markov chain parameters were used to calculate similarity between two protein sequences based on a fuzzy integral algorithm. For validation, our result was compared with both alignment-based (ClustalW) and alignment-free methods on six benchmark datasets. The results indicate that our developed algorithm has a better clustering performance for protein sequence comparison.

A larger amount of sequence data in private and public databases produced by next-generation sequencing put new challenges due to limitation associated with the alignment-based method for sequence comparison. So, there is a high need for faster sequence analysis algorithms. In this study, we developed an alignment-free algorithm for faster sequence analysis. The novelty of our approach is the inclusion of fuzzy integral with Markov chain for sequence analysis in the alignment-free model. The method estimate the parameters of a Markov chain by considering the frequencies of occurrence of all possible nucleotide pairs from each DNA sequence. These estimated Markov chain parameters were used to calculate similarity among all pairwise combinations of DNA sequences based on a fuzzy integral algorithm. This matrix is used as an input for the neighbor program in the PHYLIP package for phylogenetic tree construction. Our method was tested on eight benchmark datasets and on in-house generated datasets (18 s rDNA sequences from 11 arbuscular mycorrhizal fungi (AMF) and 16 s rDNA sequences of 40 bacterial isolates from plant interior). The results indicate that the fuzzy integral algorithm is an efficient and feasible alignment-free method for sequence analysis on the genomic scale.

In this paper, we introduce the concept of H(i) connected ditopological texture space. We develop some basic properties of bicontinuity and connectedness in term of ditopological texture space which will used in H(i) connected ditopological texture space. We have established some correspondence related to known structure such as bitopological space, fuzzy lattice and topological space.

In this paper, we developed a fuzzy code technique for molecular phylogenetic analysis. This proposed theory has potential to encode or decode information related to the evolution of sequences traversing from one stage to another in phylogenetic trees. Using this novel methodology we have encoded the sequence of RNA molecule of each species in phylogenetic trees which folds into three-dimensional structure due to transcription, termed as secondary structure.After encoding RNA sequence into the fuzzy code, we wrote mathematical formulation of RNA secondary structure. In addition we establish relation between RNA sequence and their secondary structure. We constructed the fuzzy neural network, fraction of neural neighbour in sequence space for differentiating compatible sequences. We have used technique involution metric, symmetric group, symmetric difference, etc; to establish a difference in secondary structures.