Analysis and application of rectified complex t-spherical fuzzy Dombi-Choquet integral operators for diabetic retinopathy detection through fundus images

Pankaj Kakati, Shio Gai Quek, Ganeshsree Selvachandran, Tapan Senapati, Guiyun Chen

Research output: Contribution to journalArticleResearchpeer-review

1 Citation (Scopus)


This paper proposes a rectified complex spherical fuzzy set (rCTSFS) model that enables the phase term of a complex number to function truthfully to its inherent meaning of representing directions, phases, or color hues. In addition, this paper proposes the score and accuracy functions for rectified complex spherical fuzzy numbers (rCTSFn), which allows the three types of membership degrees of an rCTSFn to fulfill human judgment/intuition. The proposed rCTSFS model proves to be a productive extension of the complex spherical fuzzy set (CSFS), complex fuzzy set (CFS), and spherical fuzzy set (SFS) models. On the other hand, Dombi t-norms prove more flexible and comprehensive than some of the other families of triangular norms, such as the algebraic t-norms and the Einstein t-norms, due to the presence of a parameter γ. The parameter γ determines the amount of aggressiveness at estimating the maximum and the minimum of a population based on a sample obtained. Therefore, this paper proposes two Dombi-Choquet integral operators, namely, the rectified complex t-spherical fuzzy arithmetic Dombi-Choquet integral (rCTSFAγ,wλ ) operator and the rectified complex t-spherical fuzzy geometric Dombi-Choquet integral (rCTSFGγ,wλ ) operator. A multi-criteria decision making (abbr. MCDM) algorithm utilizing the two Dombi-Choquet integral operators is innovated. The proposed Dombi-Choquet MCDM algorithm for the rCTSFS model is applied to an MCDM problem related to diabetic retinopathy detection on five real-life fundus images of different severity levels taken from the Messidor2 dataset. Our newly proposed algorithm proves to be the only algorithm that yields the correct diagnostic results that match the hard truth. On the other hand, none of the 50 algorithms observed among recent works in literature can produce the correct diagnostic results, even after lending the fuzzification procedure innovated in this work to them.

Original languageEnglish
Article number122724
Number of pages27
JournalExpert Systems with Applications
Publication statusPublished - 1 Jun 2024


  • Complex fuzzy set
  • Diabetic retinopathy detection
  • Dombi-Choquet integral operator
  • Fundus image
  • Fuzzy set
  • Rectified complex -spherical fuzzy sets

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