# Fuzzy logic

The roots of **Fuzzy logic** stretch back 2500 years, when Aristotle asserted that there were various degrees of true and false. However, it is only in the last 30 years, following the work carried out by Lotfi Zadeh, that this concept has been labelled **fuzzy logic**.

The theoretical basis of **fuzzy logic** is that mathematics can be used to link language and human intelligence (Zjawin, 1999). Fuzzy theory has evolved to represent data or activities that cannot be clearly determined within boundaries. It is the opposite of binary data which is always a Yes/No or 1 and 0 outcome. An extreme **fuzzy logic** set known as a crisp set only has 2 possibilities, but this is an example of a special set and is not representative of typical fuzzy sets.

The expression which defines fuzzy theory is TV ||0-1|| meaning that the truth-value lies between zero and one. (Abe 1995) As **fuzzy logic** uses approximate reasoning, the outcomes that are generated are neither exact nor inexact and when dealing with complex data, fuzzy theory can be used to simplify the results. The process also makes very complex results easier to prove due to the grouping of the data (the rules of inference). (McNeill 1994)

The first practical application of **fuzzy logic** was in the 1970's when a British engineer Ebrahim Mamdani was trying to develop an automated control system for a steam engine. The machine had to adjust the throttle to maintain the steam engine's speed and boiler pressure, but if a mathematical formula (intelligent algorithm) was used the results were poor (Sanchez 1997). However, when he tried an artificial intelligence method (a 'rule based expert system' - a type of fuzzy logic), which combined human expertise with a series of logic rules, the results were better than expected.

Fuzzy systems have increasingly becoming part of our lives and now have many uses. The idea has developed rapidly in Japan as many of the leading companies such as Nissan and Matsusisha have incorporated **fuzzy logic** into their products (Klir 1995). For example, Matsusisha have developed a **fuzzy logic** washing machine. At the beginning of the washing cycle the machine carries out a pre-wash and assesses the dirtiness of the water and so applies a certain measure of detergent to the cycle. The concept is that it maximizes the efficiency of the cycle and does not bleach the clothes with too much detergent. Other uses of **fuzzy logic** include; traffic light systems, video and television tuning automation and anti-lock brakes on motor vehicles.

The advantages of employing **fuzzy logic** to situations with multiple complex solutions, such as construction, are that linguistic, not numerical, variables are used, making it similar to the way humans think (McNeill 1994). Also rapid prototypes or budget costs can be created, as the information produced is not detailed. Other advantages are that **fuzzy logic** is cheaper to develop than other intelligent systems, it simplifies knowledge acquisition and representation and can accommodate rules on complexity.

The drawbacks of a **fuzzy logic** system are that it is very hard to develop a model from the outcome, as it is so broad and imprecise. Also compared to other control systems, **fuzzy logic** relies on detailed inputs and requires fine tuning before it can become operational. As construction projects are usually one-off designs there is little room for trial and error.

Perhaps the biggest drawback is that humans are culturally biased towards the avoidance of uncertainty (Hofstede, 1980) which **fuzzy logic** can generate, whereas, mathematically precise systems produce linear control models which minimize risk and are culturally more acceptable.

The text in this article is based on ‘Business Management in Construction Enterprise’ by David Eaton and Roman Kotapski. The original manual was published in 2008. It was developed within the scope of the LdV program, project number: 2009-1-PL1-LEO05-05016 entitled “Common Learning Outcomes for European Managers in Construction”. It is reproduced here in a slightly modified form with the kind permission of the Chartered Institute of Building.

--CIOB

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