Mathematical Modeling in Social Network Analysis： Using TOPSIS to Find Node Influences in a Social Network

In a social network analysis the output provided includes many measures and metrics. For each of these measures and metric, the output provides the ability to obtain a rank ordering of the nodes in terms of these measures. We might use this information in decision making concerning disrupting or deceiving a given network. All is fine when all the measures indicate the same node as the key or influential node. What happens when the measures indicate different key nodes？ Our goal in this paper is to explore two methodologies to identify the key players or nodes in a given network. We apply TOPSIS to analyze these outputs to find the most influential nodes as a function of the decision makers＇ inputs as a process to consider both subjective and objectives inputs through pairwise comparison matrices. We illustrate our results using two common networks from the literature： the Kite network and the Information flow network from Knoke and Wood. We discuss some basic sensitivity analysis can may be applied to the methods. We find the use of TOPSIS as a flexible method to weight the criterion based upon the decision makers＇ inputs or the topology of the network.

Using Multi-Attribute Decision Methods in Mathematical Modeling to Produce an Order of Merit List of High Valued Terrorists

The authors present a methodology and an example of preparing an order of merit list to rank terrorist based upon decision maker weights. This research used an old terrorist data set as our base data to keep the information unclassified. This data is used to demonstrate this methodology. The authors perform numerical iterative criteria weight sensitivity analysis to show the effects on the model’s outputs in changes in the weights. Through their analysis the most critical criterion is identified.

New Metrics for the Detection of Suicide Bombers

An experimental field study was conducted at the University of California at Santa Cruz USA to determine if radar cross section signals were different between a person without wearing any wires and a person wearing both a suicide vest and wires with （without） loops in the wires. The data was collected using the GunnPlexer Doppler radar at 12.5 GHz at various safe distances using various subjects both without any wires and wearing a suicide vest with detonation wires and with detonation wires and loops. The raw data was separated in its horizontal and vertical polarization signals （HH and VV）. The analysis of these two HH and VV polarization signals from the data allowed several promising metrics to be created. These metrics were individually tested in a Monte Carlo simulation which is in order to determine the probability of detection of a would-be suicide bomber. The results of the Monte Carlo simulation showed that the metrics yielded a probability of successful detection of slightly over 98% and a false positive rate of just less than 2 %. This research and its result are encouraging and suggest further testing to insure that suicide bombers can be found prior to their detonation of their bombs at a safe range.

Using Mathematical Models in Decision Making Methodologies to Find Key Nodes in the Noordin Dark Network

A Dark Network is a network that cannot be accessed through tradition means. Once uncovered, to any degree, dark network analysis can be accomplished using the SNA software. The output of SNA software includes many measures and metrics. For each of these measures and metric, the output in ORA additionally provides the ability to obtain a rank ordering of the nodes in terms of these measures. We might use this information in decision making concerning best methods to disrupt or deceive a given dark network. In the Noordin Dark network, different nodes were identified as key nodes based upon the metric used. Our goal in this paper is to use methodologies to identify the key players or nodes in a Dark Network in a similar manner as we previously proposed in social networks. We apply two multi-attribute decision making methods, a hybrid AHP & TOPSIS and an average weighted ranks scheme, to analyze these outputs to find the most influential nodes as a function of the decision makers’ inputs. We compare these methods by illustration using the Noordin Dark Network with seventy-nine nodes. We discuss sensitivity analysis that is applied to the criteria weights in order to measure the change in the ranking of the nodes.

An Alternative Approach to the Lottery Method in Utility Theory for Game Theory

In game theory, in order to properly use mixed strategies, equalizing strategies or the Nash arbitration method, we require cardinal payoffs. We present an alternative method to the possible tedious lottery method of von Neumann and Morgenstern to change ordinal values into cardinal values using the analytical hierarchy process. We suggest using Saaty’s pairwise comparison with combined strategies as criteria for players involved in a repetitive game. We present and illustrate a methodology for moving from ordinal payoffs to cardinal payoffs. We summarize the impact on how the solutions are achieved.