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Self-dual equivalence class of ternary logic functions is investigated using ternary parametron logic. Based on multiplexor (MUX) realization of a function, a self-dual function is constructed by introducing Goto's self-dualizing variable which feeds constant values to MUX circuit. Self-dual operation is an operation to transform from one function to another among functions realized by different values of self-dualizing variable. It is defined as a combination of permutation group on values and positions of variables and that on values of function. It can be formulated as an exponentiation group by these groups and the equivalence class count is obtained from the cycle index of these groups.