probability and fuzzy numbers are ranged between 0 to 1. both are explaned in similar manner. what is the crisp difference between these terms?
Fuzzy logic is a theory that states that probabilities can be combined according to certain simple rules. From a probabilistic point of view these rules may or may not be fulfilled. Therefore fuzzy logic is a probabilistic theory where one has implicitly assumed that certain often unrealistic conditions hold. Some of my colleagues simply reject to review any manuscript that contains the word fuzzy. I am less dogmatic so I have review a number of such manuscripts and recommended rejection in all the cases.
Both fuzzy logic and probability try to deal with uncertainty in some way, and often try to represent how uncertainty changes as new information arrives.
It is implicit in the meaning of "probability" that all probabilities must obey the rules (axioms) of probability, and updating of uncertainty must be done according to those axioms. There is some room for producing approximate probabilities when exact calculation is too difficult, but these would be based-on/derived-from exact probability results.
In contrast,uncertainties dealt with by fuzzy logic are not constrained to obey the axioms of probability,and rules for updating uncertainties are constructed on a pretty much ad-hoc basis, with the basic justification that the rule seems reasonable, or seems to produce reasonable results for whatever context is of concern.
An internet search on "fuzzy logic and probability" produces lots of results.
But ... there is a third topic that may be of interest: this is summarized at https://en.wikipedia.org/wiki/Conservatism_(belief_revision). It is concerned with how real people, rather than machines, update their uncertainties ... typically not according to the axioms of probability. and not according to defined rules of fuzzy logic.
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