Interaction power Heronian mean aggregation operators for multiple attribute decision making with T-spherical fuzzy information

The interaction operation laws (IOLs) between membership functions can effectively avoid the emergence of counterintuitive situations. The power average (PA) operator can eliminate the negative effect of extremely or improperly assessments on the decision results. The Heronian mean (HM) operator is capable of examining the interrelationship between the two attributes. To synthesize the powers of the IOLs, PA and HM operators in this paper, the PA and HM operators are extended to process T-spherical fuzzy evaluation information perfectly based on the IOLs, and the T-spherical fuzzy interaction power Heronian mean (T-SFIPHM) operator and its weighted form are proposed. We further present some properties of these proposed AOs and discuss several special cases. Moreover, a novel method to T-spherical fuzzy multiple attribute decision making (MADM) problems applying the proposed AO is developed. Lastly, we present a numerical example to validate its feasibility and reasonableness, and the superiority of the developed method is further illustrated by sensitivity analysis of parameters and comparison with existing methods. The results show that proposed AOs not only can capture the interactivity among membership degree (MD), abstinence degree (AD) and non-membership degree (NMD) of T-spherical fuzzy numbers (T-SFNs), bust also ensure the overall balance of variable values in the process of information fusion and realize the interrelationship between attribute variables, so the decision results can be closer to reality and more reliable.