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# Fuzzy Sets Introduction With Example

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Nasir Ahmed Mengal
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### Fuzzy Sets Introduction With Example

1. 1. 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].
2. 2. Fuzzy sets generalize classical sets, since the indicatorfunctions of classical sets are special cases of themembership functions of fuzzy sets, if the latter only takevalues 0 or 1. In fuzzy set theory, classical bivalent sets areusually called crisp sets. The fuzzy set theory can be used ina wide range of domains in which information isincomplete 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?
3. 3. Evidence Pattern Theory Recognition & Image Processing Fuzzy Logic & Fuzzy Set TheoryKnowledgeEngineering Control Theory
4. 4. Input_1 Fuzzy IF-THEN OutputInput_2 RulesInput_3
5. 5. 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???
6. 6. Summary• Fuzzy Logic can be useful in solving Human related tasks.• Evidence Theory gives tools to handle knowledge.• Membership functions and Aggregation methods can beselected according to the problem at hand.