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States of MV-algebras have been the object of intensive study and attempts ofgeneralizations. The aim of this contribution is to provide a preliminaryinvestigation for states of prelinear semihoops and hyperstates of algebras inthe variety generated by perfect and involutive MTL-algebras (IBP0-algebras forshort). Grounding on a recent result showing that IBP0-algebras can beconstructed from a Boolean algebra, a prelinear semihoop and a suitably definedoperator between them, our first investigation on states of prelinear semihoopswill support and justify the notion of hyperstate for IBP0- algebras and willactually show that each such map can be represented by a probability measure onits Boolean skeleton, and a state on a suitably defined abelian l-group.

Hyperstates of Involutive MTL-Algebras that Satisfy $(2x)^2 = 2(x^2)$