FUNDAMENTALS OF THE ANALYTIC NETWORK PROCESS- DEPENDENCE AND FEEDBACK IN DECISION-MAKING WITH A SINGLE NETWORK

The Analytic Network Process (ANP) is a multicriteria theory of measurement used to derive relative priority scales of absolute numbers from individual judgments (or from actual measurements normalized to a relative form) that also belong to a fundamental scale of absolute numbers. These judgments represent the relative influence, of one of two elements over the other in a pairwise comparison process on a third element in the system, with respect to an underlying control criterion. Through its supermatrix, whose entries are themselves matrices of column priorities, the ANP synthesizes the outcome of dependence and feedback within and between clusters of elements. The Analytic Hierarchy Process (AHP) with its independence assumptions on upper levels from lower levels and the independence of the elements in a level is a special case of the ANP. The ANP is an essential tool for articulating our understanding of a decision problem. One had to overcome the limitation of linear hierarchic structures and their mathematical consequences. This part on the ANP summarizes and illustrates the basic concepts of the ANP and shows how informed intuitive judgments can lead to real life answers that are matched by actual measurements in the real world (for example, relative dollar values) as illustrated in market share examples that rely on judgments and not on numerical data.

DECISION MAKING - THE ANALYTIC HIERARCHY AND NETWORK PROCESSES (AHP/ANP)

This is the first part of an introduction to multicriteria decision making using the Analytic Hierarchy Process (AHP) and its generalization, the Analytic Network Process (ANP). The discussion involves individual and group decisions both with the independence of the criteria from the alternatives as in the AHP and also with dependence and feedback in the entire decision structure as in the ANP. This part explains the Analytic Hierarchy Process, with examples, and presents in some detail the mathematical foundations. An exposition of the Analytic Network Process and its applications will appear in later issues of this journal.

FUNDAMENTALS OF THE ANALYTIC NETWORK PROCESS - MULTIPLE NETWORKS WITH BENEFITS,COSTS,OPPORTUNITIES AND RISKS

The general theory of the ANP enables one to deal with the benefits,opportunities,costs,andrisks(the BOCR merits)of a decision,by introducing the notion of negative priorites for C and Ralong with the rating(not comparison)of the top priority alternative synthesized for each of the fourmerits in terms of strategic criteria to enable one to combine the four B,O,C,and R values of eachalternative into a single outcome.Strategic criteria are very basic criteria individuals and groups useto assess whether they should make any of the many decisions they face in their daily operations.They do not depend on any particular decision for their priorities but are assessed in terms of the goalsand values of the individual or organization.Synthesis is made with two formulas,one multiplicativeand one additive subtractive that can give rise to negative overall priorities.This paper summarizesand illustrates basic complex decisions involving several control criteria under each of the BOCRmerits.

AN ANALYTIC HIERARCHY PROCESS MODEL OF GROUP CONSENSUS

In group decision making, a certain degree of consensus is necessary to derive a meaningful and valid outcome. This paper proposes a consensus reaching model for a group by using the Analytic Hierarchy Process （AHP）. It supports people to improve their group consensus level through an updating of their judgments. In this model, a moderator suggests the most discoraant aeclslon manet to update his judgment in each step. The proposed consensus reaching model allows decision makers to accept or reject the suggestion from the moderator. This model ensures that the judgment updating is effective and the final solution will be of acceptable consistency. Finally, a numerical example is given to illustrate the validity of the proposed consensus reaching model.

WHO WON THE 2008 OLYMPICS?A MULTICRITERIA DECISION OF MEASURING INTANGIBLES

It often happens that at the end of Olympics games the medals won by more than one country are many and close in total number as in the 2008 games where China won 100 medals with many gold ones and the United States won 110 medals but with a lesser number of gold medals. The question is： Although it is often done arbitrarily, is there a way to quantify the values of gold, silver and bronze medals legitimately to resolve this concern？ This short exposition shows that there is by using the author＇s theory for the measurement of intangibles, the Analytic Hierarchy Process.

GLOBAL AWARENESS,FUTURE CITY DESIGN AND DECISION MAKING

Our world has been changing at an exponential rate. As a result of this rapid growth, we will be forced to make changes in not only the way we live in the environment but also in the environment itself such as designing the cities of the future to be in greater harmony with the increasing population and growing complexity. The paper contains both reflections on global awareness and comprehensive criteria and their priorities for choosing the most desirable city.

Predicting the Outcome of a Tennis Tournament:Based on Both Data and Judgments

This paper is about predicting the outcome of tennis matches of the Association of Tennis Professionals(ATP)and the Women's Tennis Association(WTA)using both data and judgments.There are many factors that influence that outcome.An important question is which factors have significant influence on the outcome.We have identified numerous factors and systematically prioritized them subjectively and objectively,so as to improve the accuracy of the prediction.We then used them to predict the win-lose outcome of the 2015 US OPEN tennis matches(63 men and 31 women's games)before they took place.The tennis match prediction in sports literature thus far reported an accuracy rate of 70%.The accuracy of our proposed model which combines data and judgment reaches 85.1%.