Harmonic Mean Aggregation Operators in Spherical Fuzzy Environment and Their Group Decision Making Applications
Yaser Donyatalab, Elmira Farrokhizadeh, Seyed Davoud Seyed Garmroodi and Seyed Amin Seyfi Shishavan
Harmonic Mean as a conservative mean is the best choice to avoid outlier data. The scope of this article is to present the novel and advanced aggregation operators for the spherical fuzzy set which is based on Harmonic Mean operator by using Algebraic and Einstein Strict Archimedean T-Norm and T- Conorm. To achieve this scope, we developed and proved Spherical Fuzzy Number Algebraic Weighted Harmonic Mean (SFNAWHM), Spherical Fuzzy Number EinsteinWeighted Harmon Mean (SFNEWHM), Spherical Fuzzy Number Algebraic Ordered Weighted Harmonic Mean (SFNAOWHM), Spherical Fuzzy Number Einstein Ordered Weighted Harmonic Mean (SFNEOWHM), Spherical Fuzzy Number Algebraic Hybrid Ordered Weighted Harmonic Mean (SFNAHOWHM) and Spherical Fuzzy Number Einstein Hybrid Ordered Weighted Harmonic Mean (SFNEHOWHM). Then based on this developed aggregation operators, the new MAGDM method has been established for decision making problems and this method’s effectiveness and reliability examined by illustrative example.
Keywords: Aggregation operators, harmonic mean, spherical fuzzy sets (SFSs), algebraic strict archimedean T-norm and T- conorm, Einstein strict archimedean T-norm and T-conorm, multi-attribute group decision making (MAGD)