Abstract
In many real-life problems, decision-making is reckoned as a powerful tool to manipulate the data involving imprecise and vague information. To fix the mathematical problems containing more generalized datasets, an emerging model called q-rung orthopair fuzzy soft sets offers a comprehensive framework for a number of multi-attribute decision-making (MADM) situations but this model is not capable to deal effectively with situations having bipolar soft data. In this research study, a novel hybrid model under the name of q-rung orthopair fuzzy bipolar soft set (q-ROFBSS, henceforth), an efficient bipolar soft generalization of q-rung orthopair fuzzy set model, is introduced and illustrated by an example. The proposed model is successfully tested for several significant operations like subset, complement, extended union and intersection, restricted union and intersection, the ‘AND’ operation and the ‘OR’ operation. The De Morgan’s laws are also verified for q-ROFBSSs regarding above-mentioned operations. Ultimately, two applications are investigated by using the proposed framework. In first real-life application, the selection of land for cropping the carrots and the lettuces is studied, while in second practical application, the selection of an eligible student for a scholarship is discussed. At last, a comparison of the initiated model with certain existing models, including Pythagorean and Fermatean fuzzy bipolar soft set models is provided.
Highlights
Nowadays, multi-attribute decision-making (MADM) is playing a vital role in dealing with the vague information having multi-attributes by offering better mathematical modeling in case of various reallife problems
Decision-making performs a significant role in mathematical modeling to refine the selection of logical attributes in almost every real-life problem
We have proposed a novel hybrid model called q-ROFBSSs for MADM by combining q-ROFSs and
Summary
MADM is playing a vital role in dealing with the vague information having multi-attributes by offering better mathematical modeling in case of various reallife problems. The main feature of FFSs to handle the uncertainties in people decisions make it more cogent and efficient because FFSs deal with two dimensional (i.e., belongingness and non-belongingness) information in more wider space than IFSs and PFSs; BSSs and q-ROFSs are two different mathematical models to address uncertain MADM situations. The illustration of the proposed work comes with an example; To investigate our hybrid model, we propose subset, complement, extended union and intersection, restricted union and intersection, and OR and AND operations; Certain De Morgan’s laws for q-ROFBSSs are verified; we combine these ideas and offer an application with algorithm regarding selection of land for cropping carrots and lettuces We use this model to offer another application to help in the selection of an eligible student for scholarship; a comparison analysis with some existing models in qualitative and quantitative formats is provided; At the end, some concluding remarks and future directions are given.
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