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# Fuzzy Logic

## What Is Fuzzy Logic?

Fuzzy logic is an approach to variable processing that allows for multiple possible truth values to be processed through the same variable. Fuzzy logic attempts to solve problems with an open, imprecise spectrum of data and heuristics that makes it possible to obtain an array of accurate conclusions.

Fuzzy logic is designed to solve problems by considering all available information and making the best possible decision given the input.

### Key Takeaways

• Fuzzy logic is a heuristic approach that allows for more advanced decision-tree processing and better integration with rules-based programming.
• Fuzzy logic is a generalization from standard logic, in which all statements have a truth value of one or zero. In fuzzy logic, statements can have a value of partial truth, such as 0.9 or 0.5.
• Theoretically, this gives the approach more opportunity to mimic real-life circumstances, where statements of absolute truth or falsehood are rare.
• Fuzzy logic may be used by quantitative analysts to improve the execution of their algorithms.
• Because of the similarities with ordinary language, fuzzy algorithms are comparatively simple to code, but they may require thorough verification and testing.

## Understanding Fuzzy Logic

Fuzzy logic stems from the mathematical study of multivalued logic. Whereas ordinary logic deals with statements of absolute truth (such as, "Is this object green?"), fuzzy logic addresses sets with subjective or relative definitions, such as "tall," "large," or "beautiful." This attempts to mimic the way humans analyze problems and make decisions, in a way that relies on vague or imprecise values rather than absolute truth or falsehood.

In practice, these constructs all allow for partial values of the "true" condition. Instead of requiring all statements to be absolutely true or absolutely false, as in classical logic, the truth values in fuzzy logic can be any value between zero and one. This creates an opportunity for algorithms to make decisions based on ranges of data as opposed to one discrete data point.

In standard logic, every statement must have an absolute value: true or false. In fuzzy logic, truth values are replaced by degrees of "membership" from 0 to 1, where 1 is absolutely true and 0 is absolutely false.

## History of Fuzzy Logic

Fuzzy logic was first proposed by Lotfi Zadeh in a 1965 paper for the journal Information and Control. In his paper, titled "Fuzzy Sets," Zadeh attempted to reflect the kind of data used in information processing and derived the elemental logical rules for this kind of set.

"More often than not, the classes of objects encountered in the real physical world do not have precisely defined criteria of membership," Zadeh explained. "Yet, the fact remains that such imprecisely defined 'classes' play an important role in human thinking, particularly in the domains of pattern recognition, communication of information, and abstraction."

Since then, fuzzy logic has been successfully applied in machine control systems, image processing, artificial intelligence, and other fields that rely on signals with ambiguous interpretation.

## Special Considerations

Fuzzy logic in its most basic sense is developed through decision tree type analysis. Thus, on a broader scale, it forms the basis for artificial intelligence systems programmed through rules-based inferences.

Generally, the term fuzzy refers to the vast number of scenarios that can be developed in a decision tree-like system. Developing fuzzy logic protocols can require the integration of rule-based programming. These programming rules may be referred to as fuzzy sets since they are developed at the discretion of comprehensive models.

Fuzzy sets may also be more complex. In more complex programming analogies, programmers may have the capability to widen the rules used to determine the inclusion and exclusion of variables. This can result in a wider range of options with less precise rules-based reasoning.

Fuzzy logic can be used in trading software, where it is used to analyze market data for buy and sell signals.

## Fuzzy Semantics in Artificial Intelligence

The concept of fuzzy logic and fuzzy semantics is a central component to the programming of artificial intelligence solutions. Artificial intelligence solutions and tools continue to expand in the economy across a range of sectors as the programming capabilities from fuzzy logic also expand.

IBM’s Watson is one of the most well-known artificial intelligence systems using variations of fuzzy logic and fuzzy semantics. Specifically in financial services, fuzzy logic is being used in machine learning and technology systems supporting outputs of investment intelligence.

In some advanced trading models, the integration of fuzzy logic mathematics can also be used to help analysts create automated buy and sell signals. These systems help investors to react to a broad range of changing market variables that affect their investments.

## Examples of Fuzzy Logic

In advanced software trading models, systems can use programmable fuzzy sets to analyze thousands of securities in real-time and present the investor with the best available opportunity. Fuzzy logic is often used when a trader seeks to make use of multiple factors for consideration. This can result in a narrowed analysis for trading decisions. Traders may also have the capability to program a variety of rules for enacting trades. Two examples include the following:

• Rule 1: If the moving average is low and the Relative Strength Index (RSI) is low, then sell.
• Rule 2: If the moving average is high and the Relative Strength Index (RSI) is high, then buy.

Fuzzy logic allows a trader to program their own subjective inferences on low and high in these basic examples to arrive at their own automated trading signals.

Fuzzy logic is frequently used in machine controllers and artificial intelligence and can also be applied to trading software. Although it has a wide range of applications, it also has substantial limitations.

Because fuzzy logic mimics human decision-making, it is most useful for modeling complex problems with ambiguous or distorted inputs. Due to the similarities with natural language, fuzzy logic algorithms are easier to code than standard logical programming, and require fewer instructions, thereby saving on memory storage requirements.

These advantages also come with drawbacks, due to the imprecise nature of fuzzy logic. Since the systems are designed for inaccurate data and inputs, they must be tested and validated to prevent inaccurate results.

• 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.

• Fuzzy algorithms require broad validation and verification.

• Fuzzy control systems are dependent on human expertise and knowledge.

## What Is Fuzzy Logic in Data Mining?

Data mining is the process of identifying significant relationships in large sets of data, a field that overlaps with statistics, machine learning, and computer science. Fuzzy logic is a set of rules that can be used to reach logical conclusions from fuzzy sets of data. Since data mining is often applied to imprecise measurements, fuzzy logic is a useful way of determining relevant relationships from this kind of data.

## Is Fuzzy Logic the Same as Machine Learning?

Fuzzy logic is often grouped together with machine learning, but they are not the same thing. Machine learning refers to computational systems that mimic human cognition, by iteratively adapting algorithms to solve complex problems. Fuzzy logic is a set of rules and functions that can operate on imprecise data sets, but the algorithms still need to be coded by humans. Both areas have applications in artificial intelligence and complex problem-solving.

## What Is the Difference Between Fuzzy Logic and Neural Networks?

An artificial neural network is a computational system designed to imitate the problem-solving procedures of a human-like nervous system. This is distinct from fuzzy logic, a set of rules designed to reach conclusions from imprecise data. Both have applications in computer science, but they are distinct fields.

## The Bottom Line

Fuzzy logic is an extension of classical logic that incorporates the uncertainties that factor into human decision-making. It is frequently used to solve complex problems, where the parameters may be unclear or imprecise. Fuzzy logic is also used in investment software, where it can be used to interpret ambiguous or unclear trading signals.

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1. A. Zadeh. "Fuzzy Sets," Page 338. Information and Control, 1965.