CODEWITHSUNDEEP
algorithmprobabilityfuzzy-logic
Jack
Jack

Reputation: 133609

Fuzzy choice between a variable number of sets

I was wondering which is the simplest and most configurable way to obtain what I need in the following situation:

I know how to do it by hardcoding everything, but since it will need some tweaking I would like to apply a solution which easily allows me to configure how many sets I have and the single thresholds (start/end of increasing probability and start/end of decreasing prob). Of course I don't need any intersection between more than 2 sets each and a linear increase/decrease of probability is ok.. any good clues?

Thanks in advance!

Upvotes: 1

Views: 227

Answers (1)

Mikola
Mikola

Reputation: 9326

To assign the distribution of your probabilities, you could use Bernstein polynomials:

http://en.wikipedia.org/wiki/Bernstein_polynomial

These can be efficiently computed using de Casteljau's algorithm (basically it does DP on the recursion in the obvious way):

http://en.wikipedia.org/wiki/De_Casteljau's_algorithm

http://www.cs.mtu.edu/~shene/COURSES/cs3621/NOTES/spline/Bezier/de-casteljau.html

What you get as a result will be a set of weights on the distributions. To select one of your sets, you just generate a uniform random variable in [0,1] then choose the set it lands in based on these weights.

Here is some code in python which does this:

import random

#Selects one of the n sets with a weight based on x
def pick_a_set(n, x):

    #Compute bernstein polynomials
    weights = [ [ float(i == j)  for j in range(n) ] for i in range(n) ]
    for k in range(n):
        for j in range(n-k-1):
            for i in range(n):
                weights[j][i] = weights[j][i] * (1.0 - x) + weights[j+1][i] * x

    #Select using weights
    u = random.random()
    for k in range(n):
        if u < weights[0][k]:
            return k
        u -= weights[0][k]
    return 0

Upvotes: 1

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