The set of all nondominated solutions in linear cases and a multicriteria simplex method
Po-Lung Yu,M Zeleny +1 more
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TLDR
In this paper, a necessary and sufficient condition for a point to be non-convex is derived and a decomposition theorem for a face to be nonsmooth is given.About:
This article is published in Journal of Mathematical Analysis and Applications.The article was published on 1975-02-01 and is currently open access. It has received 377 citations till now. The article focuses on the topics: Extreme point & Convex hull.read more
Citations
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TOPSIS for MODM
TL;DR: In this article, the authors extend TOPSIS to solve a multiple objective decision making problem, and obtain a single-objective programming problem by using the max-min operator for the second-order compromise operation.
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Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives
TL;DR: In this article, a structure of domination over the objective space and the geometry of the set of all non-convex solutions for decision problems with multiple non-commensurable objectives is proposed.
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Multiple Criteria Decision Making, Multiattribute Utility Theory: The Next Ten Years
TL;DR: In this paper, the history of MCDM and MAUT is discussed and topics are discussed for their continued development and usefulness to management science over the next decade, identifying exciting directions and promising areas for future research.
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A concept of compromise solutions and the method of the displaced ideal
TL;DR: Several complementary ways of reducing the nondominated set of nondominated solutions are discussed: weight space decomposition, fuzzy weight assessment and the ideal solution displacement.
References
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Book
Nonlinear Programming
TL;DR: It is shown that if A is closed for all k → x x, k → y y, where ( k A ∈ ) k y x , then ( ) A ∉ y x .
Journal ArticleDOI
Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives
TL;DR: In this article, a structure of domination over the objective space and the geometry of the set of all non-convex solutions for decision problems with multiple non-commensurable objectives is proposed.
Journal ArticleDOI
A concept of compromise solutions and the method of the displaced ideal
TL;DR: Several complementary ways of reducing the nondominated set of nondominated solutions are discussed: weight space decomposition, fuzzy weight assessment and the ideal solution displacement.
Book
Linear multiobjective programming
TL;DR: The Origin of the Multiobjective Problem and a Short Historical Review are reviewed and a method for Generating Adjacent Extreme Points - A Second Approach (Multicriteria Simplex Method).