To make it short, I need to use OWA for aggregating certain criteria to explain user behavior on social networks. Fuzzy logic is something new for me, and terminology is very heavy (what is type 1 and type 2 anyways?) in the papers I need to read. I found some good web sites about Fuzzy logic, and I will be sharing what I learned from them, and the papers:

Universe of discourse is the range of all possible values for an input to a fuzzy system.

Support of a Fuzzy set F is the crisp set of all points in the universe of discourse U such that the membership function of F is non zero.

Membership function, μA(x): The idea comes from classical set theory. In classical theory we say that 2 and 4 are not members of odd numbers set {1,3,5,7,…,2n+1}. In this case memberships of 2 and 4 are 0 (they are not in the set), memberships of 1,3,5 are 1 (they are in the set). In fuzzy logic, an element can have a membership value between 0 and 1, and this value is its membership degree. In μA(x), A is the fuzzy set, and x is the element.

Crisp Set: If the membership degree  of each element in a set can either be 0 or 1, the set is a crisp set.

Crisp Value: If a value is a certain precise number, it is a crisp value. For example, 1 kg is equivalent to  1000 grams, so kg has a crisp value.

Linguistic label: Experts’ opinions which are presented not in mathematical values, but in language labels. “Strong”, “weak”, “big” and “small” are linguistic labels. 1.5 is not a linguistic label.

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