Generalized Maclaurin symmetric mean aggregation operators based on Archimedean t-norm of the intuitionistic fuzzy soft
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Generalized Maclaurin symmetric mean aggregation operators based on Archimedean t‑norm of the intuitionistic fuzzy soft set information Harish Garg1 · Rishu Arora1
© Springer Nature B.V. 2020
Abstract Intuitionistic fuzzy soft set (IFSS) accommodates more uncertainties within the information 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 operational laws. Meanwhile, the Maclaurin symmetric mean (MSM) has a prominent characteristic and the advantage that it can take into account the interrelation between multi-input arguments, including different attributes or different 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, firstly, 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 illustrating 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 decisionmaking · 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 judgments on the choice of an optimal alternative. The increasingly complicated decision making circumstances make it less possible for an individual decision maker to comprehensively consider. However, in sequence to negotiate the ambiguities in the data, theories * Harish Garg [email protected] http://sites.google.com/site/harishg58iitr/ 1
School of Mathematics, Thapar Institute of Engineering and Technology (Deemed University) Patiala, Patiala 147004, Punjab, India
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such as fuzzy set (FS) (Zadeh 1965), intuitionistic FS (IFS) (Atanassov 1986), linguistic interval-valued IFS (Garg and Kumar 2019), soft set (SS) (Molodtsov 1999), fuzzy SS (Maji et al. 2001b) etc., are extensively applied. In these sets, each detail was represented by an ordered pair including the degree of membership (MD) and non-membership (NMD) with the end goal that their sum is narrowed to one. Lately, decision making (DM) has been one of the sizzling subjects in the examination which comprises the following three steps: 1. Accumulate the data on a proper order to express the knowledge. 2. Obtain the overall decision value of the target by aggregating the collected at
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