Nfis: Adaptive Neuro-Fuzzy Inference

ANFIS: Adaptive Neuro-Fuzzy Inference Systems
Adriano Cruz Mestrado NCE, IM, UFRJ

Logica Nebulosa – p. 1/3

Summary
• • • • •

Introduction ANFIS Architecture Hybrid Learning Algorithm ANFIS as a Universal Approximatior Simulation Examples

Logica Nebulosa – p. 2/3

Introduction
• • • •

ANFIS: Artificial Neuro-Fuzzy Inference Systems ANFIS are a class of adaptive networks that are funcionally equivalent to fuzzy inference systems. ANFIS represent Sugeno e Tsukamoto fuzzy models. ANFIS uses a hybrid learning algorithm

Logica Nebulosa – p. 3/3

Sugeno Model
• • • •

Assume that the fuzzy inference system has two inputs x and y and one output z . A first-order Sugeno fuzzy model has rules as the following: Rule1: If x is A1 and y is B1 , then f1 = p1 x + q1 y + r1 Rule2: If x is A2 and y is B2 , then f2 = p2 x + q2 y + r2

Logica Nebulosa – p. 4/3

Sugeno Model - I

A1

B1

W1 X A2 Y

B2

W2 X x f1=p1x+q1y+r1 f2=p2x+q2y+r2 f= Y y w1.f1+w2.f2 w1+w2

Logica Nebulosa – p. 5/3

ANFIS Architecture
Layer1 Layer2 Layer3 Layer4 x W1 Prod A2 W2 Prod B1 Norm x y W1f2 Norm f Sum y W1f1 Layer5

A1 x

y B2

Logica Nebulosa – p. 6/3

Layer 1 - I
• Ol,i •

is the output of the ith node of the layer l.

Every node i in this layer is an adaptive node with a node function O1,i = µAi (x) for i = 1, 2, or O1,i = µBi−2 (x) for i = 3, 4 (or y ) is the input node i and Ai (or Bi−2 ) is a linguistic label associated with this node Therefore O1,i is the membership grade of a fuzzy set (A1 , A2 , B1 , B2 ).

• x •

Logica Nebulosa – p. 7/3

Layer 1 - II
•

Typical membership function: µA (x) = 1 1 + | x−ci |2bi ai

• ai , bi , ci •

is the parameter set.

Parameters are referred to as premise parameters.

Logica Nebulosa – p. 8/3

Layer 2
• •

Every node in this layer is a fixed node labeled Prod. The output is the product of all the incoming signals. Each node represents the fire strength of the rule Any other