# Is fuzzy logic connected to neural networks?

Fuzzy logic is typically used in control theory and engineering applications, but is it connected fundamentally to classification systems?

Once I have a trained neural network (multiple inputs, one output), I have a nonlinear function that will turn a set of inputs into a number that will estimate how close my set of given inputs are to the trained set.

Since my output number characterizes "closeness" to the training set as a continuous number, isn't this kind of inherently some sort of fuzzy classifier?

Is there a deep connection here in the logic, or am I missing something?

They are unrelated.

There is a possibility of interpreting fuzzy values as probabilities, but strictly speaking they are different: fuzzy values are vague, while probabilities reflect likelihood (see Wikipedia entry for Fuzzy Logic)

While rolling a particular number on a six-side die has a probability of $$1 \over 6$$, a roll can actually only ever have one outcome.

A fuzzy value "quite old" can simultaneously be member of a number of fuzzy sets with different degrees of membership, eg "young" with 0.001, "adolescent" with 0.1, "old" with 0.4, "ancient" with 0.7. Unless it is "defuzzified", it is simultaneously contained in all the sets.

Defuzzyfication is a way of interpreting the result of a series of fuzzy operations and finding the set that best matches, but it is not a clearly defined process such as picking a random number according to a set of probabilities (or rolling the die).

I am not sure that the sum of all fuzzy set membership values of any given fuzzy value has to add up to 1.0; whereas this condition has to hold for probabilities.

[EDIT: to clarify - probabilities are not a set; I refer here to all possible outcomes of a random event which have a certain probability of being realised. The sum of all possible event probabilities has to be 1.0]

One alternative interpretation for your application could be the confidence that the input set is identical to the training set. Which could be a fuzzy value if you wanted to do something else with it, eg by combining it with other fuzzy variables.

• There is no such thing like a “set of probabilities”. A dice has always the chance of 1/6 for a certain side. A chance like “a little bit 1/6” or “very likely 1/6” doesn't make much sense. – Manuel Rodriguez Feb 19 '19 at 10:37
• @ManuelRodriguez I'm not mentioning "sets of probabilities" anywhere. – Oliver Mason Feb 19 '19 at 11:02
• Are the outputs of neural nets explicit probabilities? Could you maybe link me to something that makes clear? Also, intuitively if you trained a neural network on pictures of bald men, somehow it's hard for me to believe that the "baldness" output is actually a probability of being bald. (Relative frequency makes some sense though) – Steven Sagona Feb 19 '19 at 23:43
• It's not a probability, it's a weight score. Basically, you put in some feature values, theses are combined, weighted, and filtered through the activation function, and then come out at the output nodes. So they are neither probabilities nor fuzzy values. – Oliver Mason Feb 20 '19 at 9:29
• Okay but now I'm a bit lost as to what your argument is. You say that fuzzy logic isnt connected to neural nets. But your reasoning is that it's because fuzzy logic isn't the same as probability. But you give no reason as to why or how probabilities are connected to neural networks. So what your point in talking about probabilities in the first place? – Steven Sagona Feb 20 '19 at 21:17