Computing a Pareto-optimal solution for multi-objective flexible linear programming in a bipolar framework
TL;DR: In this paper, a solution concept of Pareto-optimality for MOFLP problems is defined and an approach is proposed to single out such a solution forMOFLP with highest possible degree of feasibility.
Abstract: In this paper, we study the multi-objective flexible linear programming (MOFLP) problems (or fuzzy multi-objective linear programming problems) in the heterogeneous bipolar framework. Bipolarity allows us to distinguish between the negative and the positive preferences. Negative preferences denote what is unacceptable while positive preferences are less restrictive and express what is desirable. This viewpoint enables us to handle fuzzy sets representing constraints and objective functions separately and combine them in distinct ways. In this paper, a solution concept of Pareto-optimality for MOFLP problems is defined and an approach is proposed to single out such a solution for MOFLP with highest possible degree of feasibility.
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TL;DR: Two crisp linear models to solve fuzzy multiple objective linear fractional programming problems are introduced, and can generate distinct solutions to the multiple objective problem by varying the thresholds and tolerance limits imposed on the fuzzy goals.
Abstract: The aim of this paper is to introduce two crisp linear models to solve fuzzy multiple objective linear fractional programming problems. In a novel manner we construct two piece-wise linear membership functions to describe the fuzzy goal linked to a linear fractional objective. They are related to the numerator and denominator of the fractional objective function; and we show that using the fuzzy-and operator to aggregate them a convenient description of the original fractional fuzzy goal is obtained. Further on, with the help of the fuzzy-and operator we aggregate all fuzzy goals and constraints, formulate a crisp linear model, and use it to provide a solution to the initial fuzzy multiple objective linear fractional programming problem. The second model embeds in distinct ways the positive and negative information, the desires and restrictions respectively; and aggregates in a bipolar manner the goals and constraints. The main advantage of using the new models lies in the fact that they are linear, and can generate distinct solutions to the multiple objective problem by varying the thresholds and tolerance limits imposed on the fuzzy goals.
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Cites background or methods from "Computing a Pareto-optimal solution..."
...Separating the goals and constraints, and aggregating them in different ways a bipolar framework for computing a Pareto-optimal solution to multiple objective flexible linear programming is developed in [3]....
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...We next recall the example presented in [3], and adapt it by combining their first and third linear objectives in one fractional objective, and keeping their second objective unchanged, linear....
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References
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03 Jan 1988
TL;DR: A type of operator for aggregation called an ordered weighted aggregation (OWA) operator is introduced and its performance is found to be between those obtained using the AND operator and the OR operator.
Abstract: The author is primarily concerned with the problem of aggregating multicriteria to form an overall decision function. He introduces a type of operator for aggregation called an ordered weighted aggregation (OWA) operator and investigates the properties of this operator. The OWA's performance is found to be between those obtained using the AND operator, which requires all criteria to be satisfied, and the OR operator, which requires at least one criteria to be satisfied. >
6,534 citations
"Computing a Pareto-optimal solution..." refers background in this paper
...To know more about the properties and applications of OWA operators, please refer to Fullér (1996, 2007), O’Hagan (1988), Yager (1988, 1996a), Yager and Filev (1994), and Yager and Kacprzyk (1997)....
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TL;DR: It is shown that solutions obtained by fuzzy linear programming are always efficient solutions and the consequences of using different ways of combining individual objective functions in order to determine an “optimal” compromise solution are shown.
3,357 citations
01 Jan 1988
3,030 citations
TL;DR: An extension of the OWA operators which involves the use of triangular norms is introduced and a procedure for determining the measure of “orness” directly from the quantifier is suggested.
Abstract: We consider multicriteria aggregation problems where, rather than requiring all the criteria be satisfied, we need only satisfy some portion of the criteria. The proportion of the critera required is specified in terms of a linguistic quantifier such as most. We use a fuzzy set representation of these linguistic quantifiers to obtain decision functions in the form of OWA aggregations. A methodology is suggested for including importances associated with the individual criteria. A procedure for determining the measure of “orness” directly from the quantifier is suggested. We introduce an extension of the OWA operators which involves the use of triangular norms. © 1996 John Wiley & Sons, Inc.
1,056 citations
Book•
01 Oct 1997TL;DR: This volume is the first in the literature on the increasingly popular Ordered Weighted Averaging (OWA) operators, making it possible to change the form of aggregation from the `pessimistic' minimum-type aggregation through all intermediate types, to the `optimistic' maximum-type aggregations.
Abstract: This volume is the first in the literature on the increasingly popular Ordered Weighted Averaging (OWA) operators. These OWA operators make it possible to change the form of aggregation from the `pessimistic' minimum-type aggregation through all intermediate types including the conventional arithmetic mean and nonconventional aggregations, to the `optimistic' maximum-type aggregations. Included are contributions from a number of fields where these operators have been applied. These fields are decision analysis under uncertainty, learning and classification, multi-person decision-making and consensus formation, and flexible database querying and information retrieval.
936 citations