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1970
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11 pages
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Sugeno and Choquet integrals have been widely studied in the literature from a theoretical viewpoint. However, the behavior of these functionals is known in a general way, but not in practical applications and in particular cases. This paper presents the results of a numerical comparison that attempts to be a basis for a better comprehension and usefulness of both integrals
Fuzzy Sets and Systems, 1996
A general procedure for calculating the fuzzy ir-~ral (FI) is developed for monotonic and single maxima functions. In the case of monotonic functions, an iterative algorithm based on the standard iteration method (SIM) is shown to converge to the FI independently of the initial value. An alternative Newton-type procedure can be applied for both monotonic and single maxima functions provided that an appropriate initial approximation is used.
Fuzzy Sets and Systems, 1992
Starting from the concept of 'equiordered functions' we characterize two types of fuzzy integrals that can be defined on any kind of fuzzy measure: Sugeno and Choquet integrals. The characterization theorems that we obtain allow us to carry out a comparative study of these two fuzzy integrals, pointing out their formal similarities and their conceptual differences.
Fuzzy Sets and Systems, 1991
Recently, the two most general and well-known fuzzy integrals (Sugeno's integral and Choquet's integral) were characterized. It was also shown how both integrals fitted the same formal model, and they only differed in the operators used. In this paper we try to analyze whether it is possible to improve those characterization theorems, and we also study the possibility of defining other fuzzy integrals following the same model but using other operators.
Fuzzy integrals have been used to fuse the evidence or opinions from a variety of sources. These integrals are nonlinear combinations of the support functions and the (possibly subjective) worth of subsets of the sources of information, realized by a fuzzy measure. There have been many applications and extensions of fuzzy integrals and this paper proposes a fuzzy Choquet integral, where the integrand takes an interval type-2 fuzzy number and the fuzzy measure is real numbervalued. Interval type-2 fuzzy numbers encode the second-order uncertainty in a fuzzy number. Type-2 fuzzy numbers have been been shown to be useful in many applications, including computing with words and control systems. We illustrate our method on several numerical examples as well as on a bioinformatics application.
In real many problems, most of criteria have interactive characteristics, which cannot be evaluated by additive measures exactly. For the human subjective evaluation processes it will be more better to apply Choquet and Sugeno integrals model together with the definition of í µí¼ − fuzzy measure, in which the property of additive is not necessary. This paper presents the application of fuzzy integrals as tool for criteria aggregation in the decision problems and evaluating medicine with illustrations of hierarchical structure of í µí¼ − Fuzzy measure for Choquet and Sugeno integrals model.
Applied Mathematics and Computation, 2005
In this paper the integration formulas of Newton CotÕs methods with positive coefficient for fuzzy integrations in [T. Allahviranloo, Newton CotÕs methods for integration of fuzzy functions, in press] are considered and then are followed by Romberg integration to obtain improvements of the approximations of fuzzy integrations. The proposed algorithm is illustrated by solving some numerical examples.
TEMA - Trends in Applied and Computational Mathematics, 2018
In this paper we study and define an adapted fuzzy integral, based on the Sugeno integral. Moreover, we present a numerical integration formula which approximates the value of the adapted fuzzy integral. Thus, we prove that the Riemann integral and the adapted fuzzy integral are equivalent for power functions. Next, we apply the formula proposed in the numerical integration, required in the finite element method, to obtain a numerical solution of a boundary value problem for the one-dimensional Poisson equation. Finally, we observed better results of the approximate solution obtained in the example with the use of our formula when compared with the simple trapezoidal rule.
Fuzzy Sets and Systems, 2013
In decision analysis and especially in multiple criteria decision analysis, several non additive integrals have been introduced in the last sixty years. Among them, we remember the Choquet integral, the Shilkret integral and the Sugeno integral. Recently, the bipolar Choquet integral has been proposed for the case in which the underlying scale is bipolar. In this paper we propose the bipolar Shilkret integral and the bipolar Sugeno integral. Moreover, we provide an axiomatic characterization of all these three bipolar fuzzy integrals.
Fuzzy Sets and Systems, 2017
Estimation of fuzzy quantities is a topic that often appears in decision making. Some of the well-known approaches are based on the integration done with respect to the probability measure and, later on, on the possibility measure and the necessity measure. The approach considered here is focused on a fuzzy measure in general as a base of integration.
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