The paper aims to define a new kind of logic, referred to as Archimedean-Compensatory Logic, which is constructed from the unification of two different fuzzy logic systems, namely a continuous Archimedean fuzzy logic and a compensatory fuzzy logic. The paper introduces basic definitions and properties of this new theory. Continuous Archimedean logic is a t-norm and t-conorm logic system and Compensatory Fuzzy Logic can be obtained from quasi-arithmetic mean operators. We will prove the property that the preference over a pair of truth-value vectors is the same for certain predicates in the Compensatory Fuzzy Logic and the Continuous Archimedean Logic.
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