Abstract
Abstract We study P-measures on soft fuzzy σ-algebras as defined by Piasecki [46] and further investigated in [2–5], etc. We prove as main result that the space of P-measures of a soft fuzzy σ-algebra is ‘faithfully’ isomorphic to the space of probability measures of a Boolean σ-algebra. This result, we believe, may allow to employ the well-developed Boolean technique in certain ‘fuzzy’ investigations (especially in the stochastic ones) but, on the other hand, it lowers to some extent the chance for the soft fuzzy σ-algebras to be applied in quantum theories (see also [9] and [8]). (It should be noted that our result gives - as a by-product - a negative answer to the problem posed in [3].)
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