Additivity and Monotonicity in Fuzzy Measures
نویسنده
چکیده
Our paper deals with the necessary properties in Fuzzy Measures. Therefore, it belongs to Fuzzy Mathematical Analysis. The Possibility Theory was created by Zadeh in a paper of 1978. As general purpose, to obtain a way to model flexible restrictions constructed from vague pieces of information. If we study the counterparts of expectations (from Probability Theory) in Possibility Theory, we obtain the Sugeno and Choquet Integrals. This last is based on a generalization of Lebesgue Integral. We can reach the Possibility and Necessity of Fuzzy Events as particular cases of Sugeno Integrals. But with more generality, will take the aforementioned Fuzzy Measures, with detailed analysis of its fundamental classes, according the fulfillment or not of additivity and monotonic properties. In this way, I hope to advance with my paper.
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