Fuzzy logic is based on the observation that people make decisions based on imprecise and non-numerical information. Fuzzy models or sets are mathematical means of representing vagueness and imprecise information (hence the term fuzzy). These models have the capability of recognising, representing, manipulating, interpreting, and using data and information that are vague and lack certainty.[5][6]
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Fuzzification is the process of assigning the numerical input of a system to fuzzy sets with some degree of membership. This degree of membership may be anywhere within the interval [0,1]. If it is 0 then the value does not belong to the given fuzzy set, and if it is 1 then the value completely belongs within the fuzzy set. Any value between 0 and 1 represents the degree of uncertainty that the value belongs in the set. These fuzzy sets are typically described by words, and so by assigning the system input to fuzzy sets, we can reason with it in a linguistically natural manner.
Fuzzy logic and probability address different forms of uncertainty. While both fuzzy logic and probability theory can represent degrees of certain kinds of subjective belief, fuzzy set theory uses the concept of fuzzy set membership, i.e., how much an observation is within a vaguely defined set, and probability theory uses the concept of subjective probability, i.e., frequency of occurrence or likelihood of some event or condition[clarification needed]. The concept of fuzzy sets was developed in the mid-twentieth century at Berkeley [28] as a response to the lack of a probability theory for jointly modelling uncertainty and vagueness.[29]
In study19 it is proposed a fuzzy approach to measure the degree of satisfaction of graduates on the suitability of university education for working purposes. The designed fuzzy system is based on the Mamdani fuzzy inference. From the literature it is known, that the advantages of the MamdaniMethod are: 1) It is intuitive; 2) It has widespread acceptance; 3) It is simple.However, it isn't a very effective method. The reasons are the need in precise input information and also a loss of information in defuzzification process. From this viewpoint possibility measure based Aliev's fuzzy inference method is more effective20,21. This method underlies information processing in the kernel of expert system shell ESPLAN operation. We can describe advantage of this method as follows: 1) It is intuitive; 2)It has widespread acceptance; 3) It is well suited to human-like linguistic input information; 4) It allows modeling under second-order uncertainty using the possibility-probability measure; 5) Can be used as a basis of computing with words.
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