Post on 03-Dec-2014
description
Nasir Ahmed MengalRoll No - 20
Class - Final YearSubject – Artificial
Intelligence
CSE&S Department
Presentation
‘Fuzzy Sets’
Introduction...
Fuzzy set:
Fuzzy sets are sets whose elements have degrees of membership. Fuzzy sets were introduced simultaneously by Lotfi A. Zadeh and Dieter Klaua in 1965 as an extension of the classical notion of set. In classical set theory, the membership of elements in a set is assessed in binary terms according to a bivalent condition — an element either belongs or does not belong to the set.
By contrast, fuzzy set theory permits the gradual assessment of the membership of elements in a set; this is described with the aid of a membership function valued in the real unit interval [0, 1].
Fuzzy sets generalize classical sets, since the indicator functions of classical sets are special cases of the membership functions of fuzzy sets, if the latter only take values 0 or 1. In fuzzy set theory, classical bivalent sets are usually called crisp sets. The fuzzy set theory can be used in a wide range of domains in which information is incomplete or imprecise, such as bioinformatics.
Examples of fuzzy sets include: {‘Tall people’}, {‘Nice day’}, {‘Round object’} …If a person’s height is 1.88 meters is he considered ‘tall’?
What if we also know that he is an NBA player?
Fuzzy Logic & Fuzzy
Set Theory
Evidence Theory
Pattern Recognition & Image Processin
g
Control Theory
Knowledge
Engineering
Some Related Fields
Input_1 Fuzzy IF-THEN
Rules
OutputInput_2
Input_3
Fuzzy inference expert system
Fuzzy vs ProbabilityWalking in the desert, close to being
dehydrated, you find two bottles of water:The first contains deadly poison with a
probability of 0.1The second has a 0.9 membership value in the
Fuzzy Set “Safe drinks”Which one will you choose to drink from???
Summary• Fuzzy Logic can be useful in solving Human related tasks.
• Evidence Theory gives tools to handle knowledge.
• Membership functions and Aggregation methods can be selected according to the problem at hand.
THANKS…