Information theoretic measure based interactive approaches to multi-criteria sorting problems

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Ali Özarslan Phd Thesis Print Version.pdf

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2021-9

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Özarslan, Ali

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In this thesis, we develop interactive approaches for sorting alternatives evaluated on multiple criteria. We assume that the preferences of the decision maker are consistent with an additive preference function in general monotone and piecewise linear forms. We progressively solve mathematical models to identify the possible category range of the alternatives and ask the decision maker to place an alternative in each iteration. Based on the mathematical models and Monte Carlo simulations, we hypothetically assign alternatives to find the assignment frequency and the probability of an alternative to be assigned to a category. We then use an information theoretic measure, relative entropy, in the determination of the assignment uncertainties and the selection of the alternative that will be assigned to a category by the decision maker. In our non-probabilistic approach, our algorithm guarantees the assignment of all available alternatives to their true categories assuming that the preferences of the decision maker are consistent with an additive function. Our probabilistic algorithm allows the assignment of the alternatives based on the estimated assignment probabilities once the decision maker provides enough assignment information. We implement the proposed algorithms and different benchmark algorithms on three example problems from the literature as well as randomly generated problems. We consider the cases with/without category size restrictions and initial assignments in problem settings. The results show that the proposed algorithms perform well in terms of decreasing the cognitive burden of the decision maker, decreasing the misclassification of the alterantives and the length of the decision process.

Subject Keywords

Multiple Criteria Sorting, Additive Preference Function, Mathematical Programming, Relative Entropy, Category Size Restriction

URI

https://hdl.handle.net/11511/93033

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Graduate School of Social Sciences, Thesis

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Citation Formats

A. Özarslan, “Information theoretic measure based interactive approaches to multi-criteria sorting problems,” Ph.D. - Doctoral Program, Middle East Technical University, 2021.