Fermatean Hesitant Fuzzy Prioritized Heronian Mean Operator and Its Application in Multi-Attribute Decision Making

In real life, incomplete information, inaccurate data, and the preferences of decision-makers during qualitative judgment would impact the process of decision-making. As a technical instrument that can successfully handle uncertain information, Fermatean fuzzy sets have recently been used to solve the multi-attribute decision-making (MADM) problems. This paper proposes a Fermatean hesitant fuzzy information aggregation method to address the problem of fusion where the membership, non-membership, and priority are considered simultaneously. Combining the Fermatean hesitant fuzzy sets with Heronian Mean operators, this paper proposes the Fermatean hesitant fuzzy Heronian mean (FHFHM) operator and the Fermatean hesitant fuzzy weighted Heronian mean (FHFWHM) operator. Then, considering the priority relationship between attributes is often easier to obtain than the weight of attributes, this paper defines a new Fermatean hesitant fuzzy prioritized Heronian mean operator (FHFPHM), and discusses its elegant properties such as idempotency, boundedness and monotonicity in detail. Later, for problems with unknown weights and the Fermatean hesitant fuzzy information, a MADM approach based on prioritized attributes is proposed, which can effectively depict the correlation between attributes and avoid the influence of subjective factors on the results. Finally, a numerical example of multi-sensor electronic surveillance is applied to verify the feasibility and validity of the method proposed in this paper.