DECISION MAKING - THE ANALYTIC HIERARCHY ANDNETWORK 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. Thomas L. Saaty holds the Chair of University Professor, Katz Graduate School of Business, University of Pittsburgh, Pittsburgh, PA, and obtained his Ph.D. in mathematics from Yale University. Before that he was a professor at the Wharton School of the University of Pennsylvania for ten years. Prior to that he spent seven years at the Arms Control and Disarmament Agency in the State Department in Washington, DC, that carried out the arms reduction negotiations with the Soviets in Geneva. His current research interests include decision-making, planning, conflict resolution and synthesis in the brain. As a result of his search for an effective means to deal with weapons tradeoffs at the Disarmament Agency and, more generally, with decision-making and resource allocation, Professor Saaty developed The Analytic Hierarchy Process (AHP) and its generalization to dependence and feedback, the Analytic Network Process (ANP). He is co-developer of the software Expert Choice and of the software Super Decisions for decisions with dependence and feedback. He has authored or co-authored twelve books on the AHP/ANP. Professor Saaty has also written a number of other books that embrace a variety of topics, including Modern Nonlinear Equations, Nonlinear Mathematics, Graph Theory, The Four Color Problem, Behavioral Mathematics, Queuing Theory, Optimization in Integers, Embracing the Future and The Brain: Unraveling the Mystery of How It Works. His most recent book is Creative Thinking, Problem Solving & Decision Making. The book is a rich collection of ideas, incorporating research by a growing body of researchers and practitioners, profiles of creative people, projects and products, theory, philosophy, physics and metaphysics...all explained with a liberal dose of humor. He has published more than 300 refereed articles in a wide variety of professional journals. He has been on the editorial boards of Mathematical Reviews, Operations Research, Naval Research Logistics Quarterly, Mathematical and Computer Modeling, Socio-Economic Planning Sciences, Applied Mathematics Letters, and several others. He also served as consultant to many corporations and governments.     

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     

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. Thomas L. Saaty holds the Chair of University Professor, Katz Graduate School of Business, University of Pittsburgh, Pittsburgh, PA, and obtained his Ph.D. in mathematics from Yale University. Before that he was a professor at the Wharton School of the University of Pennsylvania for ten years. Prior to that he spent seven years at the Arms Control and Disarmament Agency in the State Department in Washington, DC, that carried out the arms reduction negotiations with the Soviets in Geneva. His current research interests include decision-making, planning, conflict resolution and synthesis in the brain. As a result of his search for an effective means to deal with weapons tradeoffs at the Disarmament Agency and, more generally, with decision-making and resource allocation, Professor Saaty developed The Analytic Hierarchy Process (AHP) and its generalization to dependence and feedback, the Analytic Network Process (ANP). He is co-developer of the software Expert Choice and of the software Super Decisions for decisions with dependence and feedback. He has authored or co-authored twelve books on the AHP/ANP. Professor Saaty has also written a number of other books that embrace a variety of topics, including Modern Nonlinear Equations, Nonlinear Mathematics, Graph Theory, The Four Color Problem, Behavioral Mathematics, Queuing Theory, Optimization in Integers, Embracing the Future and The Brain: Unraveling the Mystery of How It Works. His most recent book is Creative Thinking, Problem Solving & Decision Making. The book is a rich collection of ideas, incorporating research by a growing body of researchers and practitioners, profiles of creative people, projects and products, theory, philosophy, physics and metaphysics...all explained with a liberal dose of humor. He has published more than 300 refereed articles in a wide variety of professional journals. He has been on the editorial boards of Mathematical Reviews, Operations Research, Naval Research Logistics Quarterly, Mathematical and Computer Modeling, Socio-Economic Planning Sciences, Applied Mathematics Letters, and several others. He also served as consultant to many corporations and governments.     

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.     

The Discussion of Analytic Hierarchy Process for Quantitative Type Multiple Attribute Decision Systems Analysis

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ADVANCES IN DECISION ANALYSIS AND SYSTEMS ENGINEERING FOR MANAGING LARGE-SCALE ENTERPRISES IN A VOLATILE WORLD： INTEGRATING BENEFITS, OPPORTUNITIES, COSTS AND RISKS （BOCR） WITH THE BUSINESS MOTIVATION MODEL （BMM）

1. Introduction Recent advances in Information and Communication Technologies (ICT) have occurred in a number of areas includinginformation quality (Chutimaskul and Wangpipatwong 2004), strategy (Sha, Hung and Lin 2004) organization (Crowne 2004), technological change (Mitchell 2004), and utility1. Introduction Recent advances in Information and Communication Technologies (ICT) have occurred in a number of areas includinginformation quality (Chutimaskul and Wangpipatwong 2004), strateg…     

基于层次分析(AHP)的深层软基处理方案优化选择研究:一个案例

高速公路深层软基处理方案的选择涉及诸多因素．由于缺乏有效的技术-经济评估方法，以往对的方案选择往往过于注重技术可行性。这是不全面的。本史基于层次分析技术（AHP），建立了一个新的评估模型，模型的参数则通过专家的群决策知识确定，通过将多因素量化集成，得出了综合指标，用于不同方案的评价和选择．梅河高速公路建设的实践表明，这种方法十分有效并且简捷。     

A PURCHASING DECISION： SELECTING A SUPPLIER FOR A CONSTRUCTION COMPANY

1. Introduction Since the purchasing function has become vital in determining the profitability and survival of business organizations, it has been receiving considerable attention. As Sarkis and Talluri (2002) indicated, buyer-supplier relationships based solely on price are no longer acceptable. The increasing importance of supplier selection decisions is forcing organizations to rethink their purchasing and evaluation strategies because a successful purchasing decision directly depends on …     

COMPARISON OF THE ANALYTIC NETWORK PROCESS AND THE GRAPH MODEL FOR CONFLICT RESOLUTION

1. Introduction A strategic conflict is a situation in which two or more decision-makers are to make a decision that affects issues they have different preferences about (Fang et al. 1993). Conflicts are one of the most characteristic attributes of human societies. Various forms of strategic conflict exist all around us, in areas such as environmental management, international rela-tions, economic competition, and relationships among individuals. Conflicts are studied in a wide range of disci…     

采用递进Bayes估计评估导引头抗干扰性能及仿真

Bayes估计在武器系统性能评估中受到越来越多的重视,提出采用递进的Bayes估计方法,充分利用导引头研制过程中各阶段的实验数据,综合评估红外导引头抗干扰性能。文章采用层次分析法分析了试验样本采集对评估结果的影响,导出了各攻击区内实验样本的比重。最后以数字仿真验证了该方法的可行性。     

AN ANP/DNP ANALYSIS OF ECONOMIC ELEMENTS IN TODAY＇S WORLD NETWORK ECONOMY

The network economy is a term for today’s global relationship among economic elements characterized by massive connectivity. The central act of the new era is to connect everything to everything in deep web networks at many levels of mutually interdependent relations, where resources and activities are shared, markets are enlarged and costs and risk are reduced. Network systems contain both positive and negative feedback. A variety of feedback processes create complex system behavior. For such a network the Analytic Network Process (ANP) approach seems to be very appropriate. The ANP method makes it possible to deal systematically with all kinds of dependence and feedback in the system. Dynamic models try to reflect changes in real or simulated time and take into account that the network model components are constantly evolving. Dynamic models use concepts of state variables, flows, and feedback processes. The Dynamic Network Process (DNP) is an extension of ANP that can deal with time dependent priorities in a networked economy. Petr Fiala is a Professor and the Deputy Head of the Department of Econometrics, University of Economics in Prague, the Czech Republic. He is a graduate of the University of Economics in Prague, Charles University in Prague, and the Rochester Institute of Technology in Rochester, NY, USA. He holds a PhD from the University in Prague. His current research interests include modeling of production systems, supply chain management, project management, and multicriteria and group decision making. He has been on study and research tours to Germany, Russia, the USA, India and Cuba. He is a member of professional societies for Operations Research and Multiple Criteria Decision Making and is the Vice President of the Czech Society of Operations Research and the Czech Republic representative in EURO (The Association of European Operational Research Societies). He is the author of books, lecture notes and papers in quantitative models and methods in management and economics.     

基于ANP的超级决策软件介绍及其应用

从应用的角度介绍ANP（网络层次分析法）应用软件－超级决策软件系统，并利用该软件对水利水电项目导流施工方案进行评价。用同一组数据分别对ANP和AHP模型进行计算，出现了倒序现象。因此是否考虑系统内部元素间的反馈和依存关系将直接影响备选方案的排序。作者尝试性地应用该软件，说明ANP方法作为一种决策方法是可以用于工程实际的。     

基于FAHP的复杂系统的脆性过程分析

由于复杂系统具有层次结构，采用模糊层次分析法对复杂系统进行脆性分析。由模糊层次分析法得到子系统(或元件)的相对重要度排序向量，通过定义脆性激发度及激发阀值，对复杂系统的脆性是否被激发进行理论分析。通过分析，可以找出复杂系统中的脆性元件或因素，对其进行重点监测，使得最大程度避免了脆性的发生。最后以变压器故障的模糊层次分析为例，分析变压器故障的因素的相对重要度，找出易使变压器崩溃的脆性因素，说明进行复杂系统的脆性分析是必要的。     

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, and risks (the BOCR merits) of a decision, by introducing the notion of negative priorities for C and R along with the rating (not comparison) of the top priority alternative synthesized for each of the four merits in terms of strategic criteria to enable one to combine the four B, O, C, and R values of each alternative into a single outcome. Strategic criteria are very basic criteria individuals and groups use to 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 goals and values of the individual or organization. Synthesis is made with two formulas, one multiplicative and one additive subtractive that can give rise to negative overall priorities. This paper summarizes and illustrates basic complex decisions involving several control criteria under each of the BOCR merits. Thomas L. Saaty holds the Chair of University Professor, Katz Graduate School of Business, University of Pittsburgh, Pittsburgh, PA, and obtained his Ph.D. in mathematics from Yale University. Before that he was a professor at the Wharton School of the University of Pennsylvania for ten years. Prior to that he spent seven years at the Arms Control and Disarmament Agency in the State Department in Washington, DC, that carried out the arms reduction negotiations with the Soviets in Geneva. His current research interests include decision-making, planning, conflict resolution and synthesis in the brain. As a result of his search for an effective means to deal with weapons tradeoffs at the Disarmament Agency and, more generally, with decision-making and resource allocation, Professor Saaty developed The Analytic Hierarchy Process (AHP) and its generalization to dependence and feedback, the Analytic Network Process (ANP). He is co-developer of the software Expert Choice and of the software Super Decisions for decisions with dependence and feedback. He has authored or co-authored twelve books on the AHP/ANP. Professor Saaty has also written a number of other books that embrace a variety of topics, including Modern Nonlinear Equations, Nonlinear Mathematics, Graph Theory, The Four Color Problem, Behavioral Mathematics, Queuing Theory, Optimization in Integers, Embracing the Future and The Brain: Unraveling the Mystery of How It Works. His most recent book is Creative Thinking, Problem Solving & Decision Making. The book is a rich collection of ideas, incorporating research by a growing body of researchers and practitioners, profiles of creative people, projects and products, theory, philosophy, physics and metaphysics...all explained with a liberal dose of humor. He has published more than 300 referred articles in a wide variety of professional journals. He has been on the editorial boards of Mathematical Reviews, Operations Research, Naval Research Logistics Quarterly, Mathematical and Computer Modeling, Socio-Economic Planning Sciences, Applied Mathematics Letters, and several others. He also served as consultant to many corporations and government.     

一种基于正交设计的层次分析评估新方法

为进一步提高评估过程中的客观公正性,提出了一种结合正交设计思想的改进层次分析法.该方法将原评价体系中的指标和其下被评价的各个对象作为正交试验设计中的因素及其水平,然后运用本文的可调映射函数对由原层次分析法得出的排序权值和由指标归一化得出的满意度权值进行计算,并把函数值作为正交设计的结果值,从而分析得到合理的评估结果.最后给出一个应用实例.     

层次分析法(AHP)中的检验

分析了AHP(层次分析法)中现有检验指标存在的问题和应用的局限,设计了一个通用的检验指标,采用该指标,用统计学的知识进行一致性和相容性检验.该方法比通常方法使用面广、简单、精确.通过一个指标解决了AHP中的所有检验指标问题.     

Optimal hierarchy structures for multi-attribute-criteria decisions

A problem of a hierarchy structure optimization is considered. Hierarchical structures are widely used in the Analytic Hierarchy Process, conjoint analysis, and various other methods of multiple criteria decision making. The problem consists in finding a structure that needs a minimum number of pair comparisons for a given total number of the alternatives. For an optimal hierarchy, the minimum efforts are needed for eliciting data and synthesizing the local preferences across the hierarchy to get the global priorities or utilities. Special estimation techniques are developed and numerical simulations performed. Analytical and numerical results suggest optimal ways of priority evaluations for practical managerial decisions in a complex environment.     

RESEARCH ON CONSTRUCTING SYNTHETIC MATRIX IN AHP

This paper presents a new method for constructing synthetic matrix which is obtained by extending the given judgement matrices in the Analytic Hierarchy Process (AHP). The consistency relationship among the given matrices and their synthetic matrix is studied. The method can be used to deal with situations where the number of the given alternatives is larger than nine, and needs less pairwise comparisons than any others. Thus it will aid in the design of the AHP, which will reduce the information overload of decision maker, a major drawback of the original AHP algorithm. Finally, a numerical example is given to show the feasibility and effectiveness of the method.     

用网络层次分析法（ANP）评估应急桥梁设计方案

主要介绍了应用网络层次分析法(ANP)评估应急桥梁设计方案的基本步骤.ANP在综合考虑各种因素的同时,考虑到因素间的相互影响,对各因素间的依赖的反馈关系进行了描述和计算,最后进行综合排序.利用超级决策SD(Super Decisions)软件很方便的计算了一个实例,计算结果表明,应用ANP评估应急桥梁设计方案是合理的.     

多工艺方案二阶模糊综合评价

在论述零件信息模型和零件多工艺决策信息模型的基础上 ,提出了一种基于黑板结构和层次递阶工艺设计的多工艺生成模型 ,该层次递阶工艺设计结构分为工艺分析层、工艺决策层、详细工艺设计层和多工艺方案评价层 .然后针对多工艺生成模型生成的多工艺方案 ,提出了一种工艺方案的多对象、多层次二阶模糊综合评价模型 ,并对一个回转类零件三种可行工艺方案进行了模糊综合评价 ,各方案的各项指标的权重是通过采用层次分析法 ( Analytic H ierarchy Process,AH P)确定的.