A multi-attribute decision-making method for ternary hybrid decision matrices in view of (T, S)-fuzzy rough sets with fuzzy preference relations

Abstract

ABSTRACT As a significant part of modern decision science, multi-attribute decision-making (MADM) has attracted the interests of more and more researchers. In the process of decision analysis, decision-makers or experts usually give decision information in the forms of preference order, utility values or preference relation. Utility values, i.e. attribute values, generally include real-values, interval-values and linguistic-values. This article studies ternary hybrid decision matrices (THDMs), which contain the above three types of attributes. Firstly, we give a calculation method for attribute weight vectors in THDMs, and transform THDMs into fuzzy preference relations (FPRs). Secondly, we consider additive consistency of induced FPRs and introduce an inconsistency repairing method. Thirdly, we propose an MADM method for THDMs in view of (T, S)-fuzzy rough sets (FRSs) with FPRs. Finally, we give an example to explain the raised method in detail and conduct comparative analysis to illustrate the rationality and practicability of our raised method.