PROMETHEE: an extension through fuzzy mathematical programming

PROMETHEE multi-criteria methods are based on fuzzy evaluations of the differences between pairs of alternatives for each criterion. PROMETHEE II associates a crisp number to each action. PROMETHEE III associates an interval to each action and two actions are considered indifferent when they are ver...

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Published in:The Journal of the Operational Research Society Vol. 56; no. 1; pp. 119 - 122
Main Authors: FERNANDEZ-CASTRO, A. S, JIMENEZ, M
Format: Journal Article
Language:English
Published: Basingstoke Taylor & Francis 01.01.2005
Palgrave Macmillan Press
Palgrave
Taylor & Francis Ltd
Subjects:
Applied sciences
Capital budgeting
Coefficients
Decision making
Exact sciences and technology
Fuzzy sets
Integers
Linear programming
Linguistics
Mathematical intervals
Mathematical programming
Musical intervals
Objective functions
Operational research and scientific management
Operational research. Management science
Operations research
Portfolio theory
Studies
Technical Notes
Integer programming
fuzzy sets
Multicriteria analysis
Linear programming
Fuzzy programming
Budgeting
Capital
Objective function
Fuzzy set
Soft constraint
capital budgeting
Mathematical programming
ISSN:0160-5682, 1476-9360
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Abstract PROMETHEE multi-criteria methods are based on fuzzy evaluations of the differences between pairs of alternatives for each criterion. PROMETHEE II associates a crisp number to each action. PROMETHEE III associates an interval to each action and two actions are considered indifferent when they are very close to each other. PROMETHEE V applies Integer Linear Programming in order to select the subset of alternatives that maximizes the sum of PROMETHEE II scorings, subject to a set of constraints. In order to make the model more realistic, this paper proposes that some constraints are soft and some coefficients are estimated by fuzzy numbers. Fuzzy Integer Linear Programming is applied, using the PROMETHEE III scorings as objective function coefficients, in order to find the subsets of non-outranked alternatives that best satisfy the soft constraints. The new model is more realistic and fits better the fuzzy philosophy of PROMETHEE. The method is illustrated with an example.
AbstractList PROMETHEE multi-criteria methods are based on fuzzy evaluations of the differences between pairs of alternatives for each criterion. PROMETHEE II associates a crisp number to each action. PROMETHEE III associates an interval to each action and two actions are considered indifferent when they are very close to each other. PROMETHEE V applies Integer Linear Programming in order to select the subset of alternatives that maximizes the sum of PROMETHEE II scorings, subject to a set of constraints. In order to make the model more realistic, this paper proposes that some constraints are soft and some coefficients are estimated by fuzzy numbers. Fuzzy Integer Linear Programming is applied, using the PROMETHEE III scorings as objective function coefficients, in order to find the subsets of non-outranked alternatives that best satisfy the soft constraints. The new model is more realistic and fits better the fuzzy philosophy of PROMETHEE. The method is illustrated with an example.
PROMETHEE multi-criteria methods are based on fuzzy evaluations of the differences between pairs of alternatives for each criterion. PROMETHEE II associates a crisp number to each action. PROMETHEE III associates an interval to each action and two actions are considered indifferent when they are very close to each other. PROMETHEE V applies Integer Linear Programming in order to select the subset of alternatives that maximizes the sum of PROMETHEE II scorings, subject to a set of constraints. In order to make the model more realistic, this paper proposes that some constraints are soft and some coefficients are estimated by fuzzy numbers. Fuzzy Integer Linear Programming is applied, using the PROMETHEE III scorings as objective function coefficients, in order to find the subsets of non-outranked alternatives that best satisfy the soft constraints. The new model is more realistic and fits better the fuzzy philosophy of PROMETHEE. The method is illustrated with an example. [PUBLICATION ABSTRACT]
Author Jiménez, M
Fernández-Castro, A S
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  surname: JIMENEZ
  fullname: JIMENEZ, M
  organization: University of The Basque Country, Spain
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Cites_doi 10.1007/978-94-015-7949-0
10.1080/00137919808903193
10.1016/S0165-0114(99)00021-4
10.1080/00137919808903203
10.1007/978-1-4615-5645-9_6
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Copyright 2005 Operational Research Society Ltd
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Keywords Integer programming
fuzzy sets
Multicriteria analysis
Linear programming
Fuzzy programming
Budgeting
Capital
Objective function
Fuzzy set
Soft constraint
capital budgeting
Mathematical programming
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Kaufmann A (CIT0007) 1991
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Rommelfanger H (CIT0008) 1998
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SubjectTerms Applied sciences
Capital budgeting
Coefficients
Decision making
Exact sciences and technology
Fuzzy sets
Integers
Linear programming
Linguistics
Mathematical intervals
Mathematical programming
Musical intervals
Objective functions
Operational research and scientific management
Operational research. Management science
Operations research
Portfolio theory
Studies
Technical Notes
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