Triangular fuzzy decision-theoretic rough sets
Based on decision-theoretic rough sets (DTRS), we augment the existing model by introducing into the granular values. More specifically, we generalize a concept of the precise value of loss function to triangular fuzzy decision-theoretic rough sets (TFDTRS). Firstly, ranking the expected loss with triangular fuzzy number is analyzed. In light of Bayesian decision procedure, we calculate three thresholds and derive decision rules. The relationship between the values of the thresholds and the risk attitude index of decision maker presented in the ranking function is analyzed. With the aid of multiple attribute group decision making, we design an algorithm to determine the values of losses used in TFDTRS. It is achieved with the use of particle swarm optimization. Our study provides a solution in the aspect of determining the value of loss function of DTRS and extends its range of applications. Finally, an example is presented to elaborate on the performance of the TFDTRS model. (C) 2013 Elsevier Inc. All rights reserved.
decision-theoretic rough sets loss function triangular fuzzy number multiple attribute group decision making linguistic variable