A philosophical study on meaning and fuzzy sets

Abstract

This article reaches the meaning of fuzzy sets from a new philosophical point of view. The topic arises from authors practical control cases in which a simultaneous handling for fuzziness and uncertainty is need. The fuzzy sets are approached from semantics, the meaning of language. The fuzzy sets are handled philosophically as textual expressions more than data extractions. First, the problem of the meaning of a word is studied from several philosophical point of views. The meaning is concluded to be incommensurable. The meaning articulation paradigm, conducted from philosophies of Wittgenstein and Bergson in a previous study is applied to illustrate the semantics of fuzzy sets. According to the paradigm, the aspects of any use of a tool (like fuzzy sets) are; being, change and meaning. These aspects actually coexist, as separate degrees of freedom. There for the commensurability assumption of fuzzy sets may be reconsidered. A solution is suggested by applying all three aspects (being, change and meaning) to a case of using fuzzy sets. These technical systems, in which the fuzzy sets are assumed to be subcommensurable are sketched. Subcommensurability means a situation, in which the certainty of commensurability is known locally for some a priori extent.