In this paper, we propose a new hybrid model, multi Q-hesitant fuzzy soft multi-granulation rough set model, by combining a multi Q-hesitant fuzzy soft set and multi-granulation rough set. We demonstrate some useful properties of these multi Q-hesitant fuzzy soft multi-granulation rough sets. Furthermore, we define multi Q-hesitant fuzzy soft ( M k Q H F S ) rough approximation operators in terms of M k Q H F S relations and M k Q H F S multi-granulation rough approximation operators in terms of M k Q H F S relations. We study the main properties of lower and upper M k Q H F S rough approximation operators and lower and upper M k Q H F S multi-granulation rough approximation operators. Moreover, we develop a general framework for dealing with uncertainty in decision-making by using the multi Q-hesitant fuzzy soft multi-granulation rough sets. We analyze the photovoltaic systems fault detection to show the proposed decision methodology.

The uncertain data appear in majority of real-world phenomena regarding business, engineering, manufacturing, industries, medical, and other social fields. The neutrosophic sets (NSs), soft sets (SSs), and rough sets (RSs) are distinct mathematical models to deal with different types of uncertainties in data and information. Nowadays, several hybrid models are emerging as their combination or their further generalizations. In this paper, the concept of multineutrosophic fuzzy soft rough sets (MNFSRSs) by combining multineutrosophic fuzzy soft sets (MNSSs) with RSs is presented. Certain eminent features of the proposed structure are investigated. Moreover, a general decision-making (DM) algorithm is described for DM problems to indicate the effectiveness of the presented model.

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The main objective of this research study is to amplify the schematic representation of human reasoning by launching the most generalized fantastic theories of bipolar type-2 fuzzy set (BT2FS) and bipolar type-2 fuzzy soft set (BT2FS   f S). These incredible models are exclusively developed for the simultaneous capturing of both polarity and abstruseness inherent in equivocal interpretations. The proposed BT2FS   f S theory renders an outstanding parameterized framework that skilfully wipes out the high-order uncertainty of imprecise knowledge-based systems. First, we keenly provide the formal structure of both proposed models along with the deep exploration of their elementary properties. Moreover, we explore rudimentary set-theoretical operations of developed frameworks inclusive of equality, subset, complement, union, and intersection with their noticeable results. We brilliantly formulate a highly proficient algorithm using proposed theory to disentangle the real-world multiattribute decision-making conundrums with two-sided ambiguous information. Finally, we holistically scrutinize an empirical analysis for the selection best way to cultivate the dessert city to demonstrate the remarkable accountability of the proposed methodology.

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