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Strict Fuzzy Sets and Strict Fuzzy Probability

Youssef Prince Abed, Abdul Hadi Nabih Ahmed, Hamiden Abd Elwahed Khalifa


Fuzzy sets have been introduced by Zadeh (1965) as a generalization of classical set theory. Each element in fuzzy belongs to the set by certain degree which is specified by membership function. From this stand point, an extension of classical probability theory is reached "fuzzy probability". However, the definition of membership function and fuzzy set operations are not strict enough to attain the law of non-contradiction and the law of exclude the middle. In this paper, we will strictly define membership function and consequently redefining fuzzy probability such that, each element has a degree of belongness to the set and still satisfying such desirable laws.


Fuzzy sets, Fuzzy probability, Strict fuzzy Sets, Strict fuzzy probability, Maximum least strict fuzz likelihood function, Strict fuzzy expectation.

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