A T-spherical fuzzy set is a more powerful mathematical tool to handle uncertain and vague information than several fuzzy sets, such as fuzzy set, intuitionistic fuzzy set, Pythagorean fuzzy set, q-rung orthopair fuzzy set, and picture fuzzy set. The Aczel–Alsina t-norm and s-norm are significant mathematical operations with a high premium on affectability with parameter activity, which are extremely conducive to handling imprecise and undetermined data. On the other hand, the Hamy mean operator is able to catch the interconnection among multiple input data and achieve great results in the fusion process of evaluation information. Based on the above advantages, the purpose of this study is to propose some novel aggregation operators (AOs) integrated by the Hamy mean and Aczel–Alsina operations to settle T-spherical fuzzy multi-criteria decision-making (MCDM) issues. First, a series of T-spherical fuzzy Aczel–Alsina Hamy mean AOs are advanced, including the T-spherical fuzzy Aczel–Alsina Hamy mean (TSFAAHM) operator, T-spherical fuzzy Aczel–Alsina dual Hamy mean (TSFAADHM) operator, and their weighted forms, i.e., the T-spherical fuzzy Aczel–Alsina-weighted Hamy mean (TSFAAWHM) and T-spherical fuzzy Aczel–Alsina-weighted dual Hamy mean (TSFAAWDHM) operators. Moreover, some related properties are discussed. Then, a MCDM model based on the proposed AOs is built. Lastly, a numerical example is provided to show the applicability and feasibility of the developed AOs, and the effectiveness of this study is verified by the implementation of a parameters influence test and comparison with available methods.
The purpose of this manuscript is to develop a novel MAIRCA (Multi-Attribute Ideal-Real Comparative Analysis) method to solve the MCDM (Multiple Criteria Decision-Making) problems with completely unknown weights in the q-rung orthopair fuzzy (q-ROF) setting. Firstly, the new concepts of q-ROF Lance distance are defined and some related properties are discussed in this paper, from which we establish the maximizing deviation method (MDM) model for q-ROF numbers to determine the optimal criteria weight. Then, the Lance distance-based MAIRCA (MAIRCA-L) method is designed. In it, the preference, theoretical and real evaluation matrices are calculated considering the interaction relationship in q-ROF numbers, and the q-ROF Lance distance is applied to obtain the gap matrix. Finally, we manifest the effectiveness and advantage of the q-ROF MAIRCA-L method by two numerical examples.
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