A Probabilistic Integral Study of Quasiproduct Overa Nonadditive Measure

Abstract

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.

Keywords

• f-continuous non-additive measure
• λ-fuzzy operator
• fuzzy quasi-product probability integrals