Einstein Aggregation Research Articles

Multicriteria decision-making approach with hesitant interval-valued intuitionistic fuzzy sets.

The definition of hesitant interval-valued intuitionistic fuzzy sets (HIVIFSs) is developed based on interval-valued intuitionistic fuzzy sets (IVIFSs) and hesitant fuzzy sets (HFSs). Then, some operations on HIVIFSs are introduced in detail, and their properties are further discussed. In addition, some hesitant interval-valued intuitionistic fuzzy number aggregation operators based on t-conorms and t-norms are proposed, which can be used to aggregate decision-makers' information in multicriteria decision-making (MCDM) problems. Some valuable proposals of these operators are studied. In particular, based on algebraic and Einstein t-conorms and t-norms, some hesitant interval-valued intuitionistic fuzzy algebraic aggregation operators and Einstein aggregation operators can be obtained, respectively. Furthermore, an approach of MCDM problems based on the proposed aggregation operators is given using hesitant interval-valued intuitionistic fuzzy information. Finally, an illustrative example is provided to demonstrate the applicability and effectiveness of the developed approach, and the study is supported by a sensitivity analysis and a comparison analysis.

The induced intuitionistic fuzzy Einstein aggregation and its application in group decision-making

Einstein product and Einstein sum are good alternatives to the algebraic product and algebraic sum, respectively. Nevertheless, it seems that in the literature there is little investigation on aggregation techniques using the Einstein operations on IFS for aggregating a collection of intuitionistic fuzzy value (IFV). The induced ordered weighted averaging operator is more suitable for aggregating individual preference relations into a collective fuzzy preference relation. In order to deal with more complex group decision-making problem with intuitionistic fuzzy information, the paper develops an I-IFOWA ϵ operator which generalizes some of the intuitionistic fuzzy Einstein aggregation operators, such as the IFWA ϵ operator, IFOWA ϵ operator, IFA ϵ , as well as IF maximum operator and IF minimum operator. Furthermore, the authors apply the I-IFOWA ϵ operator and the IFWA ϵ operator to multiple attribute group decision-making with intuitionistic fuzzy information, and give an illustrative example to show the effectiveness of the developed methods.

Induced hesitant interval-valued fuzzy Einstein aggregation operators and their application to multiple attribute decision making

In this paper, we investigate the multiple attribute decision making MADM problems with hesitant interval-valued fuzzy information. We first introduce some operations on hesitant fuzzy sets, such as Einstein sum, Einstein product, Einstein exponentiation, etc., and propose the hesitant interval-valued fuzzy sets. Then, we further develop some new Einstein aggregation operators with hesitant interval-valued fuzzy information, such as the hesitant interval-valued fuzzy Einstein weighted average HIVFEWA operator, hesitant interval-valued fuzzy Einstein weighted geometric HIVFEWG operator, hesitant interval-valued fuzzy Einstein ordered weighted average HIVFEOWA operator, hesitant interval-valued fuzzy Einstein ordered weighted geometric HIVFEOWG operator, induced hesitant interval-valued fuzzy Einstein ordered weighted averaging I-HIVFEOWA operator and induced hesitant interval-valued fuzzy Einstein ordered weighted geometric I-HIVFEOWG operator. Then, we apply the induced hesitant interval-valued fuzzy Einstein ordered weighted averaging I-HIVFEOWA operator and induced hesitant interval-valued fuzzy Einstein ordered weighted geometric I-HIVFEOWG operator to deal with multiple attribute decision making under the hesitant interval-valued fuzzy environments. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.