The 2-tuple linguistic $m$-polar fuzzy sets (2TL $m$FSs) are acknowledged to represent the multi-polar information owing to the practical structure of $m$-polar fuzzy sets with the help of linguistic terms. The TOPSIS and ELECTRE series are efficient and widely used methods for solving multi-attribute decision-making problems. This paper aim to augment the literature on multi-attribute group decision making focusing on the the strategic approaches of TOPSIS and ELECTRE-I methods for the 2TL $m$FSs. In the 2TL $m$F-TOPSIS method, the relative closeness index is used to rank the alternatives. For the construction of concordance and discordance sets, the superiority and inferiority of alternatives over each other are accessed by using the score and accuracy functions. In the 2TL $m$F ELECTRE-I, selection of the best alternative is made by the means of an outranking decision graph. At the final step of the 2TL $m$F ELECTRE-I method, a supplementary approach is developed for the linear ranking of alternatives based on the concordance and discordance outranking indices. The structure of the proposed techniques are illustrated by using a system flow diagram. Finally, two case studies are used to demonstrate the correctness, transparency, and effectiveness of the proposed methods for selecting highway construction project manager and the best textile industry.