Two kinds of orthopair soft sets as novel approaches to granular computing based on parametrization

Document Type : Original Article


1 Islamabad Model College for Boys G-11/1, Islamabad, Pakistan

2 Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan

3 Department of Applied Mathematics, Xi an University of Posts and Telecommunications, Xi an, China


This paper aims at introducing two types of orthopair soft sets, which might serve as novel approaches to granular computing based on parametrization. These generalized soft sets emerge naturally when linguistic parameters are employed to convey uncertainty attached to elements of certain sets. Concepts of uncertainty measures attached to the parameters and the whole orthopair soft sets are presented as well. The proposed uncertainty measures are useful for classifying elements of the set of parameters. Different types of granularity measures associated with parameters are presented and are extended to orthopair soft sets. Collective wisdom is helpful in decision making based on consensus. A numerical example is given to demonstrate how orthopair soft sets can be employed in this regard.