Next Article in Journal
The Development of a Fuzzy Logic System in a Stochastic Environment with Normal Distribution Variables for Cash Flow Deficit Detection in Corporate Loan Policy
Next Article in Special Issue
Counterintuitive Test Problems for Transformed Fuzzy Number-Based Similarity Measures between Intuitionistic Fuzzy Sets
Previous Article in Journal
Dynamic Vehicle Routing Problem—Predictive and Unexpected Customer Availability
Previous Article in Special Issue
Simple Additive Weighting Method Equipped with Fuzzy Ranking of Evaluated Alternatives
Open AccessArticle

Covering-Based Spherical Fuzzy Rough Set Model Hybrid with TOPSIS for Multi-Attribute Decision-Making

1
School of Managment, Fudan University, Shanghai 200433, China
2
School of Business, Ningbo University, Ningbo 315211, China
3
Department of Mathematics and Statistics, Faculty of Basic and Applied Sciences, International Islamic University, Islamabad 44000, Pakistan
4
Department of Mathematics, Islamabad Model College for Girls F-6/2, Islamabad 44000, Pakistan
5
Department of Mathmatics, Abdul Wali Khan University, Mardan 23200, Pakistan
*
Authors to whom correspondence should be addressed.
Symmetry 2019, 11(4), 547; https://doi.org/10.3390/sym11040547
Received: 28 February 2019 / Revised: 9 April 2019 / Accepted: 10 April 2019 / Published: 16 April 2019
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)
In real life, human opinion cannot be limited to yes or no situations as shown in an ordinary fuzzy sets and intuitionistic fuzzy sets but it may be yes, abstain, no, and refusal as treated in Picture fuzzy sets or in Spherical fuzzy (SF) sets. In this article, we developed a comprehensive model to tackle decision-making problems, where strong points of view are in the favour; neutral; and against some projects, entities, or plans. Therefore, a new approach of covering-based spherical fuzzy rough set (CSFRS) models by means of spherical fuzzy β -neighborhoods (SF β -neighborhoods) is adopted to hybrid spherical fuzzy sets with notions of covering the rough set. Then, by using the principle of TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) to present the spherical fuzzy, the TOPSIS approach is presented through CSFRS models by means of SF β -neighborhoods. Via the SF-TOPSIS methodology, a multi-attribute decision-making problem is developed in an SF environment. This model has stronger capabilities than intuitionistic fuzzy sets and picture fuzzy sets to manage the vague and uncertainty. Finally, the proposed method is demonstrated through an example of how the proposed method helps us in decision-making problems. View Full-Text
Keywords: fuzzy sets; spherical fuzzy sets; spherical fuzzy β-covering; spherical fuzzy β-covering neighborhoods; covering based spherical fuzzy rough set; spherical fuzzy TOPSIS methodology fuzzy sets; spherical fuzzy sets; spherical fuzzy β-covering; spherical fuzzy β-covering neighborhoods; covering based spherical fuzzy rough set; spherical fuzzy TOPSIS methodology
MDPI and ACS Style

Zeng, S.; Hussain, A.; Mahmood, T.; Irfan Ali, M.; Ashraf, S.; Munir, M. Covering-Based Spherical Fuzzy Rough Set Model Hybrid with TOPSIS for Multi-Attribute Decision-Making. Symmetry 2019, 11, 547.

Show more citation formats Show less citations formats
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