Next Article in Journal
Local Green Power Supply Plants Based on Alcohol Regenerative Gas Turbines: Economic and Environmental Aspects
Previous Article in Journal
Investigations of Damage Characteristics in Rock Material Subjected to the Joint Effect of Cyclic Loading and Impact
Previous Article in Special Issue
Energy Fluctuations in the Homogenized Hyper-Elastic Particulate Composites with Stochastic Interface Defects
Article

A Robust q-Rung Orthopair Fuzzy Information Aggregation Using Einstein Operations with Application to Sustainable Energy Planning Decision Management

1
Department of Mathematics, University of the Punjab, Lahore 54590, Pakistan
2
Research Team on Intelligent Decision Support Systems, Department of Artificial Intelligence and Applied Mathematics, Faculty of Computer Science and Information Technology, West Pomeranian University of Technology in Szczecin, ul. Żołnierska 49, 71-210 Szczecin, Poland
3
Department of Information Systems Engineering, Faculty of Economics, Finance and Management University of Szczecin, Mickiewicza 64, 71-101 Szczecin, Poland
*
Author to whom correspondence should be addressed.
Energies 2020, 13(9), 2155; https://doi.org/10.3390/en13092155
Received: 24 March 2020 / Revised: 27 April 2020 / Accepted: 27 April 2020 / Published: 1 May 2020
(This article belongs to the Special Issue Recent Advances in Stochastic Methods for Energy Analysis)
A q-rung orthopair fuzzy set (q-ROFS), an extension of the Pythagorean fuzzy set (PFS) and intuitionistic fuzzy set (IFS), is very helpful in representing vague information that occurs in real-world circumstances. The intention of this article is to introduce several aggregation operators in the framework of q-rung orthopair fuzzy numbers (q-ROFNs). The key feature of q-ROFNs is to deal with the situation when the sum of the qth powers of membership and non-membership grades of each alternative in the universe is less than one. The Einstein operators with their operational laws have excellent flexibility. Due to the flexible nature of these Einstein operational laws, we introduce the q-rung orthopair fuzzy Einstein weighted averaging (q-ROFEWA) operator, q-rung orthopair fuzzy Einstein ordered weighted averaging (q-ROFEOWA) operator, q-rung orthopair fuzzy Einstein weighted geometric (q-ROFEWG) operator, and q-rung orthopair fuzzy Einstein ordered weighted geometric (q-ROFEOWG) operator. We discuss certain properties of these operators, inclusive of their ability that the aggregated value of a set of q-ROFNs is a unique q-ROFN. By utilizing the proposed Einstein operators, this article describes a robust multi-criteria decision making (MCDM) technique for solving real-world problems. Finally, a numerical example related to integrated energy modeling and sustainable energy planning is presented to justify the validity and feasibility of the proposed technique. View Full-Text
Keywords: q-rung orthopair fuzzy numbers; Einstein norms; aggregation operators; sustainable planning decision management q-rung orthopair fuzzy numbers; Einstein norms; aggregation operators; sustainable planning decision management
Show Figures

Figure 1

MDPI and ACS Style

Riaz, M.; Sałabun, W.; Athar Farid, H.M.; Ali, N.; Wątróbski, J. A Robust q-Rung Orthopair Fuzzy Information Aggregation Using Einstein Operations with Application to Sustainable Energy Planning Decision Management. Energies 2020, 13, 2155. https://doi.org/10.3390/en13092155

AMA Style

Riaz M, Sałabun W, Athar Farid HM, Ali N, Wątróbski J. A Robust q-Rung Orthopair Fuzzy Information Aggregation Using Einstein Operations with Application to Sustainable Energy Planning Decision Management. Energies. 2020; 13(9):2155. https://doi.org/10.3390/en13092155

Chicago/Turabian Style

Riaz, Muhammad, Wojciech Sałabun, Hafiz M. Athar Farid, Nawazish Ali, and Jarosław Wątróbski. 2020. "A Robust q-Rung Orthopair Fuzzy Information Aggregation Using Einstein Operations with Application to Sustainable Energy Planning Decision Management" Energies 13, no. 9: 2155. https://doi.org/10.3390/en13092155

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop