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• W9108919 abstract "This chapter summarizes those powerset operator foundations of all mathematical and fuzzy set disciplines in which the operations of taking the image and preimage of (fuzzy) subsets play a fundamental role; such disciplines include algebra, measure theory and analysis, and topology. We first outline such foundations for the fixed-basis case—where the lattice of membership values or basis is fixed for objects in a particular category, and then extend these foundations to the variable-basis case—where the basis is allowed to vary from object to object within a particular category. Such foundations underlie almost all chapters of this volume. Additional applications include justifications for the Zadeh Extension Principle [19] and characterizations of fuzzy associative memories in the sense of Kosko [9]. Full proofs of all results, along with additional material, are found in Rodabaugh [16]—no proofs are repeated even when a result below extends its counterpart of [16]; some results are also found in Manes [11] and Rodabaugh [14, 15]." @default.
• W9108919 created "2016-06-24" @default.
• W9108919 creator A5015958599 @default.
• W9108919 date "1999-01-01" @default.
• W9108919 modified "2023-10-09" @default.
• W9108919 title "Powerset Operator Foundations For Poslat Fuzzy Set Theories And Topologies" @default.
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• W9108919 doi "https://doi.org/10.1007/978-1-4615-5079-2_3" @default.
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