Set-valued Rough Set in Multi-Attribute Decision Making with Interactive Attributes

Abstract

The proposed work introduces a new methodology for solving Multiple Attribute Decision Making (MADM) problems in which the alternatives are assessed as hesitant fuzzy linguistic value (HFLV) over the attributes. The proposed MADM problem is exhibited as a rough set model with set-valued data as HFLVs. A similarity measure is defined in the set-valued information system that aids to remove the irrelevant or redundant attributes. The uncertainty due to hesitancy in HFLVs and the linked anxiety of the decision-maker therein are derived in our work after introducing the concept of the tranquility (or anxiety) in HFLTS. The proposed work introduces a new aggregation operator, Indexed Choquet Integral (ICI) that (a) aggregates the interactive attributes, (b) incorporates the decision-maker’s level of tranquility in the aggregation process, and c) estimates the weights and capacity weights of the attributes after assimilating the level of tranquilities appropriately. A comparative analysis of our paper with similar works is made and the advantages in our work are shown. The procedure introduced in the proposed work is demonstrated through a numerical example.