In this paper, we focus on several ideas associated with linear Diophantine fuzzy soft sets (LDFSSs) along with its algebraic structure. We provide operations on LDFSSs and their specific features, elaborating them with real-world examples and statistical depictions to construct an inflow of linguistic variables based on linear Diophantine fuzzy soft (LDFSS) information. We offer a study of LDFSSs to the multi-criteria decision-making (MCDM) process of university determination, together with new algorithms and flowcharts. We construct LDFSS-TOPSIS, LDFSS-VIKOR and the LDFSS-AO techniques as robust extensions of TOPSIS (a technique for order preferences through the ideal solution), VIKOR (Vlse Kriterijumska Optimizacija Kompromisno Resenje) and AO (aggregation operator). We use the LDFSS-TOPSIS, LDFSS-VIKOR and LDFSS-AO techniques to solve a real-world agricultural problem. Moreover, we present a small-sized robotic agri-farming to support the proposed technique. A comparison analysis is also performed to examine the symmetry of optimal decision and to analyze the efficiency of the suggested algorithms.
Let [Formula: see text] be a commutative ring with [Formula: see text]. A proper ideal [Formula: see text] of [Formula: see text] is said to be a strongly quasi-primary ideal if, whenever [Formula: see text] with [Formula: see text], then either [Formula: see text] or [Formula: see text]. In this paper, we characterize Noetherian and reduced rings over which every (respectively, nonzero) proper ideal is strongly quasi-primary. We also characterize ring over which every strongly quasi primary ideal of [Formula: see text] is prime. Many examples are given to illustrate the obtained results.
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