Fuzzy Logic

Self Organizing Maps (SOM) technique was developed in 1982 by a professor, Tuevo Kohonen. Professor Kohonen worked on auto-associative memory during the 1970s and 1980s and in 1982 he presented his self-organizing map algorithm. SOMs are named as “Self-Organizing” because no supervision is required. Self-organizing maps learn on their own through unsupervised competitive learning. They … Read more

A cluster is comprised of a number of similar feature vectors group together. If there are ‘d‘ features used to describe the data, a cluster can be described as a region in d-dimensional space containing a relatively high density of points separated from other such reasons regions by regions containing a relatively low density of … Read more

Operations on Fuzzy Set 1. Subset A ⊂ B ↔ μA(x) ≤ μB(x),      ∀ x ∈ X 2. Complement Ac ↔ μAc(x) = 1 − μA(x),      ∀ x ∈ X 3. Superset A ⊃ B ↔ μA(x) ≥ μB(x),      ∀ x ∈ X The characteristic function will never exceed beyond the value of 1. It’s value varies between 0 and 1 always. 4. Intersection … Read more

1. Triangular MF 2. Trapezoidal MF 3. Gaussian MF 4. Generalized bell MF 5. Sigmoidal MF

T-norm (Triangular norm) ——> Fuzzy Intersection T-norm operator: A∩B ↔ µA∩B (x) = T (µA(x), µB(x)) = µA(x) ∧ µB(x),     ∀ x ∈ X where ∧ is for T-norm operator (example, min. product) Definition of T-norm operator A T-norm operator denoted by T(a,b) is a function mapping [0,1]×[0,1] to [0,1] that satisfies the following conditions for any … Read more