Abstract

In this paper we propose a foundation of fuzzy measurement theory, which is described in terms of C ∗- algebras . This theory is a general measurement theory for classical and quantum systems. Here we also propose the identification: “measurement” = “inference”. As a “fuzzy” aspect of our proposal, we show and prove several fuzzy syllogisms in classical systems. Since our theory is concerning measurements (and not mathematics), these syllogisms should be regarded as objective facts in our real world. That is, our theory is “objective fuzzy theory”. Therefore, we believe that our proposal is a straight approach to “fuzziness”.

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