Single machine scheduling problems with uncertain parameters and the OWA criterion

In this paper a class of single machine scheduling problems is discussed. It is assumed that job parameters, such as processing times, due dates, or weights are uncertain and their values are specified in the form of a discrete scenario set. The Ordered Weighted Averaging (OWA) aggregation operator is used to choose an optimal schedule. The OWA operator generalizes traditional criteria in decision making under uncertainty, such as the maximum, average, median or Hurwicz criterion. It also allows us to extend the robust approach to scheduling by taking into account various attitudes of decision makers towards the risk. In this paper a general framework for solving single machine scheduling problems with the OWA criterion is proposed and some positive and negative computational results for two basic single machine scheduling problems are provided

A Comparison of Discrete and Polyhedral Uncertainty Sets for Robust Network Design

We consider a network design and expansion problem, where we need to make a capacity investment now, such that uncertain future demand can be satisfied as closely as possible. To use a robust optimization approach, we need to construct an uncertainty set that contains all scenarios that we believe to be possible. In this paper we discuss how to construct two common types of uncertainty sets, which are discrete and polyhedral uncertainty, using real-world data. We employ clustering to generate a discrete uncertainty set, and place hyperplanes sequentially to generate a polyhedral uncertainty set. We then compare the performance of the resulting robust solutions for these two types of models on real-world data. Our results indicate that polyhedral models, while being popular in the recent network design literature, are less effective than discrete models both in terms of computational burden and solution quality with respect to the performance measure considered

Multicriteria pathfinding in uncertain simulated environments

Dr. James Keller, Dissertation Supervisor.Includes vita.Field of study: Electrical and computer engineering."May 2018."Multicriteria decision-making problems arise in all aspects of daily life and form the basis upon which high-level models of thought and behavior are built. These problems present various alternatives to a decision-maker, who must evaluate the trade-offs between each one and choose a course of action. In a sequential decision-making problem, each choice can influence which alternatives are available for subsequent actions, requiring the decision-maker to plan ahead in order to satisfy a set of objectives. These problems become more difficult, but more realistic, when information is restricted, either through partial observability or by approximate representations. Pathfinding in partially observable environments is one significant context in which a decision-making agent must develop a plan of action that satisfies multiple criteria. In general, the partially observable multiobjective pathfinding problem requires an agent to navigate to certain goal locations in an environment with various attributes that may be partially hidden, while minimizing a set of objective functions. To solve these types of problems, we create agent models based on the concept of a mental map that represents the agent's most recent spatial knowledge of the environment, using fuzzy numbers to represent uncertainty. We develop a simulation framework that facilitates the creation and deployment of a wide variety of environment types, problem definitions, and agent models. This computational mental map (CMM) framework is shown to be suitable for studying various types of sequential multicriteria decision-making problems, such as the shortest path problem, the traveling salesman problem, and the traveling purchaser problem in multiobjective and partially observable configurations.Includes bibliographical references (pages 294-301)

Fuzzy Sets in Business Management, Finance, and Economics

This book collects fifteen papers published in s Special Issue of Mathematics titled “Fuzzy Sets in Business Management, Finance, and Economics”, which was published in 2021. These paper cover a wide range of different tools from Fuzzy Set Theory and applications in many areas of Business Management and other connected fields. Specifically, this book contains applications of such instruments as, among others, Fuzzy Set Qualitative Comparative Analysis, Neuro-Fuzzy Methods, the Forgotten Effects Algorithm, Expertons Theory, Fuzzy Markov Chains, Fuzzy Arithmetic, Decision Making with OWA Operators and Pythagorean Aggregation Operators, Fuzzy Pattern Recognition, and Intuitionistic Fuzzy Sets. The papers in this book tackle a wide variety of problems in areas such as strategic management, sustainable decisions by firms and public organisms, tourism management, accounting and auditing, macroeconomic modelling, the evaluation of public organizations and universities, and actuarial modelling. We hope that this book will be useful not only for business managers, public decision-makers, and researchers in the specific fields of business management, finance, and economics but also in the broader areas of soft mathematics in social sciences. Practitioners will find methods and ideas that could be fruitful in current management issues. Scholars will find novel developments that may inspire further applications in the social sciences

Geometric, Feature-based and Graph-based Approaches for the Structural Analysis of Protein Binding Sites : Novel Methods and Computational Analysis

In this thesis, protein binding sites are considered. To enable the extraction of information from the space of protein binding sites, these binding sites must be mapped onto a mathematical space. This can be done by mapping binding sites onto vectors, graphs or point clouds. To finally enable a structure on the mathematical space, a distance measure is required, which is introduced in this thesis. This distance measure eventually can be used to extract information by means of data mining techniques