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Symmetry 2018, 10(5), 140; https://doi.org/10.3390/sym10050140

Multiple Criteria Group Decision-Making Considering Symmetry with Regards to the Positive and Negative Ideal Solutions via the Pythagorean Normal Cloud Model for Application to Economic Decisions

1
School of Mathematics and Physics, Anhui Polytechnic University, Wuhu 241000, China
2
School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China
3
Lithuanian Institute of Agrarian Economics, V. Kudirkos Str. 18, LT-03105 Vilnius, Lithuania
*
Author to whom correspondence should be addressed.
Received: 14 April 2018 / Revised: 23 April 2018 / Accepted: 26 April 2018 / Published: 1 May 2018
(This article belongs to the Special Issue Solution Models based on Symmetric and Asymmetric Information)
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Abstract

Pythagorean fuzzy sets are highly appealing in dealing with uncertainty as they allow for greater flexibility in regards to the membership and non-membership degrees by extending the set of possible values. In this paper, we propose a multi-criteria group decision-making approach based on the Pythagorean normal cloud. Some cloud aggregation operators are presented in this paper to facilitate the appraisal of the underlying utilities of the alternatives under consideration. The concept and properties of the Pythagorean normal cloud and its backward generation algorithm, aggregation operators and distance measurement are outlined. The proposed approach resembles the TOPSIS technique, which, indeed, considers the symmetry of the distances to the positive and negative ideal solutions. Furthermore, an example from e-commerce is presented to demonstrate and validate the proposed decision-making approach. Finally, the comparative analysis is implemented to check the robustness of the results when the aggregation rules are changed. View Full-Text
Keywords: Pythagorean fuzzy set; normal cloud; MCGDM; backward cloud transformation Pythagorean fuzzy set; normal cloud; MCGDM; backward cloud transformation
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Zhou, J.; Su, W.; Baležentis, T.; Streimikiene, D. Multiple Criteria Group Decision-Making Considering Symmetry with Regards to the Positive and Negative Ideal Solutions via the Pythagorean Normal Cloud Model for Application to Economic Decisions. Symmetry 2018, 10, 140.

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