Modified EDAS Method for MAGDM Based on MSM Operators with 2-Tuple Linguistic <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mi>T</a:mi> </a:math>-Spherical Fuzzy Sets

Abstract

The coronavirus (COVID-19) pandemic, which began in China and is fast spreading around the world, has increased the number of cases and deaths. Governments have suffered substantial damage and losses not only in the health sector but also in a variety of other areas. In this situation, it is critical to determine the most crucial vaccine that doctors and specialists should implement. In order to evaluate the many vaccines to control the COVID-19 epidemic, a decision problem based on the decisions of many experts, with some contradicting and multiple criteria, should be taken into account. This decision process is characterized as a multiattribute group decision-making (MAGDM) problem that includes uncertainty in this study. <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M2"> <a:mi>T</a:mi> </a:math> -spherical fuzzy sets are utilized for this, allowing decision-experts to make evaluations over a larger area and better deal with complicated data. The <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M3"> <c:mi>T</c:mi> </c:math> -spherical fuzzy set is a useful tool for dealing with uncertainty and ambiguity, especially where additional answers of the type “yes,” “no,” “abstain,” and “refusal” are required, and the 2-tuple linguistic terms are useful for the qualitative evaluation of uncertain data. From the perspective of the uncertainty surrounding the problems of MAGDM, we propose the notion of 2-tuple linguistic <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" id="M4"> <e:mi>T</e:mi> </e:math> -spherical fuzzy numbers (2TL <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" id="M5"> <g:mi>T</g:mi> </g:math> -SFNs) generated with the integration of <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" id="M6"> <i:mi>T</i:mi> </i:math> -spherical fuzzy numbers and 2-tuple linguistic terms. Then, the assessment based on distance from average solution (EDAS) for the ranking of alternatives based on the 2TL <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" id="M7"> <k:mi>T</k:mi> </k:math> -SFNs is investigated as a new decision-making strategy. This study provides the following significant contributions: (1) the procedure for constructing a 2TL <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" id="M8"> <m:mi>T</m:mi> </m:math> -SFNs is described, together with their aggregation operators, ranking criteria, relevant attributes, and some operational laws. (2) The traditional Maclaurin symmetric mean (MSM) operator is useful for modeling attribute interrelationships and aggregating 2TL <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" id="M9"> <o:mi>T</o:mi> </o:math> -SF information to tackle the MAGDM problems. A few recent MSM and dual MSM operators are being built to evaluate the 2TL <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" id="M10"> <q:mi>T</q:mi> </q:math> -SF information. Thus, 2-tuple linguistic <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" id="M11"> <s:mi>T</s:mi> </s:math> -spherical fuzzy Maclaurin symmetric mean (2TL <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" id="M12"> <u:mi>T</u:mi> </u:math> -SFMSM) operator, 2-tuple linguistic <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" id="M13"> <w:mi>T</w:mi> </w:math> -spherical fuzzy weighted Maclaurin symmetric mean (2TL <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" id="M14"> <y:mi>T</y:mi> </y:math> -SFWMSM) operator, 2-tuple linguistic <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" id="M15"> <ab:mi>T</ab:mi> </ab:math> -spherical fuzzy dual Maclaurin symmetric mean (2TL <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" id="M16"> <cb:mi>T</cb:mi> </cb:math> -SFDMSM) operator, and 2-tuple linguistic <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" id="M17"> <eb:mi>T</eb:mi> </eb:math> -spherical fuzzy weighted dual Maclaurin symmetric mean (2TL <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" id="M18"> <gb:mi>T</gb:mi> </gb:math> -SFWDMSM) operator are proposed. (3) We incorporate the 2TL <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" id="M19"> <ib:mi>T</ib:mi> </ib:math> -SFNs into the EDAS approach and develop a new 2TL <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" id="M20"> <kb:mi>T</kb:mi> </kb:math> -SF-EDAS method for solving the MAGDM problems based on the proposed aggregation operators in a 2TL <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" id="M21"> <mb:mi>T</mb:mi> </mb:math> -SF environment. A case study for the selection of an optimal vaccine to control the outbreak of the COVID-19 epidemic is also presented to show the validity of the proposed methodology. Furthermore, the comparative analysis with existing approaches shows the advantages and superiority of the proposed framework.