In terms of lattice,this paper discusses and demonstrates the order-reversing involution operator and its corresponding properties in bounded implicative-algebras,on the base of that bounded implicative-algebras and algebra are equivalent algebraic systems each other.

In this paper,a inverse and dual combination operator is proposed as a new genetic operator to improve genetic algorithm local searching,and a solving TSP genetic algorithm that combines uniform crossover operator which has better global searching with the new genetic operator is designed.

Secondly,an application is given about the right invertible operator pair(A,B).

Let Pr(f) (x) denote the poisson integration on sphere, for fractional integration operator Ia on Sphere it’s integration type inverse operator is researched.