What is the best resource to understand the possibility of A given B occurring in possibility space?

12 December 2015 3 10K Report

I'm currently reading this article: "R. Sujatha, T. Rajalaxmi, and B. Praba, "Fuzzy Hidden Markov Chain For Web Applications," International Journal of Information Technology & Decision Making, vol. 12, pp. 813-835, 2013."

In page 816, author investigating possibility of A given B. He was already talking about fuzzy number and then talk about possibility theory. My question is: what is the best resource to understand the possibility of A given B occurring in possibility space? (something like p(A|B) in probability theory)

Article Fuzzy hidden Markov chain for web applications

A Ramamoorthy VEC

Go through this URL and understand the conditional probability for your questions

https://books.google.co.in/books?id=lHNSZn0jr_IC&printsec=frontcover&dq=probability+and+random+processes&hl=en&sa=X&redir_esc=y#v=onepage&q=probability%20and%20random%20processes&f=false

Steve Ataky T. M

We may first ask to our selves what does the probability of A given B mean.

In fact, the conditional probability is the probability of an event occurring, given that another event has occurred. Let suppose the probability of someone doing physics at A-Level, given that he is doing chemistry may be quite high. P(A. B) stands for the probability of A occurring, given that B has occurred.

We can also say that the conditional probability of an event B is the probability that the event will occur given the (previous) knowledge that an event A has already occurred. This probability is written P(B|A), that is, the probability of B given A. In the case where events A and B are independent, that is, where event A has no effect on the probability of event B, the conditional probability of event B given event A is simply the probability of event B, that is P(B).

Thereby, if events A and B are not independent, then the probability of the intersection of A and B (the probability that both events occur) is defined by P(A and B) = P(A)P(B|A).

Anything we can help, let us know.

You can also check:

http://www.stat.yale.edu/Courses/1997-98/101/condprob.htm

http://www.mathgoodies.com/lessons/vol6/conditional.html

Mostafa Heidary

Thanks @Steve and @(A Ramamoorthy VEC).

I know probability of A given B. The thing I don't know is their possibility.

possibility is defined in fuzzy measure. (generally fuzzy logic)

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