Fuzzy on Ideal Sets and a Fuzzy on Ideal Hahn-Banach Theorem - Mernilo-Tutanes, Lezel N.; Caga-anan, Randy L. (Science Diliman: A Journal of Pure and Applied Sciences; Vol 30 No 2 (2018), 2018)
In set theory, an ideal is a collection of sets that are considered to be small or negligible, such that every subset of an element of the ideal must also be in the ideal and the union of any two elements of the ideal must also be in the ideal. A fuzzy set is a class of objects with grades of membership in the interval [0, 1]. It is used to mathematically represent uncertainty and provide a formal tool to deal with imprecisions present in many problems. We use ideals to def ine fuzzy on ideal sets, which can be seen as a generalization of the fuzzy sets. We establish some of its basic properties, and we state and prove a Hahn-Banach Theorem with the fuzzy on ideal sets, which can be seen as a generalization of a fuzzy Hahn-Banach Theorem, which in turn, is a fuzzif ied generalization of an analytic form of the classical Hahn-Banach Theorem. Mathematics Subject Classification (2010): 62B86 Keywords: Fuzzy, ideal, Hahn-Banach theorem