powerset operator foundations for catalg fuzzy set theories

نویسندگان

sergey a. solovyov

چکیده

the paper sets forth in detail categorically-algebraic or catalg foundations for the operations of taking the image and preimage of (fuzzy) sets called forward and backward powerset operators. motivated by an open question of s. e. rodabaugh, we construct a monad on the category of sets, the algebras of which generate the fixed-basis forward powerset operator of l. a. zadeh. on the next step, we provide a direct lift of the backward powerset operator using the notion of categorical biproduct. the obtained framework is readily extended to the variable-basis case, justifying the powerset theories currently popular in the fuzzy community. at the end of the paper, our general variety-based setting postulates the requirements, under which a convenient variety-based powerset theory can be developed, suitable for employment in all areas of fuzzy mathematics dealing with fuzzy powersets, including fuzzy algebra, logic and topology.

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عنوان ژورنال:
iranian journal of fuzzy systems

ناشر: university of sistan and baluchestan

ISSN 1735-0654

دوره 8

شماره 2 2011

میزبانی شده توسط پلتفرم ابری doprax.com

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