@article{Al-shami2023, 
author = {Tareq M. Al-shami and José Carlos R. Alcantud and Abdelwaheb Mhemdi},
title = {New generalization of fuzzy soft sets:    (  a  ,  b  )-Fuzzy soft sets},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {2},
pages = {2995-3025},
keywords = {multi-criteria decision-making, aggregation operators, (a, b)-fuzzy soft set, score and accuracy functions},
url = {https://www.sciopen.com/article/10.3934/math.2023155},
doi = {10.3934/math.2023155},
abstract = {Many models of uncertain knowledge have been designed that combine expanded views of fuzziness (expressions of partial memberships) with parameterization (multiple subsethood indexed by a parameter set). The standard orthopair fuzzy soft set is a very general example of this successful blend initiated by fuzzy soft sets. It is a mapping from a set of parameters to the family of all orthopair fuzzy sets (which allow for a very general view of acceptable membership and non-membership evaluations). To expand the scope of application of fuzzy soft set theory, the restriction of orthopair fuzzy sets that membership and non-membership must be calibrated with the same power should be removed. To this purpose we introduce the concept of    (  a  ,  b  )-fuzzy soft set, shortened as    (  a  ,  b  )-FSS. They enable us to address situations that impose evaluations with different importances for membership and non-membership degrees, a problem that cannot be modeled by the existing generalizations of intuitionistic fuzzy soft sets. We establish the fundamental set of arithmetic operations for    (  a  ,  b  )-FSSs and explore their main characteristics. Then we define aggregation operators for    (  a  ,  b  )-FSSs and discuss their main properties and the relationships between them. Finally, with the help of suitably defined scores and accuracies we design a multi-criteria decision-making strategy that operates in this novel framework. We also analyze a decision-making problem to endorse the validity of    (  a  ,  b  )-FSSs for decision-making purposes.}
}