In this paper

a definition of non additive measure is given

which has F-addability; the Einstein calculater is optimized

and the λ-fuzzy quasiproduct operator and λ-fuzzy quasi sum operator with adjustable parameters for practical problems are designed

and it is proved that they satisfy the conditions of T-norm and S-norm; then

based on this non-additive measure and λ-fuzzy quasiproduct operator

the definition of fuzzy quasi product probability integral is given

and the integral as a whole is regarded as a set function

and the nature of its satisfaction is studied and proved

thus enriching the theory of fuzzy measure.