The Choquet and Sugeno Integrals as Measures of Total Effectiveness of Medicines
نویسندگان
چکیده
The concepts of the Choquet and Sugeno integrals, based on a fuzzy measure, can be adopted as useful tools in estimation of the total effectiveness of a drug when appreciating its positive influence on a collection of symptoms typical of a considered diagnosis. The expected effectiveness of the medicine is evaluated by a physician as a verbal expression for each distinct symptom. By converting the words at first to fuzzy sets and then numbers we can regard the effectiveness structures as measures in the Choquet and Sugeno problem formulations. After comparing the quantities of total effectiveness among medicines, expressed as the values of the Choquet or Sugeno integrals, we accomplish the selection of the most efficacious drug.
منابع مشابه
Aggregation functions and fuzzy measures: the multi-dimensional case
Fuzzy measures were introduced by M Sugeno in in order to express a grade of fuzziness in the same way that probability measures express a grade of random ness The Sugeno fuzzy integrals are the functionals with monotonicity de ned by using fuzzy measures Later on Murofushi and Sugeno proposed another type of fuzzy integral the Choquet integral based on the Capacity Theory developed by G Choque...
متن کاملOn a modeling of decision making with a twofold integral
A Sugeno and a Choquet integrals are commonly used fuzzy integrals for aggregation. As a generalization of both integrals, the twofold integral is induced. The twofold integral enables us to interpret two measures from a different semantics viewpoint. One corresponds to the Choquet integral and the other corresponds to the Sugeno integral. Our work is about building models for the twofold integ...
متن کاملMonotone measures–based integrals: special functionals and an optimization tool
Considering the space of all non–negative measurable functions F(X,A) linked to a fixed measurable space (X,A), the Lebesgue integral can be seen as an additive, continuous from below functional L on F(X,A), related to a measure m : A → [0,∞] given by m(A) = L(1A). We introduce several other integrals which can be seen as special functionals on F(X,A). For example, the Choquet integral [7] is a...
متن کاملGENERALIZED FUZZY VALUED $theta$-Choquet INTEGRALS AND THEIR DOUBLE-NULL ASYMPTOTIC ADDITIVITY
The generalized fuzzy valued $theta$-Choquet integrals will beestablished for the given $mu$-integrable fuzzy valued functionson a general fuzzy measure space, and the convergence theorems ofthis kind of fuzzy valued integral are being discussed.Furthermore, the whole of integrals is regarded as a fuzzy valuedset function on measurable space, the double-null asymptoticadditivity and pseudo-doub...
متن کاملThe Sugeno fuzzy integral of concave functions
The fuzzy integrals are a kind of fuzzy measures acting on fuzzy sets. They can be viewed as an average membershipvalue of fuzzy sets. The value of the fuzzy integral in a decision making environment where uncertainty is presenthas been well established. Most of the integral inequalities studied in the fuzzy integration context normally considerconditions such as monotonicity or comonotonicity....
متن کامل