On Fuzzy-Mathematical Programming
01 Jan 1973-Vol. 3, Iss: 4, pp 37-46
TL;DR: The main concern is with the application of the theory of fuzzy sets to decision problems involving fuzzy goals and strategies, etc., as defined by R. E. Bellman and L. A. Zadeh.
Abstract: In problems of system analysis, it is customary to treat imprecision by the use of probability theory. It is becoming increasingly clear, however, that in the case of many real world problems involving large scale systems such as economic systems, social systems, mass service systems, etc., the major source of imprecision should more properly be labeled ‘fuzziness’ rather than ‘randomness.’ By fuzziness, we mean the type of imprecision which is associated with the lack of sharp transition from membership to nonmembership, as in tall men, small numbers, likely events, etc. In this paper our main concern is with the application of the theory of fuzzy sets to decision problems involving fuzzy goals and strategies, etc., as defined by R. E. Bellman and L. A. Zadeh [1]. However, in our approach, the emphasis is on mathematical programming and the use of the concept of a level set to extend some of the classical results to problems involving fuzzy constraints and objective functions.
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TL;DR: This paper reviews theory and methodology that have been developed to cope with the complexity of optimization problems under uncertainty and discusses and contrast the classical recourse-based stochastic programming, robust stochastics programming, probabilistic (chance-constraint) programming, fuzzy programming, and stochastically dynamic programming.
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01 Nov 1992
TL;DR: In this paper, a grey linear programming (GLP) model is introduced to the civil engineering area, which allows uncertainties in the model inputs to be communicated into the optimization process, and thereby solutions reflecting the inherent uncertainties can be derived.
Abstract: In optimization analysis by linear programming, uncertainties may exist in model coefficients and stipulations (right-hand side constraints). These uncertainties can propagate through the analysis and generate uncertainties in the results. However, among the previous methods dealing with uncertainty, some were too complicated to be applied to actual problems, and some were unable to reflect completely the uncertainties of the input and output information. In this paper, a grey linear programming (GLP) model is introduced to the civil engineering area. This method allows uncertainties in the model inputs to be communicated into the optimization process, and thereby solutions reflecting the inherent uncertainties can be derived. A grey linear programming problem can be solved easily by running a simplex program several times. The modelling approach is applied to a hypothetical problem of waste flow allocation planning within a municipal solid waste management system. The results indicate that reaso...
558 citations
11 Mar 1996
TL;DR: The most important methods are reviewed and a novel approach — interdependence in MCDM — is introduced.
Abstract: Multiple criteria decision making (MCDM) shows signs of becoming a maturing field. There are four quite distinct families of methods: (i) the outranking, (ii) the value and utility theory based, (iii) the multiple objective programming, and (iv) group decision and negotiation theory based methods. Fuzzy MCDM has basically been developed along the same lines, although with the help of fuzzy set theory a number of innovations have been made possible; the most important methods are reviewed and a novel approach — interdependence in MCDM — is introduced.
526 citations