Fuzzy and Probability Abstract: In the real world, we use measurement based, numerical, perception based or linguistic information. The probability theory is based on perception and has only two outcomes true or false. Fuzzy theory is based on linguistic information and is extended to handle the concept of partial truth. Fuzzy values are determined between true or false. Fuzzy theory was introduced by Lotfi Zadeh as a means to model the uncertainty of natural language. How can this be explained to a person with no mathematical background.
Please explain the difference of fuzzy logic and probability with a example that can be understood in general. Let's use a simple example of your height. In probability you would define your height as a particular crisp value such as 72 inches. In probability , you assume that each person has a crisp value of height i. In fuzzy logic, we would describe height using different terms such as "tall", "very tall", "moderately tall", etc. Each of these sets includes a range of heights.
Tall might be from 68 to 76 inches, "very tall" might be from 73 to 80 inches, "moderately tall" might be from 67 to 72 inches. So a given person's height might be described by more than one set. If one was, for example, 74 inches he would be in the "tall" and "very tall" set. The other thing about fuzzy sets is that set membership is not binary. In classical logic, an element is either in or our of the set. So to sum up, probability assumes that there is a definite numerical height that we can try to make assertions about, but there is a true value which may not be known to us.
Fuzzy logic deals with fuzzy sets which cover ranges of values and are not mutually exclusive. This is how classical logic works. Probability theory points out one way to turn the answer into a "maybe". An example would be throwing two fair dices. Now consider this event:. On a theoretical level, it goes back to Aristotle's Law of the Excluded Middle that states a statement must be either True or False.
This is one of the axioms foundations of probability. This is also shown in "crisp" sets in which some object is either a member of a set or it is not.
This works well for things that can be empirically measured. But falls apart when trying to deal with non-empirical things, the best example being natural language. Fuzzy logic and statistical probability is calculated pretty much same tool.
I read this topic for some time but don't get it properly. Improve this question. Abu Hanifa. Abu Hanifa Abu Hanifa 2, 1 1 gold badge 19 19 silver badges 33 33 bronze badges. That's not enough key difference for you? Well it surely is for me Add a comment. Active Oldest Votes. Once again, because sometimes it helps Fuzzy Weather 80 percent good weather means the weather is somewhere between good and bad, but more towards the good end.
Uncertain Weather You're sitting inside and have no window. Both together You can also be unsure the current state of the weather, and in addition you want to have a fuzzy concept of good weather. Improve this answer. Community Bot 1 1 1 silver badge. Arun Aditya Arun Aditya 5 5 silver badges 7 7 bronze badges. Your first example is also probability, you just exchanged the words probability with certainty. Sign up or log in Sign up using Google.
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