T-S-Ferrers Property And Interval Order Indicators

In this paper, we concentrate on the study of the Y-S-Ferrers property indicator and the interval order indicator which is closely related to the former. First, we present some properties of the T-S-Ferrers indicator including its equivalent expression, the relationship between the T-S-Ferrers indicator and the strong completeness indicator, and the relationship between the T-S-Ferrers indicator of large preference and that of strict preference. Then we give the definitions of partial interval and total interval order indicators in order to express the degrees to which a preference structure satisfies partial and total interval order respectively. Afterwards, we investigate their properties and the relationship between the T-S-Ferrers indicator and interval order indicator. Finally, we obtain an equivalent expression of the partial interval order for t-norms without zero divisors. Some similar results are obtained with the same type of indicators.