Abstract:As an indispensable branch of fuzzy mathematics

fuzzy probability integral is an important integral form that relies on fuzzy probability and fuzzy measure

and is also a powerful tool for studying fuzzy mathematics. Aiming at the definition and theorem research of fuzzy probability

fuzzy measure and its integral

two kinds of ideal γ－fuzzy operator form is given

which proves that the condition of triangular norm operator is satisfied; And under the background of the proposed relevance measure space

the definition and theorem of generalized Sugeno probability integral are given

verification of a number of theorems that satisfy the condition to prove its feasibility.