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ANFIS Metaheuristic Time Series Forecasting Class #2: Sugeno Fuzzy Inference System and Membership Functions

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Tutorial on Sugeno Fuzzy Inference System with Python: membership functions, rules, normalization, weighted average. Episode 2 of the ANFIS Metaheuristics Time Series Forecasting series.

Software: Python (NumPy, statsmodels, PyTorch, Matplotlib)
Level: Intermediate
Duration: ± 9 min
Series total: 59 min · 6 videos
Published: October 25, 2026

Episode 2 of 6 · view syllabus

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Introduction

Here is the final result, the Sugeno fuzzy inference system we calculated layer by layer. Two inputs, four if-then rules, and a smooth output surface. These five layers of calculation are exactly the same as the five layers of ANFIS in the next episode. Let's start. Hello, welcome to episode two of the ANFIS Meta Heuristics series for time series forecasting. ANFIS is a combination of a fuzzy system and a neural network. Before building it, we must understand the fuzzy part, how numerical values are converted into membership degrees and how if-then rules produce outputs. Today we are building a Sugeno fuzzy system.

Step 1: Membership Function

Create a file named fuzzy underscore sugeno dot pey. The Gaussian function is the Gaussian membership function. Degree one is exactly at the center C, then smoothly decreases according to the width S. The bell function, generalized bell, has a flatter peak with adjustable steepness. Both functions convert numbers into membership degrees between 0 and 1.

Step 2: Five Sugeno Fuzzy Inference Layers

The Sugeno class with two inputs has two fuzzy sets for each input, low and high, resulting in four rules. Each rule has a linear consequent, Z equals P X1 plus Q X2 plus R. The inference system calculates five layers, fuzzification, rule strength with operator N as multiplication, normalization of weights, output of each rule, and weighted average as the final output.

Step 3: Step-by-Step Calculation

Create a test file named test underscore fuzzy dot pey and run it for input X1 0.3 and X2 0.7. In layer 1, X1 is low with a degree of 0.923, and X2 is high with the same degree. Rule 2, if X1 is low and X2 is high, is the strongest with a weight of 0.852, after normalization 0.761, and output of 0.39. Other rules contribute slightly. Final Sugeno output 0.4053, the weighted average of the outputs of the four rules.

Step 4: Membership Function & Output Surface

Let's take a look at the graph. The low and high Gaussian membership functions overlap with each other, so that one value can simultaneously be low and slightly high. This is the core of fuzzy logic. The middle diagram shows rule 2 dominating. The 3D output surface appears smooth without jumps, because rule transitions occur gradually. In ANFIS, the center, width, and consequent will be automatically learned from the data.

Done!

Done. We already understand the Gaussian and bell-shaped membership functions. if-then rules, and 5 Sugeno inference layers. In the next episode, we will build anfis from scratch using hybrid learning. Currently working on a thesis, dissertation, or research in the field of forecasting and artificial intelligence? Cerdas Inovasi Digital helps implement the forecasting model. From the Sugeno fuzzy system and ANFIS, parameter optimization using PSO and genetic algorithm until the LSTM and Arima comparison and the Daibold Mariano test, as well as opening a Python programming course for engineering. Want to master the entire series, from chaotic time series to statistical evaluation? All 6 episodes, complete with step-by-step PDF guides, The dataset and source code are available to premium tutorial subscribers. Subscribe starting at Rp69.000 per month, save 28% with the 12-month package, or pay once Rp999.000 for lifetime access. Want just one class? Buy single class with lifetime access. Subscribe now on the premium page cerdasinovasidigital.com. Contact our WhatsApp or visit cerdasinovasidigital.com. Thank you for watching, see you in the next episode.

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Transcript

0:03Introduction

0:48Step 1: Membership Function

1:52Step 2: Five Sugeno Fuzzy Inference Layers

4:10Step 3: Step-by-Step Calculation

5:48Step 4: Membership Function & Output Surface

7:39Done!

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My notes

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Transcript

0:03Introduction

0:48Step 1: Membership Function

1:52Step 2: Five Sugeno Fuzzy Inference Layers

4:10Step 3: Step-by-Step Calculation

5:48Step 4: Membership Function & Output Surface

7:39Done!

Ask the class material

My notes

Questions & answers

Your instructor

Introduction

Step 1: Membership Function

Step 2: Five Sugeno Fuzzy Inference Layers

Step 3: Step-by-Step Calculation

Step 4: Membership Function & Output Surface

Done!

Introduction

Step 1: Membership Function

Step 2: Five Sugeno Fuzzy Inference Layers

Step 3: Step-by-Step Calculation

Step 4: Membership Function & Output Surface

Done!