Symmetric implicational algorithm derived from intuitionistic fuzzy entropy

On account of the idea of maximum fuzzy entropy and  symmetric implicational mechanism under the environment of intuitionistic fuzzy sets,  we come up with the intuitionistic fuzzy entropy derived symmetric implicational (IFESI) algorithm.  Above all, novel symmetric implicational principles are presented, and the unified solutions of the IFESI algorithm are  acquired for IFMP (intuitionistic fuzzy modus ponens) and IFMT (intuitionistic fuzzy modus ponens), which build upon in view of residual intuitionistic implications. Thereafter, the reductive properties and continuity of the  IFESI algorithm are validated for IFMP and IFMT. In addition, the IFESI algorithm is extended to the $alpha$-IFESI algorithm, and the unified solutions of the $alpha$-IFESI algorithm are obtained for IFMP and IFMT. Finally, two examples of fuzzy classification for the $alpha$-IFESI algorithm are presented to demonstrate the detailed computing process of the IFESI algorithm.