Papers
This section presents a collection of AHP/ANP papers. Whether you are a student, academic and/or professional in the field of decision making, you can help us expand this collection by sharing your papers on decision making with the Analytic Hierarchy Process (AHP) and the Analytic Network Process (ANP).
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Paper results for keyword: Fuzzy setsFuzzy judgments and fuzzy sets
Thomas Saaty, Liem TranJournal: International Journal of Strategic Decision Sciences Using fuzzy set theory has become attractive to many people. However, the many references cited here and in other works, little thought is given to why numbers should be made fuzzy before plunging into the necessary simulations to crank out numbers without giving reason or proof that it works to ...
Read MoreOn the invalidity of fuzzifying numerical judgments in the Analytic Hierarchy Process
Thomas Saaty, Liem TranJournal: Mathematical and Computer ModellingFuzzy set theory has serious difficulties in producing valid answers in decision-making by fuzzifying judgments. No theorems are available about its workability when it is applied indiscriminately as a number crunching approach to numerical measurements that represent judgments. When judgments ar...
Read MoreThe Analytic Hierarchy Process: A new approach to deal with fuzziness in architecture
Thomas SaatyJournal: Architectural Science ReviewA degree of fuzziness accompanies complex architectural problems. The concept of fuzziness can be compared to the hierarchy of the nervous system. Three types of fuzziness can be isolated: instantaneous, ongoing and long term. In this paper, the need for the development of a conceptually simple f...
Read MoreMeasuring the fuzziness of sets
Thomas SaatyJournal: Journal of CyberneticsSet theory begins to be useful when there is some natural criterion for defining belonging to a set. Sets of objects without properties are uninteresting. Elements are assigned to sets because they share properties or conform to a rule. A set of elements is said to be fuzzy when we allow some ele...
Read MoreOperations Research: Some Contributions to Mathematics: Applied mathematics gets a new surge of life from techniques of operations research
Thomas SaatyJournal: ScienceThe discussion of fuzzy sets indicates that set theory should be extended to make it more suitable for the development of algebraic structures with wider applications. Stochastic optimization, a synthesis of the three areas of continuum mathematics, is a rapidly growing field particularly in the ...
Read MoreExploring the interface between hierarchies, multiple objectives and fuzzy sets
Thomas SaatyJournal: Fuzzy sets and systemsThe complexity of experience acquired through our senses and as interpreted by our mind, is fuzzy and must remain so as long as the meaning of things change as they are embedded in larger or different contexts to relate them to new ideas and new experiences. Here we give a method for measuring th...
Read More
Fuzzy judgments and fuzzy sets
Thomas Saaty, Liem TranJournal: International Journal of Strategic Decision Sciences Using fuzzy set theory has become attractive to many people. However, the many references cited here and in other works, little thought is given to why numbers should be made fuzzy before plunging into the necessary simulations to crank out numbers without giving reason or proof that it works to ...
Read MoreOn the invalidity of fuzzifying numerical judgments in the Analytic Hierarchy Process
Thomas Saaty, Liem TranJournal: Mathematical and Computer ModellingFuzzy set theory has serious difficulties in producing valid answers in decision-making by fuzzifying judgments. No theorems are available about its workability when it is applied indiscriminately as a number crunching approach to numerical measurements that represent judgments. When judgments ar...
Read MoreThe Analytic Hierarchy Process: A new approach to deal with fuzziness in architecture
Thomas SaatyJournal: Architectural Science ReviewA degree of fuzziness accompanies complex architectural problems. The concept of fuzziness can be compared to the hierarchy of the nervous system. Three types of fuzziness can be isolated: instantaneous, ongoing and long term. In this paper, the need for the development of a conceptually simple f...
Read MoreMeasuring the fuzziness of sets
Thomas SaatyJournal: Journal of CyberneticsSet theory begins to be useful when there is some natural criterion for defining belonging to a set. Sets of objects without properties are uninteresting. Elements are assigned to sets because they share properties or conform to a rule. A set of elements is said to be fuzzy when we allow some ele...
Read MoreOperations Research: Some Contributions to Mathematics: Applied mathematics gets a new surge of life from techniques of operations research
Thomas SaatyJournal: ScienceThe discussion of fuzzy sets indicates that set theory should be extended to make it more suitable for the development of algebraic structures with wider applications. Stochastic optimization, a synthesis of the three areas of continuum mathematics, is a rapidly growing field particularly in the ...
Read MoreExploring the interface between hierarchies, multiple objectives and fuzzy sets
Thomas SaatyJournal: Fuzzy sets and systemsThe complexity of experience acquired through our senses and as interpreted by our mind, is fuzzy and must remain so as long as the meaning of things change as they are embedded in larger or different contexts to relate them to new ideas and new experiences. Here we give a method for measuring th...
Read More