24 Fuzzy set theory
Capturing the truth in ‘usually’
Boolean logic states that a concept is either true or false; i.e., 1 = true, 0 = false. Boolean logic uses the operators and, or, and not with each assessing a condition and returning 1 or 0. However, fuzzy logic posits that a concept possesses a degree of truth varying between 0 and 1 [1]. Fuzzy logic would be most applicable to vague, or subjectively judged, concepts. For example, a freshly brewed cup of coffee can be judged as ‘hot’, evidenced by the emerging steam. However, one may judge the coffee to be very hot, while another may judge it to be mildly hot. The state of ‘hot’ can be concluded to be likely, but with a degree of truth [2]. Several individuals could estimate this degree of truth to be 0.65, 0.75, 0.80; i.e., it is likely the coffee is hot, but different people have varying judgments on how hot the coffee is.
Fuzzy logic represents uncertain information and then focuses on formal principles of approximate reasoning or imprecise modes of reasoning [2]. Fuzzy logic assesses truths on a scale of what is ‘usually’ or ‘likely’ true, or what is ‘not quite true’, based on common sense knowledge [2]. It should be clear that any of these qualifiers inherently reflects some uncertainty.
References
- Scientific American, 1999. What is ’fuzzy logic’? Are there computers that are inherently fuzzy and do not apply the usual binary logic?
- Zadeh, L. A., 1988. Fuzzy logic. Computer 21, 83.
- Excerpted from – Emma K. Redfoot, Kelley M. Verner, R. A. Borrelli (2022). Applying analytic hierarchy process to industrial process design in a nuclear renewable hybrid energy system. Progress in Nuclear Energy 145, 104083