Fuzzy Logic and Algebra: Course Outline (MAT-619 )
Introduction, The Concept of Fuzziness: Examples; Mathematical Modeling; Operations of fuzzy sets;Fuzziness as uncertainty, Algebra of Fuzzy Sets: Boolean Algebra and lattices; Equivalence relations and partitions; Composing mappings; Alpha-cuts; Images of alpha-level sets;Operations on fuzzy sets. Fuzzy Relations: Definition and examples; Binary Fuzzy relations Operations onFuzzy relations; fuzzy partitions. Fuzzy Semigroups: Fuzzy ideals of Semigroups; Fuzzy quasi-ideals; Fuzzy bi-ideals of Semigroups; Characterization of different classes of Semigroups by the properties of their fuzzy ideals fuzzy quasi-ideals and fuzzy bi-ideals. Fuzzy Rings: Fuzzy ideals of rings; Prime; semi prime fuzzy ideals;Characterization of rings using the properties of fuzzy ideals.
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