δ-equality of intuitionistic fuzzy sets: a new proximity measure and applications in medical diagnosis

Intuitionistic fuzzy set is capable of handling uncertainty with counterpart falsities which exist in nature. Proximity measure is a convenient way to demonstrate impractical significance of values of memberships in the intuitionistic fuzzy set. However, the related works of Pappis (Fuzzy Sets Syst 39(1):111–115, 1991), Hong and Hwang (Fuzzy Sets Syst 66(3):383–386, 1994), Virant (2000) and Cai (IEEE Trans Fuzzy Syst 9(5):738–750, 2001) did not model the measure in the context of the intuitionistic fuzzy set but in the Zadeh’s fuzzy set instead. In this paper, we examine this problem and propose new notions of δ-equalities for the intuitionistic fuzzy set and δ-equalities for intuitionistic fuzzy relations. Two fuzzy sets are said to be δ-equal if they are equal to an extent of δ. The applications of δ-equalities are important to fuzzy statistics and fuzzy reasoning. Several characteristics of δ-equalities that were not discussed in the previous works are also investigated. We apply the δ-equalities to the application of medical diagnosis to investigate a patient’s diseases from symptoms. The idea is using δ-equalities for intuitionistic fuzzy relations to find groups of intuitionistic fuzzified set with certain equality or similar degrees then combining them. Numerical examples are given to illustrate validity of the proposed algorithm. Further, we conduct experiments on real medical datasets to check the efficiency and applicability on real-world problems. The results obtained are also better in comparison with 10 existing diagnosis methods namely De et al. (Fuzzy Sets Syst 117:209–213, 2001), Samuel and Balamurugan (Appl Math Sci 6(35):1741–1746, 2012), Szmidt and Kacprzyk (2004), Zhang et al. (Procedia Eng 29:4336–4342, 2012), Hung and Yang (Pattern Recogn Lett 25:1603–1611, 2004), Wang and Xin (Pattern Recogn Lett 26:2063–2069, 2005), Vlachos and Sergiadis (Pattern Recogn Lett 28(2):197– 206, 2007), Zhang and Jiang (Inf Sci 178(6):4184–4191, 2008), Maheshwari and Srivastava (J Appl Anal Comput 6(3):772–789, 2016) and Support Vector Machine (SVM)

An intuitionistic approach to scoring DNA sequences against transcription factor binding site motifs

Background: Transcription factors (TFs) control transcription by binding to specific regions of DNA called transcription factor binding sites (TFBSs). The identification of TFBSs is a crucial problem in computational biology and includes the subtask of predicting the location of known TFBS motifs in a given DNA sequence. It has previously been shown that, when scoring matches to known TFBS motifs, interdependencies between positions within a motif should be taken into account. However, this remains a challenging task owing to the fact that sequences similar to those of known TFBSs can occur by chance with a relatively high frequency. Here we present a new method for matching sequences to TFBS motifs based on intuitionistic fuzzy sets (IFS) theory, an approach that has been shown to be particularly appropriate for tackling problems that embody a high degree of uncertainty. Results: We propose SCintuit, a new scoring method for measuring sequence-motif affinity based on IFS theory. Unlike existing methods that consider dependencies between positions, SCintuit is designed to prevent overestimation of less conserved positions of TFBSs. For a given pair of bases, SCintuit is computed not only as a function of their combined probability of occurrence, but also taking into account the individual importance of each single base at its corresponding position. We used SCintuit to identify known TFBSs in DNA sequences. Our method provides excellent results when dealing with both synthetic and real data, outperforming the sensitivity and the specificity of two existing methods in all the experiments we performed. Conclusions: The results show that SCintuit improves the prediction quality for TFs of the existing approaches without compromising sensitivity. In addition, we show how SCintuit can be successfully applied to real research problems. In this study the reliability of the IFS theory for motif discovery tasks is proven