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).
Search papers by keyword:
Paper results for keyword: Set theoryMeasuring 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 MoreThe number of vertices of a polyhedron
Thomas SaatyJournal: The American Mathematical MonthlyThe number of vertices of a polyhedron
Read MoreParametric objective function (part 1)
Saul Guss, Thomas SaatyJournal: Journal of the Operations Research Society of AmericaIn the linear programming problem where there is a linear function to be optimized (called the objective function), it is desirable to study the behaviour of solutions when the (cost) coefficients in the objective function are parametrized. The problem is then to find the set of xj (j = 1, 2, …, ...
Read More
Measuring 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 MoreThe number of vertices of a polyhedron
Thomas SaatyJournal: The American Mathematical MonthlyThe number of vertices of a polyhedron
Read MoreParametric objective function (part 1)
Saul Guss, Thomas SaatyJournal: Journal of the Operations Research Society of AmericaIn the linear programming problem where there is a linear function to be optimized (called the objective function), it is desirable to study the behaviour of solutions when the (cost) coefficients in the objective function are parametrized. The problem is then to find the set of xj (j = 1, 2, …, ...
Read More