A total order for the graded numbers used in decision problems
Let us consider a classical problem of decision-making with fuzzy rewards. In order to choose the alternative which corresponds to the best fuzzy reward, we need to use a total order for the fuzzy numbers involved in the problem. In this paper, we consider a definition of such a total order, which is based upon two subjective aspects: the degree of optimism/pessimism and the liking for risk/safety. We also use the graded numbers which are analogous to the fuzzy numbers. However, the operations with graded numbers are carried out as a simple extension of operations with real intervals.
total order graded number decision problem fuzzy reward fuzzy number