Chapter 8 Fuzzy Associative Memories 苏亚 2006-11-27
Chapter 8 Fuzzy Associative Memories 苏亚 2006-11-27
Outline 1.Introduction 2.FAM >FAM as mapping >FAM as encoding 3.Fuzzy and neural Association Memories >Neural vs.fuzzy representation of structured knowledge >FAMs as mapping >Max-Min Composition
Outline 1. Introduction 2. FAM ØFAM as mapping ØFAM as encoding 3. Fuzzy and neural Association Memories ØNeural vs. fuzzy representation of structured knowledge ØFAMs as mapping ØMax-Min Composition
Introduction We have introduced the unit hypercube Size and fuzziness Points Distance between in hypercube points Subset Relations between Fuzzy Associative fuzzy cubes:mapping Memories
Introduction Ø We have introduced the unit hypercube Points in hypercube Distance between points Size and fuzziness Subset Relations between fuzzy cubes: mapping Points in hypercube Distance between points Size and fuzziness Subset Relations between fuzzy cubes: mapping Fuzzy Associative Memories
FAM Fuzzy system >Fuzzy set:points in a cube >Fuzzy system:Transform between cubes Fuzzy set Points hypercube Fuzzy System hypercube hypercube
FAM Fuzzy system ØFuzzy set: points in a cube ØFuzzy system: Transform between cubes Fuzzy set Points hypercube Fuzzy System hypercube hypercube
FAM Fuzzy associative memories are transformations Intput" Fuzzy Output Space System Space Fuzzy Set
FAM Fuzzy associative memories are transformations Fuzzy System Fuzzy Set Output Space n I p I n t p u t I Space
FAM FAM as mapping map balls of input to balls of output map close point to close point
FAM FAM as mapping ümap balls of input to balls of output ümap close point to close point
FAM FAM as encoding Encode the association as (A,B) Encode structured knowledge as "IF ..THEN
FAM FAM as encoding üEncode the association as (A, B) üEncode structured knowledge as " IF ... THEN ...
FAM FAM Rule 1 (4,B) B 0 FAM Rule 2 (A2,B2) B 02 m FAM Rule m () →B FAM System
FAM FAM System FAM Rule m FAM Rule 1 ( , ) A1 B1 ( , ) A2 B2 FAM Rule 2 ( , ) Am Bm B1 B2 Bm B 1 2 m A
Fuzzy and neural Association Memories Both Association Memories Similarities? Differences?
Fuzzy and neural Association Memories Ø Both Association Memories Ø Similarities? Ø Differences?
Fuzzy and neural Association Memories Similarities: 1.They are model-free estimator 2.Learn from samples 3.Numerical,unlike Al
Fuzzy and neural Association Memories Similarities: 1. They are model-free estimator 2. Learn from samples 3. Numerical, unlike AI
