Fuzzy Measures and Integrals as Aggregation Operators : Solvingthe
نویسنده
چکیده
The aim of this paper is to shed some light on the use of fuzzy measures and integrals as aggregation operators in multicriteria decision making. These techniques have been widely used on an ad hoc basis, but with no ax-iomatization. It is possible to obtain preference representation theorems in multicriteria decision making problems, relying on a formal parallelism between decision under uncertainty and multicriteria decision making. Though, it raises some commensurability problems. In this paper, we show how to obtain an axioma-tization of multicriteria decision making problems , in a very natural way, and we show how to solve the commensurability problem in a particular case.
منابع مشابه
Defining Fuzzy Measures: A Comparative Study with Genetic and Gradient Descent Algorithms
Due to limitations of classical weighted average aggregation operators, there is an increase usage of fuzzy integrals, like the Sugeno and Choquet integrals, as alternative aggregation operators. However, their applicability has been threatened by the crux of determining the fuzzy measures in real problems. One way to determine these measures is by using learning data and optimizing the paramet...
متن کاملAggregation 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 کاملAggregation operators for fuzzy ontologies
Fuzzy ontologies extend classical ontologies to allow the representation of imprecise and vague knowledge. Although a relatively important amount of work has been carried out in the field during the last years and they have been successfully used in several applications, several notions from fuzzy logic have not been considered yet in fuzzy ontologies. Among them are aggregation operators, math...
متن کاملASSOCIATED PROBABILITY INTUITIONISTIC FUZZY WEIGHTED OPERATORS IN BUSINESS START-UP DECISION MAKING
In the study, we propose the Associated Probability Intuitionistic Fuzzy Weighted Averaging (As-P-IFWA) and the Associated Probability Intuitionistic Fuzzy Weighted Geometric (As-P-IFWG) aggregation operators with associated probabilities of a fuzzy measure presenting an uncertainty. Decision makers' evaluations are given as intuitionistic fuzzy values and are used as the arguments of the aggre...
متن کاملNegations and aggregation operators based on a new hesitant fuzzy partial ordering
Based on a new hesitant fuzzy partial ordering proposed by Garmendia et al.~cite{GaCa:Pohfs}, in this paper a fuzzy disjunction ${D}$ on the set ${H}$ of finite and nonempty subsets of the unit interval and a t-conorm ${S}$ on the set $bar{{B}}$ of equivalence class on the set of finite bags of unit interval based on this partial ordering are introduced respectively. Then, hesitant fuzzy negati...
متن کامل