Selection of alternative based on linear programming and the extended fuzzy TOPSIS under the framework of dual hesitant fuzzy sets

Everything in the world almost resembles each other which could find out with the help of some measures. Similarity measure (SM) is one of them that play a dominant role in decision-making (DMg\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M_{g}$$\end{document}). The higher the value of the SM, the more the things will match perfectly. Weights of criteria appear to specify that the decision-makers (DMs) recognize the significance of public views and their influence on reaching an ideal solution. Sometimes DMs hesitate or they are uncertain to assign the weights to the criteria because of their similar nature. Linear programming (LP) technique has been implemented to evaluate the weights of criteria to reduce the complexity of DMs so that they can avoid biasedness. An extension of fuzzy sets (FSs) named dual hesitant fuzzy sets (DHFSs) is utilized to handle ambiguous and uncertain information. Based on the Hausdorff metric and the Hamming distance, SM is developed to establish the multiple criteria decision-making (MCDM) approach to resolve the problems. Moreover, based on the proposed SM, the technique for order of preference similar to the ideal solution (TOPSIS) is extended to strengthen the obtained outcomes. The effectiveness of the suggested approach is validated by considering a practical example. To support the outcomes obtained by using the proposed model, sensitivity analysis (SA) and time complexity (TC) analysis have been performed. A comprehensive comparison with other techniques is performed to validate the proposed MCDM model.