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Convex Aggregation Operators and Their Applications to Multi-Hesitant Fuzzy Multi-Criteria Decision-Making
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Information 2018, 9(9), 226; https://doi.org/10.3390/info9090226

Hesitant Probabilistic Fuzzy Information Aggregation Using Einstein Operations

1
Department of Applied Mathematics, Pukyong National University, Busan 608-737, Korea
2
Department of Mathematics, Korea Maritime University, Busan 606-791, Korea
*
Authors to whom correspondence should be addressed.
Received: 8 August 2018 / Revised: 1 September 2018 / Accepted: 3 September 2018 / Published: 4 September 2018
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Abstract

In this paper, a hesitant probabilistic fuzzy multiple attribute group decision making is studied. First, some Einstein operations on hesitant probability fuzzy elements such as the Einstein sum, Einstein product, and Einstein scalar multiplication are presented and their properties are discussed. Then, several hesitant probabilistic fuzzy Einstein aggregation operators, including the hesitant probabilistic fuzzy Einstein weighted averaging operator and the hesitant probabilistic fuzzy Einstein weighted geometric operator and so on, are introduced. Moreover, some desirable properties and special cases are investigated. It is shown that some existing hesitant fuzzy aggregation operators and hesitant probabilistic fuzzy aggregation operators are special cases of the proposed operators. Further, based on the proposed operators, a new approach of hesitant probabilistic fuzzy multiple attribute decision making is developed. Finally, a practical example is provided to illustrate the developed approach. View Full-Text
Keywords: hesitant probabilistic fuzzy element (HPFE); Einstein operations; hesitant probabilistic fuzzy Einstein aggregation operators; multiple attribute decision making (MADM). hesitant probabilistic fuzzy element (HPFE); Einstein operations; hesitant probabilistic fuzzy Einstein aggregation operators; multiple attribute decision making (MADM).
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Park, J.H.; Park, Y.K.; Son, M.J. Hesitant Probabilistic Fuzzy Information Aggregation Using Einstein Operations. Information 2018, 9, 226.

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