Fuzzy set theoretic approach of assigning weights to objectives in multieriteria decision making

Rao, Jinghai; Roy, Nilima

doi:10.1080/00207728908910222

Cited by 18 publications

(5 citation statements)

References 4 publications

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“…Methods for selecting the weights have been the focus of considerable research and discussion in fields ranging from statistics to social science (e.g., Akaike 1973, Saaty 1988, Rao and Roy 1989, Goodwin and Wright 2004. Weights are often constrained such that w i ≥ 0 and k i=1 w i = 1 to aid in interpreting weights as relative importance of objectives.…”

Section: Pareto Optimal Solutions and Specification Of Preferencesmentioning

confidence: 99%

A guide to multi-objective optimization for ecological problems with an application to cackling goose management

Williams

Kendall

2017

Ecological Modelling

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Choices in ecological research and management are the result of balancing multiple, often competing, objectives. Multi-objective optimization (MOO) is a formal decision-theoretic framework for solving multiple objective problems. MOO is used extensively in other fields including engineering, economics, and operations research. However, its application for solving ecological problems has been sparse, perhaps due to a lack of widespread understanding. Thus, our objective was to provide an accessible primer on MOO, including a review of methods common in other fields, a review of their application in ecology, and a demonstration to an applied resource management problem. A large class of methods for solving MOO problems can be separated into two strategies: modelling preferences pre-optimization (the a priori strategy), or modelling preferences post-optimization (the a posteriori strategy). The a priori strategy requires describing preferences among objectives without knowledge of how preferences affect the resulting decision. In the a posteriori strategy, the decision maker simultaneously considers a set of solutions (the Pareto optimal set) and makes a choice based on the trade-offs observed in the set. We describe several methods for modelling preferences pre-optimization, including: the bounded objective function method, the lexicographic method, and the weighted-sum method. We discuss modelling preferences post-optimization through examination of the Pareto optimal set. We applied each MOO strategy to the natural resource management problem of selecting a population target for cackling goose (Branta hutchinsii minima) abundance. Cackling geese provide food security to Native Alaskan subsistence hunters in the goose's nesting area, but depredate crops on private agricultural fields in wintering areas. We developed objective functions to represent the competing objectives related to the cackling goose population target and identified an optimal solution first using the a priori strategy, and 2 Williams and Kendall • Multi-Objective Optimization then by examining trade-offs in the Pareto set using the a posteriori strategy. We used four approaches for selecting a final solution within the a posteriori strategy; the most common optimal solution, the most robust optimal solution, and two solutions based on maximizing a restricted portion of the Pareto set. We discuss MOO with respect to natural resource management, but MOO is sufficiently general to cover any ecological problem that contains multiple competing objectives that can be quantified using objective functions.

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Section: Pareto Optimal Solutions and Specification Of Preferencesmentioning

confidence: 99%

A guide to multi-objective optimization for ecological problems with an application to cackling goose management

Williams

Kendall

2017

Ecological Modelling

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“…Initial work on the weighted-sum method can be found in [ 49 ] with many subsequent applications and citations. Rao and Roy proposed a method for determining weights based on fuzzy set theory [ 50 ]. Marler and Arora provided insight into how the weighted-sum method works and have explored the significance of the weights with respect to preferences, the Pareto optimal set, and the objective-function values [ 51 ].…”

Section: Uncertain Portfolio Selection Modelmentioning

confidence: 99%

An Artificial Bee Colony Algorithm for Uncertain Portfolio Selection

Chen

2014

The Scientific World Journal

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Portfolio selection is an important issue for researchers and practitioners. In this paper, under the assumption that security returns are given by experts' evaluations rather than historical data, we discuss the portfolio adjusting problem which takes transaction costs and diversification degree of portfolio into consideration. Uncertain variables are employed to describe the security returns. In the proposed mean-variance-entropy model, the uncertain mean value of the return is used to measure investment return, the uncertain variance of the return is used to measure investment risk, and the entropy is used to measure diversification degree of portfolio. In order to solve the proposed model, a modified artificial bee colony (ABC) algorithm is designed. Finally, a numerical example is given to illustrate the modelling idea and the effectiveness of the proposed algorithm.

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“…Consequently, many authors have developed systematic approaches to selecting weights, surveys of which are provided by Eckenrode (1965), Hobbs (1980), Hwang and Yoon (1981), and Voogd (1983). Rao and Roy (1989) provide a method for determining weights based on fuzzy set theory. For cases in which the relative importance of the objective functions is unclear, Wierzbicki (1986) provides an algorithm that calculates weights based on the aspiration point and the utopia point.…”

Section: Converting Moop To Soopmentioning

confidence: 99%

Cellular Automata in Topology Optimization of Continuum Structures

Sanaei¹,

Babaei²

2011

Int. J. Eng. Sci. Tech

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In this paper, an optimization algorithm based on cellular automata (CA) is developed for topology optimization of continuum structures with shear and flexural behavior. The design domain is divided into small triangle elements and each cell is considered as a finite element. The stress analysis is performed by the Constant Strain Triangles (CST) finite elements method. The thicknesses of the individual cells are taken as the design variables, while the weight of the structure and the ratio of the Von Mises equivalent stress to the yield stress in each cell are considered as the two objective functions to minimize. Using the weighted sum method, the multi-objective optimization problem (MOOP) is converted to the single-objective optimization problem (SOOP) and then the optimization problem is solved by the developed method. The paper reports the results of several design experiments, comparing with the existing reported results.

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Fuzzy set theoretic approach of assigning weights to objectives in multieriteria decision making

Cited by 18 publications

References 4 publications

A guide to multi-objective optimization for ecological problems with an application to cackling goose management

A guide to multi-objective optimization for ecological problems with an application to cackling goose management

An Artificial Bee Colony Algorithm for Uncertain Portfolio Selection

Cellular Automata in Topology Optimization of Continuum Structures

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