What Is Fuzzy Logic? Definition, Meaning, Examples, and History

What Is Fuzzy Logic?

Fuzzy logic is an approach to variable processing, where the same variable can process multiple possible values for truth. In essence, Fuzzy Logic is an attempt to solve problems where the available data and rules of engagement are open-ended, imprecise and ill-defined in nature, yet return a plausible range of accurate results.

It works by processing incomplete data in something akin to the manner used by a human brain: taking every little scrap of information to hand, and deciding what to do based on what is considered the best course of action with the information provided.

Key Takeaways

Fuzzy logic use could easily enhance decision-tree processing, and complicated decision trees become easier to code using a rules-based programming language.

Fuzzy logic is a generalisation of ordinary logic, in which all statements have a truth value that is one or zero. In fuzzy logic statements can have the value one, neither one nor zero, or zero, depending on how much they are true, say, 0.9 or 0.5.

In principle, this allows the approach more freedom to replicate real-world scenarios, in which genuine assertions of truth or falsehood are hard to come by.

Quantitative analysts might use fuzzy logic to fine-tune the running of their algorithms.

Because of decisional equivalence with our everyday way of thinking of things, fuzzy algorithms are actually somewhat easier to program, but then do require more thorough checking and testing.

Understanding Fuzzy Logic

Fuzzy logic is rooted in the mathematical theory of multivalued logic, a branch of mathematics that deals with sets that have a vague, imprecise, or subjective definition, rather than just a black-and-white true/false definition. Examples are things like ‘tall’, ‘large’, ‘beautiful’ and so on. Fuzzy logic mimics the way people analyse problems and make decisions, relying on vague approximations or intermediate degrees of truth, rather than black-and-white accuracy; thus it deals with shades of grey, despite the no-pain-no-gain Asian origins story mentioned above.

In reality, all these constructs admit incomplete values of the ‘true’ condition. Providing that the above venn-like diagrams involve ellipses rather than discs, as is often the case, one doesn’t have to assign values such as zero or one – as is the case in classical logic – to statements as categories of pure truth or falsity, but can allow the truth-values to be any point on the continuum between zero and one. Structurally, this enables algorithms to make determinations based upon the range of the data rather than one data point.

Fuzzy logic is now applied throughout our world in uses as diverse as: aerospace, automotive traffic control, business decision-making, industrial processes, artificial intelligence and machine learning.

In standard logic, truth-value is categorical: a statement is either true or false. Fuzzy logic replaces truth values with membership degrees between 0 and 1, where 1 represents absolute truth and 0 represents absolute falsity.

History of Fuzzy Logic

Fuzzy logic was proposed by Lotfi Zadeh in a paper published in 1965 in the journal Information and Control. The article, called ‘Fuzzy Sets’, formulated the rudimentary logical rules for the kind of set that attempts to approximate the data with which information processing is often done.

‘In the real physical world, however, the classes of objects occurring in nature seldom, if ever, have such sharply defined criteria of class membership,’ he wrote. ‘Yet, the precise classifications which are so highly valued in mathematics and related fields lean heavily on the existence of sharp boundaries.’ For Zadeh, these imprecisely defined ‘classes’ were crucial ‘in the domains of pattern recognition; in the communication of information; and in the domain of abstraction’.

Since then, the principles of fuzzy logic have been applied to machine control systems and image processing, among other applications where signals are ambiguous in their interpretation.

Fuzzy Logic and Decision Trees

So fuzzy logic in its most naive iteration is based on a sort of decision tree analysis. At a higher level, then, it gives rise to rule-based artificial intelligence systems.

In a general sense, fuzzy is used to refer to the myriad of possibilities that can be generated in a rules-based framework such as the decision tree. Codifying fuzzy logic regimes require the function of rule-based programmes; these programmes can be called fuzzy sets because they are created at the discretion of probabilistic modelling.

(Fuzzy sets could be more complex as well. In more complex programming analogies, programmers might have the ability to widen the rules used to determine the inclusion/exclusion of variables. This would produce a wider range of possibilities with less-precise rules-based reasoning.)

It is used for analysing market data used by trading software to alert for buy and sell signals.

Fuzzy Semantics in Artificial Intelligence

This fuzzy logic and fuzzy semantics is essential to program for artificial intelligence (AI) solutions that are being scaled in the economy in ever-increasing numbers of industries as such programming from fuzzy logic expands too.

Among the best-known applications of AI are those using variations of fuzzy logic and fuzzy semantics, such as the computer ‘Watson’ developed by IBM. Fuzzy logic is already being used in machine learning and technology systems that support financial service outputs of investment intelligence.

Some of what are called advanced trading models replace those trailing stop-loss buy/sell algorithms with ethereal mathematics of fuzzy logic – which attempt, in as much as anything can, to help the ‘analyst’ construct automated buy and sell investment signals to ‘help investors react to almost infinite variables of change’.

Examples of Fuzzy Logic

Sophisticated software trading models, for instance, can use programmable fuzzy sets to ‘think about’ thousands of securities, evaluate the available opportunity in real time, and then present the investor with the best available prospect. Fuzzy logic enters the picture when the trader wants to create multiple factors that need consideration, which can lead to a narrowing of the pool of analysis chosen for a trading decision. Trading decisions may also be actuated via programmed rules, such as the following two examples:

Rule 1: If the moving average is low and the RSI is low, then sell.

Rule 2: if the moving average is high and the Relative Strength Index (RSI) is high, then buy the SPY.

Using fuzzy logic, a trader can also program their own subjective inferences on what is low and what is high in these simple examples to get their own signalling mechanism, automated.

Pros and Cons of Fuzzy Logic

Besides being used in machine controllers and artificial intelligence as a fuzzy-logic system, fuzzy logic can also be used in trading software. But, regardless of its applications, it still has many limitations.

Since fuzzy logic resembles human decision-making, it becomes most useful for modelling complicated, ill-defined problems with ambiguous or garbled inputs. Because of this similarity to human logic and language, fuzzy logic algorithms are easier to code than conventional ‘dry’, logical syntax and programme languages and, because of that, they require fewer instructions – which means, of course, that they require less memory storage.

There are drawbacks to these advantages, however, due to fuzzy logic’s inherently inexact nature. Because fuzzy systems are designed to deal with inaccurate data and inputs, they must be tested and validated to avoid giving inaccurate results.

Pros and Cons of Fuzzy Logic

Pros

Fuzzy logic is more likely to reflect real-world problems than classical logic.

Fuzzy logic algorithms have lower hardware requirements than classical boolean logic.

Fuzzy algorithms can produce accurate results with imprecise or inaccurate data.

What Is Fuzzy Logic in Data Mining?

Data mining is the goal of identifying meaningful relations in big data-sets. This is an area that sits between statistics, machine learning and computer science. Fuzzy logic is a set of rules that can be used to reach some form of deterministic conclusion from a fuzzy set of inputs. Since data mining is often applied to data that contains noisy low-precision measurements, fuzzy logic provides a means of extracting meaningful relations from such data.

Is Fuzzy Logic the Same as Machine Learning?

Fuzzy logic is frequently referred to bundled together with machine learning; but it is not the same thing. Machine learning, a field that has seen a resurgence of interest, refers to computational systems or algorithms that, in an iterative manner, adapt through experience to a large, complex problem by refining their ability to solve it. Fuzzy logic, as opposed to machine learning, are rules and functions that work on non-precise data sets, requiring an initial encoding by humans, but the algorithms themselves need to be written by humans. Both areas involve applications in artificial intelligence and complex problem-solving.

What Is the Difference Between Fuzzy Logic and Neural Networks?

An artificial neural network is a simulation of the way a human-like nervous system might solve problems – not to be confused with the fuzzy-logic systems that are based on a set of stipulative rules for reaching conclusions from indefinite data. These are different topics, although both find application in computer science.

What Are the Components of Fuzzy Logic?

Fuzzy logic is often described as having four components:

Fuzzification. Converting specific input values into some level of membership of fuzzy sets, based on how well they fit.

Fuzzy rules / knowledge base: that is, our If-Then rules. The brain criteria or situation in which these rules are more or less relevant. If statements often come from expert knowledge, but can also be derived in more quantitative ways.

Fuzzy method. The system of things that make up the foundation of fuzzy systems: fuzzy variables, if-then rules, and fuzzy inference method The degree to which an input variable might be a member of the fuzzy variable mentioned therein. The fuzzy variable itself describes the action that the input variable participates in. If an input variable is a member of this fuzzy variable by a certain amount, say 75 percent, then the action that the variable performs involves assignment in the fuzzy inference process to 75 percent membership grade.Note how rule 1 handles the case where sales are above 100 (that is, where the variable commodity reaches a fuzzy value of 1.) Since ?r1? is greater than 0.1, sales will be assigned a 100 percent membership grade to ‘small’ in the result of fuzzy inference, making them definitely small. The score is also small; Fernando will be denied the prize, with rule 3 coming into play just as it did in the previous scenario. 3.

Defuzzification. The process of converting the fuzzy conclusions into detailed output values.

The Bottom Line

This is known as fuzzy logic, which is an extended version of classical logic that allows for parameters of human decision-making that are inexact, unclear or ambiguous. Fuzzy logic is commonly used to solve complex problems, particularly in situations where the parameters are ambiguous or unspecified. For instance, fuzzy logic is an underlying technology behind investment software. Fuzzy logic can help to make sense of ambiguous or unspecified trading signals.