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Iranian Journal of Fuzzy Systems، جلد ۸، شماره ۲، صفحات ۱-۴۶
عنوان فارسی POWERSET OPERATOR FOUNDATIONS FOR CATALG FUZZY SET THEORIES
چکیده فارسی مقاله 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 xed-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 انگلیسی POWERSET OPERATOR FOUNDATIONS FOR CATALG FUZZY SET THEORIES
چکیده انگلیسی مقاله 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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نویسندگان مقاله sergey a solovyov | sergey a
department of mathematics, university of latvia, zellu iela 8, lv-1002 riga, latvia and institute of mathematics and computer science, university of latvia, raina bulvaris 29, lv-1459 riga, latvia

نشانی اینترنتی http://ijfs.usb.ac.ir/article_259_70ec1ad6ec163ed0aae61e0371fe26ac.pdf
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