Aggregation functions and fuzzy measures: the multi-dimensional case
نویسندگان
چکیده
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 Choquet in Many authors have investigated on the characteriza tion of Sugeno and Choquet integrals P Wakker D Schmeidler D Dubois H Prade R Sabbadin J L Marichal Both fuzzy integrals have proved to be very useful as aggregation operators
منابع مشابه
Trapezoidal intuitionistic fuzzy prioritized aggregation operators and application to multi-attribute decision making
In some multi-attribute decision making (MADM) problems, various relationships among the decision attributes should be considered. This paper investigates the prioritization relationship of attributes in MADM with trapezoidal intuitionistic fuzzy numbers (TrIFNs). TrIFNs are a special intuitionistic fuzzy set on a real number set and have the better capability to model ill-known quantities. Fir...
متن کامل(T) FUZZY INTEGRAL OF MULTI-DIMENSIONAL FUNCTION WITH RESPECT TO MULTI-VALUED MEASURE
Introducing more types of integrals will provide more choices todeal with various types of objectives and components in real problems. Firstly,in this paper, a (T) fuzzy integral, in which the integrand, the measure andthe integration result are all multi-valued, is presented with the introductionof T-norm and T-conorm. Then, some classical results of the integral areobtained based on the prope...
متن کاملHesitant q-rung orthopair fuzzy aggregation operators with their applications in multi-criteria decision making
The aim of this manuscript is to present a new concept of hesitant q-rung orthopair fuzzy sets (Hq-ROFSs) by combining the concept of the q-ROFSs as well as Hesitant fuzzy sets. The proposed concept is the generalization of the fuzzy sets, intuitionistic fuzzy sets, hesitant fuzzy sets, and Pythagorean fuzzy sets as well as intuitionistic hesitant fuzzy sets (IHFSs) and hesitant Pythagorean fuz...
متن کاملON THE FUZZY SET THEORY AND AGGREGATION FUNCTIONS: HISTORY AND SOME RECENT ADVANCES
Several fuzzy connectives, including those proposed by Lotfi Zadeh, can be seen as linear extensions of the Boolean connectives from the scale ${0,1}$ into the scale $[0,1]$. We discuss these extensions, in particular, we focus on the dualities arising from the Boolean dualities. These dualities allow to transfer the results from some particular class of extended Boolean functions, e.g., from c...
متن کاملOn extension of fuzzy measures to aggregation functions
In the paper we study a method extending fuzzy measures on the set N = {1, . . . , n} to n-ary aggregation functions on the interval [0, 1]. The method is based on a fixed suitable n-ary aggregation function and the Möbius transform of the considered fuzzy measure. This approach generalizes the wellknown Lovász and Owen extensions of fuzzy measures. We focus our attention on the special class o...
متن کامل