Quick building of fuzzy equivalence matrix in granular computing

The fuzzy quotient space model is a hybrid model between quotient space theory and fuzzy set theory, which are two important methods in granular computing models, and it is based on fuzzy equivalence relation. There are many algorithms with high complexity for computing the fuzzy equivalence matrices. A new algorithm is proposed to compute the fuzzy equivalence matrices in this paper, and its time and space complexity is o(n²). An example also illustrates this algorithm. This result would be very helpful for designing efficient algorithms for huge data processing.