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

Download

Ali Özarslan Phd Thesis Print Version.pdf

Date

2021-9

Author

Özarslan, Ali

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

344
views

136
downloads

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

Collections

Graduate School of Social Sciences, Thesis

Suggestions

OpenMETU
Core

Interactive Approaches to Multiple Criteria Sorting Problems: Entropy-Based Question Selection Methods Özarslan, Ali; Karakaya, Gülşah (2022-08-01) In this study, interactive approaches for sorting alternatives evaluated on multiple criteria are developed. The possible category ranges of alternatives are defined by mathematical models iteratively under the assumption that the preferences of the decision maker (DM) are consistent with an additive utility function. Simulation-based and model-based parameter generation methods are proposed to hypothetically assign the alternatives to categories. A practical approach to solve the incompatibility problem of...
Interactive approaches for biobjective problems with progressively changing solution sets Karakaya, Gülşah (Wiley, 2021-01-01) In this study, we develop interactive approaches to find a satisfactory alternative of a decision maker (DM) having a quasiconvex preference function where the alternative set changes progressively. In this environment, we keep searching the available set of alternatives and estimating the preference function of the DM. As new alternatives emerge, we make better use of the available preference information and eventually converge to a preferred alternative of the DM. We test our approaches on biobjective, mu...
An interactive probabilistic approach to multi-criteria sorting BUGDACI, Asli Gul; KOKSALAN, Murat; Ozpeynirci, Selin; Serin, Yaşar Yasemin (2013-10-01) This article addresses the problem of sorting alternatives evaluated by multiple criteria among preference-ordered classes. An interactive probabilistic sorting approach is developed in which the probability of an alternative being in each class is calculated and alternatives are assigned to classes keeping the probability of incorrect assignments below a specified small threshold value. The decision maker is occasionally required to place alternatives to classes. The probabilities for unassigned alternativ...
A Probabilistic and interactive approach to multiple criteria sorting Mutlu, Sinem; Köksalan, Murat; Serin, Yaşar Yasemin; Department of Industrial Engineering (2015) In this thesis, we develop a method in order to assign alternatives that are evaluated by multiple criteria into preference ordered classes probabilistically. Our motivation is that; when there are large sets of alternatives, placement could be realized in a fast and effective way based on a reasonable misclassification ratio. We assume that the underlying utility function of Decision Maker (DM) is additive. We first ask DM to place reference alternatives into the classes. We develop an interactive probabil...
A Mathematical programming evaluation approach for multiple criteria sorting problems Civelek, Merve; Karasakal, Esra; Department of Operational Research (2019) Multiple criteria sorting problem is to assign alternatives, evaluated according to multiple criteria, into predefined preference ordered classes. In this study, a new distance metric based sorting method is developed to solve multiple criteria sorting problems without specifying class thresholds between preference-ordered classes. The aim of the proposed method is to assign each alternative to one class or a set of possible adjacent classes considering the distance to class centroids. In the proposed metho...

Citation Formats

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