Hi r/fuzzylogic,

Home automation systems are one of the most natural real-world applications for fuzzy control, yet mainstream smart home platforms (like Home Assistant) still rely almost entirely on binary thresholds, PID controllers, or custom scripting.

To bridge this gap, I’ve built a full fuzzy inference engine for Home Assistant and just submitted a formal proposal to have it integrated into Home Assistant Core as a built-in helper:

👉 **[Home Assistant Architecture Discussion #1504: Built-in Fuzzy Logic Controller Helper](https://github.com/home-assistant/architecture/discussions/1504)\*\*

### What Was Built

The integration brings declarative linguistic control to smart home entities:

- **Inference Engines**: Both Mamdani and Sugeno (zero-order and first-order).

- **Membership Functions**: Standard Triangular (`trimf`), Trapezoidal (`trapmf`), Gaussian (`gaussmf`), Sigmoidal (`sigmf`), and Generalized Bell (`gbellmf`).

- **Linguistic Hedges**: Support for concentration/dilation modifiers (`very`, `extremely`, `somewhat`, `slightly`, `not`) evaluated both inline in rules and on term definitions.

- **Defuzzification Algorithms**: Centroid (COG), Bisector (BOA), Mean of Maxima (MOM), SOM, LOM, Center of Sums (COS), and Weighted Average.

- **Full Observability**: Exposes real-time rule firing strengths ($\alpha$-cuts), term memberships, and universe distributions directly to the Home Assistant dashboard for live diagnostics.

- **Optimized for Embedded/IoT**: Pre-compiles DNF rule condition trees, membership function closures, and defuzzification dispatch tables on initialization for $O(1)$ evaluation on low-power devices (Raspberry Pi, ODROID, home servers).

### Core Problem Solved

In smart homes, controlling non-linear multi-input processes—such as HVAC fan modulation (indoor temp + outdoor delta + relative humidity), excess solar power diversion, or weather-aware irrigation—typically causes threshold "hunting" or requires complex PID tuning that fails due to large thermal lags. Fuzzy inference handles these naturally with simple, human-readable rules.

### Source Code

The working implementation and unit test suite are open source on GitHub:

🔗 **[dougransom/fuzzy_system](https://github.com/dougransom/fuzzy_system)\*\*

### Call to Action

As fuzzy logic practitioners, your insights on rule formulation, inference models, and real-world control applications would be invaluable for this proposal.

Please check out the discussion on GitHub and add your perspective on how fuzzy systems can best serve smart home automation:

👉 **[Comment on Home Assistant Architecture Discussion #1504](https://github.com/home-assistant/architecture/discussions/1504)\*\*

hello friends!

I'm new to fuzzy and I'm studying fuzzy applied to complex judicial decisions..

I've started with zadeh to learn the basics.. what else would you recommend?

Check out a wonderful paper with DOI: 10.3390/en17143434 which discusses the application of interval type-2 fuzzy logic systems in controlling linear stages within a feedback-error-learning (FEL) control structure. mdpi.com/2867642 #mdpienergies via @energies_mdpi

He was a professor at the University Leipzig, Germany and died unexpectedly in 2015 with only 72 years. He wrote more than 150 scientific papers with a focus on multi value logic and fuzzy logic. He left 3 children.

The fuzzy boom in Japan after the year 1990 is commonly recognized as the starting point in mainstream adoption of Fuzzy logic for practical application. A seldom mentioned much earlier project was done in Germany in the year 1987: Vitra (Visual translator) was based on Fuzzy logic to convert camera signals of traffic scenes into textual description. Typical words used in the Vitra software were: near, far, left, right which are describing relations and proximity.

Even i'm not the author of the library, i can give a short overview about the project. The software library is located within the python ecosystem and is known under two different names: scikit-fuzzy and skfuzzy. It can be installed with the normal pip installer and depends on external libraries like Matplotlib, NumPy and other. The syntax for the rule parser is a bit complicated but can be mastered with little amount of effort. Here is an example.

rule="IF the obstacle is Near AND the speed is Fast, THEN the brake pressure is High." written in skfuzzy:

from skfuzzy import control as ctrl

obstacle = ctrl.Anticedent(np.arange(0, 11, 1), 'obstacle')
speed = ctrl.Anticedent(np.arange(0, 11, 1), 'speed')
brake = ctrl.Consequent(np.arange(0, 11, 1), 'brake')
rule1 = ctrl.Rule(obstacle['near'] & speed['fast'], brake['high'])

The library was released in 2013 and has endless amount of functions for c-means clustering, interval subtraction and different membership functions like triangular, gaussian and of course trapezoidal.

Good afternoon, everyone. It's a pleasure to speak with you today about what might seem like a paradoxical concept: customer relationship management with fuzzy logic for a surveillance camera. We are accustomed to thinking of surveillance as a security tool—a binary system of observation, where an event either occurs or it doesn't. However, by integrating a sophisticated AI with fuzzy logic principles, we can transform this passive security instrument into an active sensor for customer behavior.

Traditional surveillance systems operate on a limited, black-and-white logic. A camera detects a person’s presence or their absence. It identifies an object or a breach. This binary approach provides critical security data, but it utterly fails to capture the nuances of human interaction that are essential for effective customer relationship management. How does a camera know if a customer is "interested" in a product, "frustrated" with a layout, or "satisfied" with their experience? These are not discrete states; they are a spectrum of behaviors that require a more sophisticated form of analysis.

This is where fuzzy logic, as developed by Lotfi Zadeh, becomes our key tool. Instead of boolean values of true or false, fuzzy logic allows variables to exist on a continuum between 0 and 1. We can program our camera-linked AI to move beyond simple detection and into qualitative analysis of behavior. The camera, in this new paradigm, becomes a sophisticated CRM sensor, feeding a fuzzy inference system with a variety of CRM-relevant inputs.

Consider the following fuzzy variables that can be derived from visual data:

• Degree of Interest: How long a customer is looking at a specific item or display. This isn't a yes/no; it's a value, say from 0.0 (no interest) to 1.0 (very high interest).
• Customer Agitation: Analyzed through body language—pacing, hand gestures, or repeated checks of a watch. This can be quantified as a value from 0.0 (calm) to 1.0 (highly frustrated).
• Engagement Level: The level of interaction with a product or a screen. A quick glance might be a 0.2, while active manipulation of an item might be a 0.8.

These fuzzy inputs are then processed by a set of "if-then" rules to generate actionable outputs. For instance:

• IF "Degree of Interest" is high AND "Customer Agitation" is low, THEN trigger a "Potential Sale" alert to a store associate.
• IF "Degree of Interest" is medium AND "Customer Agitation" is high, THEN trigger a "Customer Needs Assistance" alert to an associate in that area.
• IF "Engagement Level" is low AND "Movement Speed" is slow, THEN a "Lost Customer" alert might be generated, suggesting an opportunity to provide directions.

By moving from simple security monitoring to nuanced behavioral analysis, the surveillance camera transforms into a proactive component of a CRM strategy. It enables businesses to respond to customer needs in real-time, optimize store layouts, and improve the overall shopping experience. This is a clear demonstration of how advanced AI, when applied with an understanding of human behavior, can turn a security device into a powerful engine for customer satisfaction.

The following text is written as a dialogue, instead of a monologue.

Alex: Hey Ben, got a minute? I was just looking at our CRM data, and it's frustrating how much we're missing. We're classifying customers as "loyal" or "not loyal," and it feels so rigid.

Ben: I know what you mean. It's an oversimplification. A customer who buys once a year but spends a lot isn't "loyal" by our system, but they're definitely a valuable asset. So, what's the alternative?

Alex: I've been researching something called fuzzy logic. Instead of binary true/false statements, it deals with degrees of truth. It's perfect for handling the kind of ambiguity we see in customer behavior.

Ben: Fuzzy logic? Like, vague logic? How would that help?

Alex: Think of it this way: a traditional system might say a customer is either 100% "loyal" or 0% "loyal." A fuzzy system recognizes that a customer can be loyal to a certain degree. For example, a customer could be 85% "loyal," 60% "frequent," and 10% "at-risk."

Ben: I see. So it's about nuance. But how do you calculate those percentages?

Alex: That's where the "fuzziness" comes in. We'd define rules based on our data, but they aren't hard and fast. For example, a rule might be: "IF a customer's purchase frequency is 'high' AND their average spend is 'very high,' THEN their loyalty is 'very high.'" The key is that "high" and "very high" are defined by membership functions, not a single number. A purchase of 10 items per month might be considered 90% "high" and 20% "very high."

Ben: That makes a lot more sense. So we're moving from a simple classification to a more complex, multi-dimensional score?

Alex: Exactly. And this isn't just for loyalty. We could use it for churn prediction. Instead of "will churn" or "won't churn," we get a churn risk score. This lets our support team prioritize customers who are at a "high risk" of leaving, even if they haven't stopped buying completely. They could get a proactive call or an exclusive offer.

Ben: That's a huge step up from just reacting when a customer goes silent. What other applications could this have?

Alex: It could be used to analyze customer sentiment from open-ended feedback or support tickets. Instead of just "positive" or "negative," we could get a score for "very satisfied," "slightly disappointed," or "neutral." This provides a more accurate picture of a customer's overall experience. It helps us predict what they might need next, even if they haven't explicitly asked for it.

Ben: So, it's about making our CRM more intelligent and human-centric by embracing the ambiguity of human behavior. It sounds like a powerful way to personalize our outreach and improve customer satisfaction. Where do we even start with implementing something like this?

Alex: That's the next step! I have some ideas on how we could build a small prototype to demonstrate the value. Let's talk to the tech team and see what's possible.

1. Who is credited with introducing the concept of fuzzy sets and fuzzy logic? a) Alan Turing b) Marvin Minsky c) Lotfi A. Zadeh d) John McCarthy

2. In what year was Lotfi A. Zadeh's seminal paper "Fuzzy Sets" published, which introduced the concept of fuzzy logic? a) 1950 b) 1965 c) 1972 d) 1980

3. What primary limitation of classical set theory and Boolean logic did fuzzy logic aim to address? a) The inability to process very large amounts of data. b) Difficulties in representing uncertainty, vagueness, and imprecision. c) The lack of computing power for complex mathematical calculations. d) The need to precisely model purely random events.

4. What fundamental mathematical concept did Lotfi A. Zadeh introduce as the basis of fuzzy logic? a) Binary Logic b) Neural Networks c) Fuzzy Sets d) Quantum Algorithms

5. How was fuzzy logic initially received within the Western academic community? a) With immediate and widespread acceptance. b) With skepticism and criticism, particularly in the US. c) Primarily as a purely biological model. d) It was ignored as a pure theory without practical application.

6. Which country was instrumental in being the first to successfully apply fuzzy logic in real-world industrial systems, particularly in the control system of the Sendai Subway? a) USA b) Germany c) Japan d) Soviet Union

7. In which application area did fuzzy logic find early and very successful use? a) Financial modeling and stock trading b) Image and speech recognition c) Control engineering and control systems d) Cryptography and data security

8. How does a fuzzy set fundamentally differ from a classical (crisp) set? a) Classical sets can only contain numbers, while fuzzy sets only contain text. b) Classical sets have sharp boundaries (an element is either fully included or not at all), while fuzzy sets allow for degrees of membership between 0 and 1. c) Classical sets are infinite, while fuzzy sets are always finite. d) Classical sets use probabilities, while fuzzy sets are strictly based on yes/no decisions.

9. What term did Zadeh coin for variables whose values are words or sentences in a natural language (e.g., "tall," "warm," "fast")? a) Semantic Variants b) Probability Variables c) Linguistic Variables d) Contextual Variables

10. Beyond control engineering, which other area of Artificial Intelligence has fuzzy logic significantly influenced? a) Robotics and autonomous navigation. b) Expert systems and decision-making under uncertainty. c) Artificial neural networks and deep learning. d) Computer vision and image processing.

Correct Answers:

1. c) Lotfi A. Zadeh
2. b) 1965
3. b) Difficulties in representing uncertainty, vagueness, and imprecision.
4. c) Fuzzy Sets
5. b) With skepticism and criticism, particularly in the US.
6. c) Japan
7. c) Control engineering and control systems
8. b) Classical sets have sharp boundaries (an element is either fully included or not at all), while fuzzy sets allow for degrees of membership between 0 and 1.
9. c) Linguistic Variables
10. b) Expert systems and decision-making under uncertainty.

Multiple Choice Quiz: Fuzzy Logic in Pattern Recognition

1. What is the primary characteristic that distinguishes fuzzy logic from classical (Boolean) logic in the context of pattern recognition? a) Fuzzy logic uses only binary (0 or 1) values. b) Fuzzy logic allows for degrees of truth, rather than just absolute true or false. c) Fuzzy logic is exclusively used for supervised learning. d) Fuzzy logic does not use sets or set operations.

2. In fuzzy logic, what does a "membership function" represent? a) The probability that an element belongs to a set. b) A crisp boundary defining whether an element is inside or outside a set. c) The degree to which an element belongs to a fuzzy set, typically a value between 0 and 1. d) A statistical distribution of data points.

3. Which of the following is the main purpose of "fuzzification" in a fuzzy logic system for pattern recognition? a) Converting fuzzy outputs into crisp values. b) Defining the rules for inference. c) Transforming crisp input data into fuzzy sets or linguistic terms. d) Optimizing the membership functions.

4. When classifying a pattern using fuzzy logic, if an object has a membership degree of 0.8 in "Class A" and 0.3 in "Class B", what does this typically imply? a) The object definitely belongs to Class A and definitely not to Class B. b) The object belongs to Class A with a higher degree of certainty than to Class B. c) The object cannot be classified. d) The object is equally likely to belong to Class A or Class B.

5. Which fuzzy clustering algorithm is widely used in pattern recognition for partitioning data points into fuzzy clusters, where each point can belong to multiple clusters with varying degrees of membership? a) K-Means Clustering b) Hierarchical Clustering c) DBSCAN d) Fuzzy C-Means (FCM)

6. One significant advantage of using fuzzy logic in pattern recognition, particularly for real-world data, is its ability to: a) Achieve faster computation for all types of data. b) Handle imprecision, uncertainty, and vagueness in data and definitions. c) Eliminate the need for any human expert knowledge. d) Guarantee optimal solutions in all classification tasks.

7. What is "defuzzification" primarily concerned with in a fuzzy inference system for pattern recognition? a) Creating fuzzy rules from crisp data. b) Converting fuzzy linguistic outputs (e.g., "high", "medium") into a single, crisp numerical output. c) Defining the shape of membership functions. d) Identifying input features for the pattern.

8. In a fuzzy pattern recognition system, how might fuzzy rules (e.g., IF-THEN rules) be utilized? a) To directly assign crisp class labels without any inference. b) To model relationships between input features and output classes based on linguistic terms. c) To randomly generate membership functions. d) To perform statistical hypothesis testing on the data.

9. Which of these scenarios is most likely to benefit from a fuzzy logic approach in pattern recognition? a) Classifying emails as spam or not spam using very clear, distinct keywords. b) Distinguishing between handwritten digits where boundaries between digits (e.g., 7 and 9) can be ambiguous. c) Detecting a specific, highly predictable signal in a very clean dataset. d) Performing simple arithmetic calculations on precise numbers.

10. Compared to traditional crisp classification methods, fuzzy pattern recognition methods often provide: a) Less interpretability due to complex mathematical functions. b) A crisp, hard boundary for classification that avoids ambiguity. c) More nuanced and descriptive results by indicating degrees of belongingness. d) Significantly slower processing times for all datasets.

Correct Answers:

1. b) Fuzzy logic allows for degrees of truth, rather than just absolute true or false.
2. c) The degree to which an element belongs to a fuzzy set, typically a value between 0 and 1.
3. c) Transforming crisp input data into fuzzy sets or linguistic terms.
4. b) The object belongs to Class A with a higher degree of certainty than to Class B.
5. d) Fuzzy C-Means (FCM)
6. b) Handle imprecision, uncertainty, and vagueness in data and definitions.
7. b) Converting fuzzy linguistic outputs (e.g., "high", "medium") into a single, crisp numerical output.
8. b) To model relationships between input features and output classes based on linguistic terms.
9. b) Distinguishing between handwritten digits where boundaries between digits (e.g., 7 and 9) can be ambiguous.
10. c) More nuanced and descriptive results by indicating degrees of belongingness.

Fuzzy Logic: Commercial Software and Hardware

1. Which of the following is a common application area for commercial fuzzy logic systems? a) High-frequency trading b) Autonomous vehicles c) Cryptographic algorithms d) Database management

2. Which software tool is well-known for providing a graphical environment for designing and simulating fuzzy logic systems? a) Microsoft Excel b) MATLAB Fuzzy Logic Toolbox c) Adobe Photoshop d) Oracle SQL Developer

3. In commercial fuzzy logic controllers, what is the process of converting crisp (numerical) inputs into fuzzy sets called? a) Defuzzification b) Inference c) Fuzzification d) Aggregation

4. Which of the following hardware components is specifically designed to accelerate fuzzy logic computations? a) Graphics Processing Unit (GPU) b) Tensor Processing Unit (TPU) c) Fuzzy Logic Controller (FLC) chip d) Central Processing Unit (CPU)

5. Which industry has widely adopted fuzzy logic for improving the efficiency and control of household appliances? a) Aerospace b) Consumer electronics c) Pharmaceutical d) Construction

6. What is the primary goal of the "defuzzification" step in a fuzzy logic system? a) To define the fuzzy membership functions. b) To apply fuzzy operators (like AND, OR) to the fuzzy sets. c) To convert a fuzzy output back into a crisp (numerical) value. d) To establish the rule base of the fuzzy system.

7. Which of the following is a key advantage of using fuzzy logic in commercial applications? a) It requires precise and noise-free input data. b) It can effectively handle uncertainty and vagueness in data. c) It always provides a single, definitive "true" or "false" output. d) Its design process is strictly linear and deterministic.

8. Which programming language is commonly used for implementing fuzzy logic algorithms in commercial software? a) HTML b) CSS c) Python d) Assembly language

9. In the context of commercial control systems, fuzzy logic is often integrated with other AI techniques. Which of the following is a common combination? a) Fuzzy logic and blockchain technology b) Fuzzy logic and neural networks c) Fuzzy logic and quantum computing d) Fuzzy logic and relational databases

10. Which of the following companies is known for offering commercial software or hardware solutions related to fuzzy logic? a) SpaceX b) MathWorks c) Tesla d) Amazon

Answers:

1. b) Autonomous vehicles
2. b) MATLAB Fuzzy Logic Toolbox
3. c) Fuzzification
4. c) Fuzzy Logic Controller (FLC) chip
5. b) Consumer electronics
6. c) To convert a fuzzy output back into a crisp (numerical) value.
7. b) It can effectively handle uncertainty and vagueness in data.
8. c) Python
9. b) Fuzzy logic and neural networks
10. b) MathWorks

Fuzzy Logic Quiz

1. What is the core concept behind fuzzy logic? (a) Crisp and definite values (b) Probabilistic reasoning (c) Degrees of truth (d) Boolean algebra

2. In fuzzy logic, a membership function assigns values to elements of a set. What is the range of these membership values? (a) 0 or 1 (b) -1 to 1 (c) 0 to 1 (d) Any real number

3. Which of the following is a common type of membership function? (a) Gaussian (b) Exponential (c) Logarithmic (d) Tangent

4. What is the fuzzy logic equivalent of the Boolean AND operator? (a) Maximum (b) Minimum (c) Average (d) Sum

5. What is the fuzzy logic equivalent of the Boolean OR operator? (a) Minimum (b) Maximum (c) Product (d) Difference

6. The process of converting crisp input values into fuzzy sets is called: (a) Defuzzification (b) Fuzzification (c) Inference (d) Aggregation

7. The process of converting a fuzzy set back into a crisp value is called: (a) Fuzzification (b) Inference (c) Defuzzification (d) Composition

8. Which of the following is a common defuzzification method? (a) Min-max composition (b) Sum of products (c) Center of gravity (centroid) (d) Mamdani implication

9. Fuzzy logic is particularly well-suited for systems that involve: (a) Precise measurements (b) Binary decisions (c) Uncertainty and vagueness (d) Deterministic behavior

10. Which of the following is a real-world application of fuzzy logic? (a) Cryptography (b) Database management (c) Washing machines (d) Compiler design

Answers

1. (c) Degrees of truth
2. (c) 0 to 1
3. (a) Gaussian
4. (b) Minimum
5. (b) Maximum
6. (b) Fuzzification
7. (c) Defuzzification
8. (c) Center of gravity (centroid)
9. (c) Uncertainty and vagueness
10. (c) Washing machines

Hey guys, I have Fuzzy Sets as my elective paper, I have a doubt in defuzzification method "Weighted average", to my understanding it is applicable only to symmetric function, then it is not applicable for the following right?

Can anyone please clarify this~~!!

I need help finding data to train and apply fuzzy logic. If you know any platforms, websites, or applications that could help, please don't hesitate to share. Thank you very much! My system includes a battery, a fuel cell, and engine PMSP.

I. Prolegomena: The Ontological Primacy of Vagueness

• A. Historical Precursors to Fuzzy Conceptualizations: From Aristotle to Lukasiewicz.
  • Subtopic: The limitations of bivalent logical systems in modeling phenomenological uncertainty.
  • Subtopic: The nascent inklings of multivalued logic within scholastic dialectics.
• B. The Epistemological Necessity of Fuzzy Set Theory.
  • Subtopic: The inadequacy of crisp sets in representing real-world, non-discrete data.
  • Subtopic: The introduction of the "membership function" as a tool for quantifiable ambiguity.
• C. Defining the Universe of Discourse: A Multidimensional Hyperplane.
  • Subtopic: The delineation of relevant variables within a non-Euclidean, fuzzy space.
  • Subtopic: The complexities of defining the boundaries of fuzzy sets within a non-linear, dynamic system.

II. The Algorithmic Choreography of Fuzzy Inference

• A. Fuzzy Operators: A Lexicon of Linguistic Hedges.
  • Subtopic: The nuanced application of "AND," "OR," and "NOT" within fuzzy domains.
  • Subtopic: The intricate interplay of t-norms and s-norms in fuzzy set manipulation.
• B. Rule-Based Systems: The Articulation of Heuristic Imperatives.
  • Subtopic: The formulation of "IF-THEN" rules as a framework for expert knowledge encoding.
  • Subtopic: The process of fuzzyfication and defuzzyfication.
• C. The Confluence of Fuzzy Logic and Adaptive Control.
  • Subtopic: The application of fuzzy logic to create self-adjusting systems.
  • Subtopic: The complexities of real time processing of fuzzy values.

III. The Transcendent Applications and Future Trajectories

• A. Fuzzy Logic in Advanced Computational Paradigms.
  • Subtopic: The integration of fuzzy logic with neural networks and genetic algorithms.
  • Subtopic: The application in high level artificial intelligence.
• B. The Quantum Entanglement of Fuzzy Logic and Information Theory.
  • Subtopic: The theoretical implications of fuzzy logic within quantum computing.
  • Subtopic: The exploration of fuzzy entropy and its implications for information processing.
• C. Eschatological Considerations: The Future of Fuzzy Logic in a Post-Singularity World.
  • Subtopic: Speculative extrapolations on the role of fuzzy logic in emergent computational systems.
  • Subtopic: Ethical ramifications of fuzzy logic in autonomous decision-making processes.

IV. Post-Lecture Colloquium: A Discourse on the Nuances of Fuzzy Axiomatics

• A. Open Forum for the Dissection of Ambiguous Theoretical Constructs.
• B. Collaborative Exploration of Unresolved Paradoxes within Fuzzy Set Theory.
• C. The Formulation of Novel Axiomatic Frameworks for Future Research.

On a busy street, there are endless amount of cars, buses and trucks who are driving in both directions. The objective is to count and categorize them. For reason of simplification there are only three length-related categories available:

carlength=Neuron({"short":[0,5], "medium":[5,10], "long":[10,20]})

The measurement apparatus provides a signal with the precise length in meters, for example: 4.52 meters. Such kind of precision isn't needed in statistics so the signal gets discretized into a categorical variable with the help of a binning algorithm. The method "setcrisp()" iterates over all possible categories and determines the membership function for each category. In other words, it checks, if the measured signal fits to one of the bins. The result is stored in the neuron.

def setcrisp(self,crisp):
  for i in self.data:
    a=self.data[i][0]
    b=self.data[i][1]
    self.fuzzyvalue[i]=self.getmf(a,b,crisp)

To investigate the system under practical conditions, some random measurements are needed which are simulated in a loop:

for i in range(10):
  signal=round(random.random()*20,2)
  carlength.setcrisp(signal)
  print(signal,carlength.fuzzyvalue)

The overall program is available in the appendix. After starting the program, the following result gets generated:

5.84 {'short': 0, 'medium': 1, 'long': 0}
14.38 {'short': 0, 'medium': 0, 'long': 1}
11.65 {'short': 0, 'medium': 0, 'long': 1}
9.27 {'short': 0, 'medium': 1, 'long': 0}
6.36 {'short': 0, 'medium': 1, 'long': 0}
7.07 {'short': 0, 'medium': 1, 'long': 0}
18.64 {'short': 0, 'medium': 0, 'long': 1}
9.68 {'short': 0, 'medium': 1, 'long': 0}
9.85 {'short': 0, 'medium': 1, 'long': 0}
5.55 {'short': 0, 'medium': 1, 'long': 0}

What we see is a list with measured car length in the simulation and the mapped category to the signal. For example, the first line assigns the length=5.84 meter value to the category "medium".

There is no need for using dedicated Fuzzy membership functions which are working with overlapping categories. In the simplified example, all the categories are boolean. That means, a car belongs either to the medium or to long category, but never to both at the same time. This fits better to classical statistics and it allows to convert the data into a histogram.

import random

class Neuron():
  def __init__(self,data):
    self.data=data
    self.fuzzyvalue={}
  def setcrisp(self,crisp):
    for i in self.data:
      a=self.data[i][0]
      b=self.data[i][1]
      self.fuzzyvalue[i]=self.getmf(a,b,crisp)
  def getmf(self,a,b,crisp): # Binning membership function
    # input: [0,4] 1.5, return: value between 0 and 1
    if a <= crisp < b: return 1 # in between
    else: return 0

if __name__ == '__main__':
  carlength=Neuron({"short":[0,5], "medium":[5,10], "long":[10,20]})
  for i in range(10):
    signal=round(random.random()*20,2)
    carlength.setcrisp(signal)
    print(signal,carlength.fuzzyvalue)

The best way to learn something in computer science is a hands on approach. Instead of using existing software created by someone else, the idea is to implement an algorithm from scratch. Not because the resulting software is more efficient, but because it allows to learn something about a domain.

Programming an entire Fuzzy inference system (FIS) is a very complex task which goes beyond this mini tutorial. What can be explained instead, is how to implement a single neuron as a building block for a larger FIS. Instead of using multiple Fuzzy membership functions only a simplified membership function is introduced which is basically a binning algorithm.

The program starts with a Python class which provides a membership function:

class Neuron():
  def __init__(self,data):
    self.data=data
    self.fuzzyvalue={}
  def getmf(self,a,b,crisp): 
    # Binning membership function
    # input: [0,4] 1.5, return: value between 0 and 1
    if a <= crisp < b: return 1 # in between
    else: return 0

This class gets initialized from the command line by creating a new neuron for storing the x_position of a measured signal:

xpos=Neuron({"left":[-4,0], "right":[0,4]})

To apply a crisp value to the Neuron, some additional methods are needed. The sourcecode of the class including a simple demo are given at the end of this tutorial. It takes less than 30 lines of code. The example shows how to assign random values to the xpos Neuron and investigate what the translated Fuzzy values are. The idea is, that a value like x=2 gets converted into multiple bins for the left and right position. In the example, the x=2 gets converted into {'left': 0, 'right': 1} That means it belongs to the category right:

xpos=Neuron({"left":[-4,0], "right":[0,4]})
xpos.setcrisp(2)
xpos.show()

Binning allows to categorize data. There are intervals available and the algorithm decides which of the intervals fits to the input data.

Let me give another example. Suppose we send the crisp value x=5 to the neuron:

xpos=Neuron({"left":[-4,0], "right":[0,4]})
xpos.setcrisp(5)
xpos.show()
# output: {'left': 0, 'right': 0}

In such a case, no interval fits to the value. The bins for (left, right) are both empty. This is because the membership function, which was initialized first, returns for the x=5 value a 0 in return.

With this explanation, this mini tutorial ends. A possible further exercise would be to create a second neuron which stores the yposition and contains of the bins for (up, down). Feel free to implement this neuron.

class Neuron():
  def __init__(self,data):
    self.data=data
    self.fuzzyvalue={}
    self.reset()
  def reset(self): # set fuzzy values to 0
    for i in self.data:
      self.fuzzyvalue[i]=0
  def show(self):
    print(self.data)
    print(self.fuzzyvalue)
  def setcrisp(self,crisp): 
    for i in self.data:
      a=self.data[i][0]
      b=self.data[i][1]
      self.fuzzyvalue[i]=self.getmf(a,b,crisp)
  def getmf(self,a,b,crisp): 
    # Binning membership function
    # input: [0,4] 1.5, return: value between 0 and 1
    if a <= crisp < b: return 1 # in between
    else: return 0

if __name__ == '__main__':
  xpos=Neuron({"left":[-4,0], "right":[0,4]})
  for i in range(-5,5):
    print(i)
    xpos.setcrisp(i)
    xpos.show()
    xpos.reset()

Hey guys. Recently i have been developing a fuzzy logic crate. It's has been a great journey and I learned a lot. As of now I have implemented Both Mamdani and TSK inference systems. I have a road map in mind and want to improve it continuously. You can check it out from links below. My next step is to add type 2 fuzzy systems. I am currently styding Mechatronics Engineering for my masters degree so I need your help to point out my mistakes and help me improve it. Thank you guys

https://crates.io/crates/fuzzy-logic_rs

https://github.com/MechaNeurons/fuzzy-logic-rs