Multi-valued logic based on probability-generated aggregators

We consider the problem of decision-making under uncertainty and suggest the method of constructing truth values of the events using probability-generated aggregators. We prove the equivalence (in non-limiting cases) between the fuzzy logic based on the probability-generated aggregators and the Lukasiewicz probabilistic logic based on model-theoretic scheme. In addition, we demonstrate the relation between the suggested construction and the Nilsson and the Reichenbach probabilistic logics. The suggested method provides effective techniques for resolving uncertainties in the decision-making tasks and bridges the gap between probabilistic and fuzzy approaches to multivalued logic. In addition to formal statements and proofs, the report includes several examples, which clarify the suggested constructions and demonstrate their correspondence with the known methods.