A Family of Fuzzy and Defuzzified c-Means Algorithms

This paper proposes a family of fuzzy and hard c-means algorithms. The hard clustering algorithms are derived from defuzzifying a generalized entropy-based fuzzy c-means whereby cluster volume size variables and covariance variables are introduced into hard clustering algorithms. Sequential algorithms are also derived by using advanced formulas of matrix multiplication. Crisp c-means as well as c-regression models are studied. Moreover effectiveness and efficiency of the proposed algorithms are compared using artificial as well as real data sets