Fuzzy logic arose from the mathematical study of multivalued logic. In contrast to ordinary logic, which deals with statements of absolute truth, such as black or white, fuzzy logic deals with sets with subjective or relative definitions, such as “tall,” “huge,” or “lovely.” This tries to replicate how people think about problems and make decisions, relying on ambiguous or imprecise values rather than absolute truth or falsity.1

In a restricted sense, fuzzy logic refers to a method of approximate reasoning, but in its broadest sense, it refers to a mathematical theory of classes with ambiguous or “fuzzy” boundaries. Unlike classical logic, which requires all claims to be either absolutely true or absolutely false, fuzzy logic allows truth values to range from zero to one. This allows algorithms to make conclusions based on ranges of data rather than a single discrete data point. These structures all allow for partial values of the “true” criterion in practice.2

Fuzzy logic is a type of variable processing that permits many truth values to be processed using the same variable. The method relies on an open, imprecise spectrum of information to solve problems, as well as heuristics that allow for accurate conclusions to be reached in a variety of ways. Fuzzy logic is used to solve problems by taking into account all relevant data and generating the best choice possible given the input. Theoretically,this indicates that the technique is better suited to match real-life situations in which unequivocal truth or untruth claims are rare. 1

So, how does fuzzy logic differ from standard logic? 

The key difference between standard and fuzzy logic is that:

  • Standard logic requires each statement to have an absolute value: true or false.
  • Truth values are substituted in fuzzy logic by degrees of “membership,” ranging from 0 to 1, with 1 being absolutely true and 0 being totally false.1

The Applications of Fuzzy Logic

The concept of fuzzy logic is gaining popularity in the corporate and industrial worlds, as well as among the general public. 

  • In the absence of comprehensive and accurate information, fuzzy sets and fuzzy logic are useful mathematical tools for modeling; uncertain systems in industry, nature, and the humanities; and facilitators for common-sense thinking in decision making. 
  • Fuzzy logic is often used in complicated situations, such as those that are difficult to describe with traditional mathematical methods, and the goal is to arrive at a decent approximate solution.2
  • In order to make subtle adjustments to changes in the environment, control systems based on fuzzy logic are utilized in many consumer electronic products. 
  • Concepts and approaches from fuzzy logic have also proven useful in linguistics, disease diagnosis, behavioral sciences, and even stock market analysis.2 
  • It is now necessary to construct a quantitative measurement of a wide range of ambiguous events, including the idea of probability. Because fuzzy logic, as a mathematical theory, widens the current framework and creates a world that incorporates new concepts, it has piqued the interest of theorists from the start.3

Introducing more children to fuzzy math could be appealing, rational, and a great idea. However, if teaching fuzzy math and fuzzy mathematical knowledge is too difficult, it is more prudent to teach ordinary math and ordinary mathematical knowledge using fuzzified educational approaches.3

References:

  1. Fuzzy Logic Definition. (n.d.). Retrieved June 10, 2022, from https://www.investopedia.com/terms/f/fuzzy-logic.asp
  2. fuzzy logic | mathematics | Britannica. (n.d.). Retrieved June 10, 2022, from https://www.britannica.com/science/fuzzy-logic
  3. Lee, B.-S., Kang, M.-, & Kwang. (1997). Fuzzy Concept and Mathematics Education. Journal of the Korea Society of Mathematical Education Series D: ÙÛÏÐâ¦ùÊÎçëÀùÊüåò¼ ½Ã¸®Áî D: Research in Mathematical Education <â¦ùÊÎçëÀaeÚϼ>, 1(1), 75–85.
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