THE PROPERTIES OF HUMAN BEING'S DECISION MAKING

In order to honor Thomas Saaty, the developer of Analytic Hierarchy Process (AHP)/ Analytic Network Process (ANP), and focus on the paper he wrote just before he died, this essay mentions the rank order problem due to the addition/deletion of irrelevant alternatives over which there were controversies in the AHP. Saaty ended the controversies with the explanation that both rank preservation and rank reversal are possible depending on the decision making circumstance. In this paper, we will summarize the three properties that fundamentally act on how to prioritize and aggregate the subjective judgments of human beings in ranking alternatives: comparisons, judgmental dependency and rank order. This essay also mentions the rank order in relation to the cases of addition/deletion of irrelevant criteria from previous studies. This essay closes by expressing gratitude to Thomas Saaty for his work. https://doi.org/10.13033/ijahp.v9i3.528

Controllability Robustness of Linear Interval Systems with/without State Delay and with Unstructured Parametric Uncertainties

The robust controllability problem for the linear interval systems with/without state delay and with unstructured parametric uncertainties is studied in this paper. The rank preservation problem is converted to the nonsingularity analysis problem of the minors of the matrix under discussion. Based on some essential properties of matrix measures, two new sufficient algebraically elegant criteria for the robust controllability of linear interval systems with/without state delay and with unstructured parametric uncertainties are established. Two numerical examples are given to illustrate the applications of the proposed sufficient algebraic criteria, where one example is also presented to show that the proposed sufficient condition for the linear interval systems having no state delay and no unstructured parametric uncertainties can obtain less conservative results than the existing ones reported recently in the literature.

Rank Reversal and Rank Preservation in TOPSIS

TOPSIS has been in use for more than 20 years in many fields. However, few researches have studied its defect of rank reversal. This paper, by studying the fundamental cause for the rank reversal problem in TOPSIS, put forward an improvement on TOPSIS based on the decision maker’s subjective preferences, which can, proved by a numerical example, overcome the rank reversal problem and lead to more scientific decision result that is in more agreement with the decision makers’ subjective intensions.