标题：saaty
个人介绍
1948年获哥伦比亚联合学院学士学位
1949年获美国天主教大学物理学硕士学位
1951年获耶鲁大学数学硕士学位
1953年获耶鲁大学数学专业博士学位
成就
在决策科学最杰出贡献的是创立了层次分析法（AHP）理论及其推广方法——网络程序法（ANP）理论，发展了考虑依赖和反馈决策的ANP数学理论，构建了基于利益、机会、成本和风险的决策模式。是当今决策科学领域屈指可数的大师级人物。
层次分析法简介
层次分析法(Analytic Hierarchy Process简称AHP)是Saaty教授于70年代初期提出的，AHP是对定性问题进行定量分析的一种简便、灵活而又实用的多准则决策方法。它的特点是把复杂问题中的各种因素通过划分为相互联系的有序层次，使之条理化，根据对一定客观现实的主观判断结构(主要是两两比较)把专家意见和分析者的客观判断结果直接而有效地结合起来，将一层次元素两两比较的重要性进行定量描述。而后，利用数学方法计算反映每一层次元素的相对重要性次序的权值，通过所有层次之间的总排序计算所有元素的相对权重并进行排序。该方法自1982年被介绍到我国以来，以其定性与定量相结合地处理各种决策因素的特点，以及其系统灵活简洁的优点，迅速地在我国社会经济各个领域内，如能源系统分析、城市规划、经济管理、科研评价等，得到了广泛的重视和应用。
用AHP分析问题大体要经过以下五个步骤：(1)建立层次结构模型；(2)构造判断矩阵；(3)层次单排序；(4)层次总排序；(5)一致性检验。其中后三个步骤在整个过程中需要逐层地进行。
1.建立层次结构模型
运用AHP进行系统分析，首先要将所包含的因素分组，每一组作为一个层次，按照最高层、若干有关的中间层和最低层的形式排列起来。 对于决策问题，通常可以将其划分成层次结构模型。
其中：
最高层：表示解决问题的目的，即应用AHP所要达到的目标。
中间层：它表示采用某种措施和政策来实现预定目标所涉及的中间环节，一般又分为策略层、约束层、准则层等。
最低层：表示解决问题的措施或政策(即方案)。
标明上一层因素与下一层因素之间的联系。 如果某个因素与下一层次所有因素均有联系， 那么称这个因素与下一层次存在完全层次关系。有时存在不完全层次关系，即某个因素只与下一层次的部分因素有联系。 层次之间可以建立于层次。 于层次从属于主层次的某个因素，它的因素与下一层次的因素有联系，但不形成独立层次，层次结构模型往往用结构模型图表示。
2.构造判断矩阵
任何系统分析都以一定的信息为基础。AHP的信息基础主要是人们对每一层次各因素的相对重要性给出的判断， 这些判断用数值表示出来，写成矩阵形式就是判断矩阵。 判断矩阵是AHP工作的出发点。构造判断矩阵是AHP的关键一步。
判断矩阵表示针对上一层次某因素而言， 本层次与之有关的各因素之间的相对重要性。【例如】
3.层次单排序
所谓层次单排序是指，根据判断矩阵计算对于上一层某因素而言， 本层次与之有联系的因素的重要性次序的权值。 它是本层次所有因素相对上一层次而言的重要性进行排序的基础。
层次单排序可以归结为计算判断矩阵的特征根和特征向量问题， 即对判断矩阵B，计算满足                     BW ＝λmaxW
的特征根与特征向量，式中λmax为B的最大特征根， W为对应于λmax的正规化特征向量，W的分量Wi是相应因素单排序的权值。
为了检验矩阵的一致性，需要计算它的一致性指标CI，定义
CI＝(λmax－n)/(n－1)
显然，当判断矩阵具有完全一致性时，CI＝0。λmax－n愈大，CI愈大，矩阵的一致性愈差。为了检验判断矩阵是否具有满意的一致性， 需要将CI与平均随机一致性指标RI进行比较。
4.层次总排序
利用同一层次中所有层次单排序的结果，就可以计算针对上一层次而言，本层次所有因素重要性的权值，这就是层次总排序。 层次总排序需要从上到下逐层顺序进行，对于最高层下面的第二层，其层次单排序即为总排序。
5.一致性检验
所获奖励
[1]    2009年获匹斯堡大学校长杰出研究奖
[2]    2008年获INFORMS影响奖，运筹学和管理学研究协会奖励其在AHP中的杰出贡献。
[3]    2005年，当选美国国家工程院院士
[4]    2003年获国际多准则学会金质奖
[5]    基于saaty的层次分析法理论，国际层次分析法协会建立，并先后在匹斯堡、华盛顿、温哥华、天津、神户、伯尼尔、巴厘岛等地召开国际会议。
[6]    2000年获金质奖奖励，国际多准则决策协会奖励其在决策中的贡献
[7]    1998年当选为国际管理学会会员
[8]    1984年获贝塔•伽玛•西格玛奖章
[9]    1982年，获哥伦比亚联合学院校友年度荣誉
[10] 1982年Thomas L. Saaty奖项设立，奖励在数学和管理的最佳研究论文。
[11] 1977年美国管理科学协会奖励其在管理科学实践中的贡献：苏丹运输计划
[12] 1973年获美国数学协会莱斯特福特奖，表彰其在四色理论中的出色贡献
[13] 1970年当选西班牙国家科学院院士
[14] 1959年当选为美国科学发展协会会员
学术论文
近5年在《EUROPEAN JOURNAL OF OPERATIONAL RESEARCH》等期刊发表SCI论文14篇，引用73次。出版学术著作5部。出版关于AHP/ANP著作12部，关于AHP和领导决策方面的非技术性著作已被翻译成几种语言畅销全球。
[1] Extending the Measurement of Tangibles to Intangibles, (with Mujgan Sagir), Int. J. of Informations Technology and Decision Making, Vol. 8, No. 1, pp. 7-27, 2009. 
[2] Relative Measurement and Its Generalization in Decision Making; Why Pairwise Comparisons are Central in Mathematics for the Measurement of Intangible Factors The Analytic Hierarchy/Network Process, Royal Academy of Sciences, Spain, Series A. Mathematics, November, pp. 251-318, 2008
[3] Making decisions in hierarchic and network systems, (with Mariya Sodenkamp), Int. J. Applied Decision Sciences, Vol.1, No. 1, pp. 24-79, 2008.
[4] Who Won the 2008 Olympics? Journal of Systems Science and Systems Engineering, Vol. 17, No, 4,pp.473-486, Dec. 2008.
[5] Synthesis of Complex Criteria Decision Making: A Case Towards a Consensus Agreement for a Middle East Conflict Resolution, (with J. Zoffer et al.) Group Decision and Negotiation, 17: 363-385, 2008.
[6] The Analytic Network Process, Iranian Journal of Operations Research, Vol.1 No.1 pp.1-27, 2008.
[7] The analytic hierarchy and analytic network measurement processes: Applications to decisions under Risk, European Journal of Pure and Applied Mathematics, Vol.1, No.1, pp. 122-196, 2008.
[8] Decision Making with the Analytic Hierarchy Process, Int.J. Services Sciences, Vol. 1, No. 1, 2008.
[9] Time Dependent Decision making; Dynamic Priorities In the AHP/ANP: Generalizing from Points to Functions and from Real to Complex Variables, Mathematical and computer Modelling, Vol. 46, No. 7-8, pp. 860-889, October 2007.
[10] Dispersion of Group Judgments, (with Luis Vargas), Mathematical and computer Modelling, Vol. 46, No. 7-8, pp. 918-925, October 2007.
[11] On the Invalidity of Fuzzifying Numerical Judgments in the Analytic Hierarchy Process, (with Liem T. Tran), Mathematical and computer Modelling, Vol. 46, No. 7-8, pp. 962-975, October 2007.
[12] Multi-decisions Decision-Making: In Addition to Wheeling and Dealing, our national Political Bodies Need a Formal Approach for Prioritization, Mathematical and computer Modelling, Vol. 46, No. 7-8, pp. 1001-1016, October 2007.
[13] The Analytic Hierarchy Process and Human Resource Allocation: Half the Story (with Kirti Peniwati and Jennifer Shang), Mathematical and computer Modelling, Vol. 46, No. 7-8, pp. 1041-1053, October 2007.
[14] The Analytic Hierarchy Process: How to Measure Intangibles in a Meaningful Way Side by Side with tangibles, Transactions from International Symposium on Quality Function Deployment, 19th Symposium, pp. 113-135, 2007.
[15] Group decision-making: Head-count versus intensity of preference,(with Jennifer Shang) Socio-Economic Planning Sciences 41, pp. 22-37, 2007. 
[16] There is no Mathematical Validity for Using Fuzzy Number Crunching in the Analytic Hierarchy Process, Journal of Systems Science and Systems Engineering, V0l. 15, No. 4, December 2006.
[17] What is AHP/ANP, Proceedings of the First Japanese Symposium on the Analytic Hierarchy Process, Meijo University, Nagoya, Japan, December, 2006, pp.3-50.
[18] The Unknown in Decision Making: What to do about it, European Journal of Operational Research, 174, 2006, 349-359, with M. Ozdemir.
[19] The Analytic Hierarchy Process: Wash Criteria Should not be Ignored, International Journal of Management and Decision Making, Vol. 7, Nos.2/3, 2006 with L. Vargas
[20] Rank from comparisons and from ratings in the analytic hierarchy/network processes, European Journal of Operational Research 168 (2006) 557-570.
[21] A framework for making a better decision (with Michael Niemira), Research Review, Vol. 13, No. 1, 2006.
[22] Making and Validating Complex Decisions with the AHP/ANP, Journal of Systems Science and Systems Engineering, published at Tsinghua University, Beijing Vol. 14, No. 1, March, 2005, pages 1-36.
[23] The Possibility of Group Welfare Functions, Information Technology and Decision Making, Vol.4, No.2, 2005, pages 167-176, with L. Vargas.
[24] Los conflictos y la resolución de conflictos, Poliantea, Politécnico Grancolombiano, Bogotá, Colombia, No.2 July-December 2004.
[25] An Analytic Network Process model for financial-crisis forecasting, International Journal of Forecasting, Volume 20, Issue 4, October-December 2004, Pages 573-587 with Michael P. Niemira. 
[26] The Analytic Hierarchy Process in Medical Diagnosis, the Encyclopedia of Biostatistics, John Wiley and Sons, 2004.
[27] Automatic Decision-Making: Neural Firing and Response, Journal of Systems Science and Systems Engineering, published at Tsinghua University, Beijing Vol. 13, No. 4, December, 2004, pages 385-404.
[28] Fundamentals of the Analytic Network Process: Multiple Networks with Benefits, Costs, Opportunities and Risks, Journal of Systems Science and Systems Engineering, published at Tsinghua University, Beijing, Vol. 13, No. 3, September, 2004, pages 348-379.
[29] Fundamentals of the Analytic Network Process: Dependence and Feedback in Decision-Making with a Single Network, Journal of Systems Science and Systems Engineering, published at Tsinghua University, Beijing, Vol. 13, No. 2, June, 2004, pages 129-157.
[30] Decision Making- The Analytic Hierarchy and Network Processes (AHP/ANP), Journal of Systems Science and Systems Engineering, published at Tsinghua University, Beijing, Vol. 13, No. 1, March 2004, pages 1-35.
[31] Rank from Comparisons and from Ratings in the Analytic Hierarchy/ Network Processes, European Journal of Operational Research, 168, 2006, pages 557-570.
[32] Why the Magic Number Seven Plus or Minus Two, Mathematical and Computer Modelling, 38, 2003 pages 233-244 (With M. Ozdemir)
[33] Theory of the Analytic Hierarchy and Analytic network process- Examples Part 2.2, The International Journal of Systems Research and Information Technologies, 2,2003.
[34] Time Dependent Decision-Making; Dynamic Priorities in the AHP/ANP, Generalizing from Points to Functions and From Real to Complex Variables, Proceedings of the 7th ISAHP Symposium on the AHP, Bali, Indonesia, August, 2003 
[35] Theory of the Analytic hierarchy Process, Part 2.1, The International Journal of Systems Research and Information Technologies, 1,2003.
[36] Decision-making with the AHP: Why is the principal eigenvector necessary, European Journal of Operational Research 145 (2003) 85-9. 
[37] Priorities as Dominance in Derived measurement: Invariance of the Principal Eigenvector, International Journal of Information Technology and Decision Making, Vol. 2, No. 2 (2003) 185-195 (With M. Ozdemir).
[38] Negative Priorities in the Analytic Hierarchy Process, Mathematical and Computer Modelling 37 (2003) 1063-1075 (With M. Ozdemir).
[39] The Allocation of Intangible Resources: The Analytic Hierarchy Process and Linear programming," Socio-Economic Planning Sciences 37 (2003) 169-184. (With L. Vargas and K. Dellmann). 
[40] How to Make and Justify a Decision: The Analytic Hierarchy Process (AHP); Part 1. Examples and Applications, The Journal of the Ukrainian Academy of Sciences, 2002, 1.
[41] Decision Making with the Analytic Hierarchy Process, The Iranian Academy of Sciences in their Journal, Scientia Iranica, Vol. 9, No. 3, July 2002.
[42] Forecasting the Resurgence of the US Economy in 2001: An Expert Judgment Approach, Socio-Economic Planning Sciences, 36(2002) 77-91, (with Andrew R.Blair, Robert Nachtmann, and Rozann Whitaker)
[43] Wrote preface for the book, Modernes Entscheiden mit AHP und Expert Choice, by Oliver Meixner and Rainer Haas of Vienna, Austria, published in German in 2001
[44] "In the Brain Ratio Scales Are Critical for Modeling Neural Synthesis," Proceedings of the 5th International Conference on Artificial Neural Networks and Genetic Algorithms (ICANNGA), Academy of Sciences, The Czech Republic, Prague, April 22-25, 2001
[45] "Hypermatrix of the Brain," Proceedings of the 5th International Conference on Artificial Neural Networks and Genetic Algorithms (ICANNGA), Academy of Sciences, The Czech Republic, Prague, April 22-25, 2001
[46] "Deriving the AHP 1-9 Scale from First Principles," ISAHP 2001 Proceedings, Bern, Switzerland, August, 2-4, 2001
[47] "Decision Making with the AHP: Why is the Principal Eigenvector Necessary?," ISAHP 2001 Proceedings, Bern, Switzerland, August, 2-4, 2001
[48] "Decision Making with the Analytic Network Process (ANP) and Its "Super Decisions" Software: The National Missile Defense (NMD) Example," ISAHP 2001 Proceedings, Bern, Switzerland, August, 2-4, 2001
[49] "The Decision by the US Congress on China's Trade Status: A Multicriteria Analysis," Socio-Economic Planning Sciences, 35(2001) 243-252, (with Yeonmin Cho).
[50] "Ratio Scales are Essential in Neural Synthesis," Invited Lecture, Academy of Sciences, Prague, The Czech Republic, Springer Verlag, to appear April 2001.
[51] "Hypermatrix of the Brain," Invited Lecture, Academy of Sciences, Prague, The Czech Republic, Springer Verlag, to appear April 2001.
[52] "Como Tomar Una Decisions y," published in a new magazine on decision making in Argentina: Decisiones: Toma de Decisiones, January 2000, Vol. I, No.1, Buenos Aires, Argentina.
教材与论著
[1] Principia Mathematica Decernendi: Mathematical Principles of Decision Making, RWS Publications, 4922 Ellsworth Avenue, Pittsburgh, PA 15213, 2010.
[2] The Encyclicon Volume 2 (with Brady Cillo), RWS Publications, 4922 Ellsworth Avenue, Pittsburgh, PA 15213, 2008.
[3] Group Decision Making: Drawing Out and Reconciling Differences (with Kirti Peniwati), RWS Publications, 4922 Ellsworth Avenue, Pittsburgh, PA 15213, 2008.
[4] Decision Making with the Analytic Network Process: Economic, Political, Social and Technological Applications with benefits, Opportunities, Costs and Risks, (with L.G. Vargas), 2006, Springer's International Series.
[5] Theory and Applications of the Analytic Network Process, RWS Publications, 4922 Ellsworth Avenue, Pittsburgh, PA 15213, 2005.
[6] The Encyclicon (with M. Ozdemir), RWS Publications, 4922 Ellsworth Avenue, Pittsburgh, PA 15213, 2004.
[7] Creative Thinking, Problem Solving & Decision Making, RWS Publications, 4922 Ellsworth Avenue, Pittsburgh, PA 15213, 2001.
[8] Models, Methods, Concepts and Applications of the Analytic Hierarchy Process (with L.G. Vargas), Kluwer Academic Publishers, Boston, 2000.
[9] The Brain, Unraveling the Mystery of How it Works: The Neural Network Process, RWS Publications, 4922 Ellsworth Avenue, Pittsburgh, PA 15213, 2000.
主要兼职
是下列组织的成员：美国工程院、美国数学学会、美国数学协会、美国运筹学会、国际战略研究所、世界未来学会、国际和平科学学会、国际管理学会、贝塔•伽玛•西格玛组织。
担任下列8家学术杂志的副编辑：
Socio-Economic Planning Sciences
The International Journal of Systems
Measurement and Decisions
The Journal of Mathematical Modeling
Information Technology and Decision Makingr
Journal of Multi-Criteria Decision Analysis、Journal of Systems Science and Systems Engineering (JSSSE)
International Journal of Organizational Analysis
Applied Mathematical Letters.