Vol.:(0123456789) Artifcial Intelligence Review https://doi.org/10.1007/s10462-020-09925-3 1 3 Generalized Maclaurin symmetric mean aggregation operators based on Archimedean t‑norm of the intuitionistic fuzzy soft set information Harish Garg 1  · Rishu Arora 1 © Springer Nature B.V. 2020 Abstract Intuitionistic fuzzy soft set (IFSS) accommodates more uncertainties within the informa- tion by considering the parameterization feature than the intuitionistic fuzzy sets and hence its applications are more extensive. Archimedean T-conorm and T-norm (ATT), consists of T-norm and T-conorm classes, is as an essential source to make the comprehensive opera- tional laws. Meanwhile, the Maclaurin symmetric mean (MSM) has a prominent character- istic and the advantage that it can take into account the interrelation between multi-input arguments, including diferent attributes or diferent experts. Motivated by these chief characteristics, in this article, we extend the MSM operators to the IFSS based on ATT. In this paper, a method is exploited to solve the multi-criteria decision-making (MCDM) problems under the IFSS environment. To it, frstly, some generalized intuitionistic fuzzy soft operational laws are introduced based on ATT. Secondly, we reveal some averaging and geometric aggregation operators based on MSM operator. Further, some desirable features and particular cases of it are tested and build up with a new technique for illus- trating MCDM problems. Finally, an illustration is given to exhibit the methodology and approach’s supremacy is shown through a comparative study with prevailing techniques. Keywords Maclaurin symmetric mean · Aggregation operators · Multi criteria decision- making · Intuitionistic fuzzy soft set · Archimedean t-norm 1 Introduction Multi-criteria decision making (MCDM) aims to attain a general solution for a decision making issue in which various trained specialists are invited to participate in their judg- ments on the choice of an optimal alternative. The increasingly complicated decision mak- ing circumstances make it less possible for an individual decision maker to comprehen- sively consider. However, in sequence to negotiate the ambiguities in the data, theories * Harish Garg harishg58iitr@gmail.com http://sites.google.com/site/harishg58iitr/ 1 School of Mathematics, Thapar Institute of Engineering and Technology (Deemed University) Patiala, Patiala 147004, Punjab, India