Abstract:

P(ρ,σ)-sets is the general case of P-sets. Based on the conception of P(ρ,σ)-set (XPρ, XPFσ ), the relation between internal P(ρ,σ)-set and internal P-set is studied. Internal P(ρ,σ)-set and internal P-set relation theorem, internal P(ρ,σ)-set and numerical value ρ relation theorem, internal P(ρ,σ)-set’s range, other characteristics of internal P(ρ,σ)-set, the finiteness theorem of internal P(ρ,σ)-set, the set chain theorem of internal P(ρ,σ)-set, the internal P(ρ,σ)-set probability interval finite partition theorem, and its corollary, generation, reduction, identification theorem of internal P(ρ,σ)-set, filter generation theorem of internal P(ρ,σ)-set are obtained. Finally, internal P(ρ,σ)-set application is given.

Key words: internal P(ρ,σ)-set; finiteness; probability; identification; filter; finite partition