What Is Fuzzy Logic? Definition, Working, Pros and Cons
As per fuzzy logic, there can be multiple versions of truth instead of the true/false binary proposed by 0 and 1.
Fuzzy logic is defined as a problem-solving approach that proposes multiple truth variables, which can be any real number between 1 and 0, as opposed to the binary version of the truth, which can either be 1 or 0. This article explains the definition of fuzzy logic, its working, merits, and demerits.
Table of Contents
What Is Fuzzy Logic?
Fuzzy logic is a problem-solving approach that proposes multiple truth variables, which can be any real number between 1 and 0, as opposed to the binary version of the truth, which can either be 1 or 0.
In our everyday lives, we cannot always choose to simply say Yes or No. This happens because you may encounter circumstances where you lack sufficient knowledge to make a judgment. Alternatively, you could be slightly puzzled yourself. For instance, if someone asks if you are present on a specific day next month, you will likely not respond immediately with a Yes or No because you cannot be certain about your plans that day.
Not easy, right? In such scenarios, fuzzy logic, a form of artificial intelligence, enables computers to handle ambiguous input data.
Fuzzy logic is used as a decision-making strategy when a machine learning framework or artificial intelligence is used. It may be stated generally as evaluating actual variable values ranging from 0 and 1. Fuzzy logic is applied to represent real numbers between 0 and 1.
Fuzzy refers to anything that is rather ambiguous. When a scenario is ambiguous, the computer may be unable to generate a True or False conclusion. According to Boolean Logic, 1 represents True, and 0 represents False. In contrast, a fuzzy logic method considers all the ambiguities of an issue, where there could be more potential values than True and False.
Fuzzy logic is used to achieve precise values as problem resolutions. Fuzzy logic views human thinking as the most important data format for making precise conclusions. It captures the precise value from a decision tree analysis.
Fuzzy logic was created in 1965 at the University of California by Lotfi Zadeh, who dubbed it “fuzzy”. He believed that conventional computer logic could not handle confusing or imprecise data. Like humans, a computer may integrate a wide range of values within True and False. These can be Definitely yes, Maybe yes, Can’t say, Maybe no, and Definitely no.
The fuzzy logic controller (FLC) is a mechanism used to regulate the operation of a physical system. FLC regulates washers, air conditioners, heaters, fan regulators, traffic controls, and the controller for the brake system, among other applications. When a precise mathematical explanation of the issue is not attainable, we use FLC.
Fuzzy logic is particularly helpful in modeling complicated issues with uncertain or distorted inputs because it mirrors human decision-making. Due to their parallels with common speech, fuzzy logic programs are simpler to implement than conventional logical programming or object-oriented programming. Moreover, it needs fewer instructions, thus reducing memory storage needs.
Here is a simple example of fuzzy logic to help you understand what it means:
Problem question: Is it sunny outside today?
Boolean solution: Yes (1) or No (0).
In accordance with standard Boolean algebra, the algorithm will accept a specific input and create a definite output, either Yes or No. This is represented accordingly by 1 and 0. But once you apply fuzzy logic, several other answers emerge.
Fuzzy logic solution:
- Very sunny with rare clouds (0.95)
- Moderately sunny (0.75)
- Partly sunny and partly cloudy (0.5)
- A little sunny but mostly cloudy (0.3)
- Very cloudy with rare sunny periods (0.1)
According to the above illustration, Fuzzy Logic offers a larger range of outputs, including very, slightly, and not at all. These numbers between 0 and 1 represent the range of possible outcomes.
Fuzzy logic delivers an acceptable alternative when precise reasoning cannot be offered. A fuzzy logic-based method utilizes all relevant facts to solve a problem. It then makes the optimal choice based on the inputs provided.
Fuzzy logic vs. probability
Although the phrases seem identical, fuzzy logic and probability are not synonymous. Fuzzy logic is a philosophy with degrees of imperfect truth. Probability, on the other hand, deals with clear concepts and assertions — ideas that can be either true or untrue. The probability of a statement is the degree of confidence in its veracity.
The distinction between fuzzy logic with probability lies in their respective meanings. Probability is related to events, not facts, and occurrences would either occur or not. There is no ambiguity involved. In contrast, fuzzy logic essentially attempts to capture the essence of ambiguity. It largely refers to the degree of truth.
Probability theory cannot be used to reason with propositions that are neither completely true nor untrue.
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How Does Fuzzy Logic Work?
Fuzzy Logic is highly beneficial for simulating human thought in a controlled ecosystem. It is more concerned with acceptable logic, which closely resembles how the actual world functions. It is intended to handle uncertainty and is adept at drawing conclusions from the result. To use fuzzy logic, one needs to follow these steps:
- Select what you are trying to control: The user must understand what he is attempting to manage, the needed reaction, potential system flaws, and how to operate the system.
- Identify the relationship between input, output, and potential variations and error/exception: Users must evaluate the connection between outputs and inputs and choose the minimal number of input variables and error rate for fuzzy logic.
- Create the if/then rule: By using the rule-based architecture of fuzzy logic, firstly decompose the control issue into a sequence of “IF A AND B THEN C“ rules that specify the intended response under specified situations. The rule’s complexity is determined by the number of inputs and variables connected with each input.
- Write the code function: Create a membership function for fuzzy logic that defines the weighted value of input and output elements.
- Outline the cycle of operations: Create a method for fuzzy logic before and after its hardware or software implementation.
- Test your systems: System testing and result evaluation enable you to fine-tune membership functions as well as rules. Repeatedly test and adjust to achieve the desired outcomes.
Fuzzy logic aims to answer challenges with an open, imperfect spectrum of facts and heuristics, which allows for various correct conclusions. Per the fuzzy logic controller’s operating concept, the output depends on the likelihood of the input state. It operates on the notion of output choice founded on assumptions via fuzzy sets. Each set comprises linguistic variables that define the output’s state.
To comprehend the exact functioning of fuzzy logic, let’s understand its primary architectural building blocks.
1. Rules base
This consists of the collection of rules and If-Then conditions required to arrive at judgments. However, recent advancements in Fuzzy Logic significantly decreased the number of laws in the rule base. This collection of rules is also known as a knowledge base.
2. Fuzzification process
In this stage, distinct integers are turned into fuzzy sets. A crisp set consists of components with similar characteristics. Depending on specific reasoning, an element may or may not belong to the set. Crisp sets are built on binary logic, or responses of Yes or No.
Using this architectural component, the error signals, as well as physical data, are transformed into a fuzzy subset that has been normalized. In every Fuzzy Logic framework, a fuzzifier divides the incoming signals into the following five states: a large positive or LP, a medium positive or MP, a small or S, a medium negative or MN, and a large negative or LN. The fuzzification process turns sensor inputs (like room temperature) into a form suitable for further processing by the control system.
3. Inference engine
It aids in determining the degree of compatibility among fuzzy inputs and rules. It selects which rules must be executed for the current input field based on the percent match. The applicable rules are then integrated to produce the control actions. In a fuzzy logic system, the inference system and the database combined are referred to as the controller.
By creating fuzzy inferences based on the inputs and “if-then“ rules, this approach helps simulate the human thinking process.
4. Defuzzification
This is the opposite of the fuzzy process. Through mapping, the fuzzy data is transformed into precise values. There are several defuzzification algorithms available for this purpose, but the optimal one is chosen based on the input. This is a complex procedure that employs many computational approaches, including the maximum membership concept, the weighted average technique, and the centroid method.
5. Sets of linguistic variables
Linguistic variables are essentially the system’s input and output variables. Most of the entries in these fields are words and phrases from natural languages with no numeric value. Variables in linguistics may be broken down into linguistic terminology.
6. Membership functions
The membership function is a graphical chart that describes the mapping between each point in the input space and a membership number between 0 and 1. It permits the quantification of linguistic concepts and the graphical representation of a fuzzy collection. A numeric value may be fuzzified by several membership functions. Complex membership functions are not used since they do not add accuracy to the result.
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Importance of Fuzzy Logic
Decision tree analysis is used to construct fuzzy logic in its rudimentary form. Consequently, it serves as the foundation for artificial intelligence (AI) algorithms built with rule-based conclusions. Fuzzy logic and fuzzy semantics (linguistic variables) are fundamental to the programming of AI technologies. Even as the programming capacities of fuzzy logic increase, AI solutions and applications continue to proliferate across various industries.
Watson, developed by IBM, is among the most popular AI systems utilizing fuzzy logic or fuzzy semantics. In the financial services industry, fuzzy logic is employed with machine learning and related technology systems to provide investment intelligence reports.
Fuzzy logic and machine learning are sometimes clubbed together. However, they are not identical. Machine learning alludes to computing systems that simulate human cognition by adjusting algorithms to tackle complicated problems repeatedly. Fuzzy logic is a collection of rules or functions that can work on inaccurate datasets, but humans must still write the algorithms. Both disciplines have applicability in artificial intelligence and the solution of complicated problems.
Data mining is the practice of uncovering meaningful correlations in huge data sets. It is a discipline that intersects with mathematics, machine learning, and computer science. Fuzzy logic principles may be used on fuzzy data sets to achieve logical conclusions. Fuzzy logic is a good method for detecting meaningful correlations from this type of data since data mining often involves imperfect measurements.
Analysts may generate automatic buy and sell signals by using fuzzy logic mathematics in certain sophisticated trading algorithms. These technologies assist investors in responding to a vast array of fluctuating market conditions that impact their assets.
Fuzzy logic is also widely used in washers and dryers. Fuzzy logic-powered washing machines feature sensors that continually monitor temperature fluctuations. Accordingly, it modifies the controls and processes. These systems are effective, productive, and cost-effective.
Fuzzy logic regulates the washing, factors like temperature, spinning velocity, wash time, water input, and rinse performance for optimal results. They learn from past washing experiences and remember washing algorithms to improve washing outcomes.
Most systems are built on energy-saving methods that enable you to conserve electricity when doing your laundry. Even if you clean several clothing items two or three times every week, these tools help you save electricity. The sensors are used to monitor the whole washing procedure and make any required modifications or corrections to provide the best possible washing results.
In their dishwashers, manufacturers such as Panasonic employ comparable technologies. Fuzzy logic is used to change the cleaning cycles and wash and rinse techniques of dishwashers. The efficiency of the machine is also dependent on how many dishes are loaded into the dishwasher.
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Pros and Cons of Fuzzy Logic
Fuzzy logic is used extensively in controllers, artificial intelligence, and trading software. While it has many uses, it also has significant limitations.
Fuzzy logic is particularly helpful for modeling complex problems with uncertain or distorted inputs because it mirrors human decision-making. Due to their parallels with common speech, fuzzy logic techniques are simpler to implement than conventional logical programming and need fewer instructions, reducing memory storage needs.
These benefits are accompanied by disadvantages owing to the imperfect structure of fuzzy logic. Since the systems are intended to accommodate erroneous data or sources, they must be verified and validated to avoid producing false results.
The major pros of fuzzy logic include the following:
- This system can operate with any sort of input, including inaccurate, distorted, or noisy data.
- Set theory and other mathematical principles are a part of fuzzy logic, and the explanation for this is straightforward.
- As it mirrors human thinking and decision-making, it offers an efficient solution to complex challenges in all areas of life.
- The algorithms may be explained with little data, using little memory.
- This form of reasoning requires less storage space and may be encoded with less data.
- The system is easily modifiable to enhance or alter performance.
- Fuzzy logic may be written when the feedback sensor fails to function.
- Classical logic is less likely to depict real-world challenges than fuzzy logic.
Some of its challenges include the following:
- There is a need for extensive validation and verification of fuzzy algorithms.
- Fuzzy control methods rely on human skill and understanding.
- Unless specifically configured, these systems will be incapable of recognizing machine learning or neural network platforms.
- Defining precise fuzzy sets or membership functions takes time and effort.
- Fuzzy logic is only sometimes correct. Therefore, the apparent findings depend on preconceptions and might not be broadly accepted.
- Numerous scholars have offered various fuzzy logic solutions to a particular situation, resulting in ambiguity. With fuzzy logic, there is no systematic strategy to solve a specific issue.
Fuzzy logic presents an alternate method of approaching real-world computer challenges. It readily applies to various applications or control systems, yielding long-term advantages. Given its compatibility with “degree of truth,“ it paves the way for several advancements in computing. It is not, however, the only answer for all problems — it has significant limits in terms of precision and its failure to pivot, based on its errors, as it is with machine learning.
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Takeaway
Fuzzy logic is a crucial concept developers must understand today. Modern apps no longer deal with simple problems like adding numerical figures or recording text. They tell users what they should watch, the products they should buy, and the best way to get to a new restaurant. These are complex problems that require nuanced handling, with room for a degree of ambiguity. Fuzzy logic gives you the best possible solution without wasting resources on trying to find the only solution to a problem.
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