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The human cognition and interaction with the outside world involves structure with no sharp boundaries in which the transition of membership to non-membership function is gradual rather than abrupt. The concept of cut sets and fuzzy numbers were developed and intensive research has been taking place and applied in human cognition. In this paper, we have introduced matrix-cut for trapezoidal fuzzy number by studying its properties, arithmetic operations and decomposition theorems. Finally, the Trapezoidal Intuitionistic Fuzzy number (TFN) and its arithmetic properties using matrix cut have also been proposed.

CUT SETS ON TRAPEZOIDAL FUZZY NUMBER AND INTUITIONISTIC FUZZY NUMBER: A NEW PERSPECTIVE