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Introduction: The soft set theory has drawn the attention of many researchers, particularly for dealing with uncertainty in decision-making problems. Despite its remarkable advantages, the soft set theory has only been used to tackle decision-making problems that aim to choose the best option. However, there exist different forms of decision-making problems that involve different forms of uncertainty. Methods: In this study, we present various algorithms based on the soft set theory in order to handle the cases where one has different uncertainty forms in decision-making problems. Some new concepts such as object code, personal object code, parameter significance weight and new distance measures have been introduced to the literature for the construction of these algorithms. Furthermore, we show the application results of those algorithms and provide several examples. Results and Conclusions: As a result, a comparison among the application results of the algorithms implies that the best objects might not always yield the most efficient outcomes. [ABSTRACT FROM AUTHOR]

Multiple-attribute group decision-making (MAGDM) technique is often used to make decisions when several optimal options are under consideration. It can be difficult to select a reasonable optimal option for the decision maker under consideration of insufficient information. The theory of Hamy mean (HM) operators are used to express correlation among different input arguments and provide a smooth approximation during the decision-making process. Recently, Aczel Alsina aggregating expressions gained a lot of attention from numerous mathematicians under different fuzzy circumstances. This article aims to illustrate the notion of a Pythagorean fuzzy (PyF) set (PyFS) with some restricted constraints, such as a sum of the square of truth membership value and falsity membership value. We developed a series of new approaches under consideration of the HM tools, including PyF Aczel Alsina Hamy mean (PyFAAHM), and PyF Aczel Alsina weighted Hamy mean (PyFAAWHM) operators. Further, we also extend the theory of Dual Hamy mean (DHM) operators and derived a series of new methodologies such as PyF Aczel Alsina Dual Hamy mean (PyFAADHM) and PyF Aczel Alsina weighted Dual Hamy mean (PyFAAWDHM) operators. To demonstrate the flexibility of our derived approaches, we illustrate an application of a multinational company considering the MAGDM technique. An experimental case study is also illustrated to evaluate a reasonable option from a group of options. We see the advantages and compatibility of our findings by comparing the results of existing approaches with the results of currently discussed methodologies. [ABSTRACT FROM AUTHOR]