Multi-expert decision-making with incomplete and noisy fuzzy rules and the monotone test

The use of Fuzzy Inference System (FIS) in decision making problems has received little attention so far. This may be due to the difficulty in gathering a complete set of fuzzy rules, which is free from noise, and the complexity in constructing an FIS model that is able to satisfy a number of important properties, including the monotonicity property. Previously, we have proposed a single-input Monotone-Interval FIS (MI-FIS) model, which can handle incomplete and non-monotone fuzzy rules. Besides that, we have proposed the idea of a monotone test (MT) for a set of fuzzy rules, which give an indication pertaining to the degree of monotonicity of a fuzzy rules set. In this paper, a multi-input MI-FIS model is firstly presented. The focus of this paper is on the use of MI-FIS and MT for undertaking multi expert decision-making (MEDM) problems. A three-phase MEDM framework consists of modelling, aggregation, and exploitation phases is proposed. In the modelling phase, an MT index for each fuzzy rule base from each expert, which is potentially non-monotone and incomplete, is obtained. The provided fuzzy rule bases are also modelled as MI-FISs. In the aggregation phase, an overall collective rating score of an alternative from a number of experts is obtained through the fuzzy weighted averaging operator. We suggest including MT as part of the aggregation phase. In exploitation phase, a rank ordering procedure among the alternatives is established using a possibility method. The developed framework is evaluated with simulated information. The results show that including the MT index in the aggregation phase is able to increase the robustness of the proposed FIS-MEDM model in the presence of noisy fuzzy rule sets

LEARNFCA: A FUZZY FCA AND PROBABILITY BASED APPROACH FOR LEARNING AND CLASSIFICATION

Formal concept analysis(FCA) is a mathematical theory based on lattice and order theory used for data analysis and knowledge representation. Over the past several years, many of its extensions have been proposed and applied in several domains including data mining, machine learning, knowledge management, semantic web, software development, chemistry ,biology, medicine, data analytics, biology and ontology engineering. This thesis reviews the state-of-the-art of theory of Formal Concept Analysis(FCA) and its various extensions that have been developed and well-studied in the past several years. We discuss their historical roots, reproduce the original definitions and derivations with illustrative examples. Further, we provide a literature review of it’s applications and various approaches adopted by researchers in the areas of dataanalysis, knowledge management with emphasis to data-learning and classification problems. We propose LearnFCA, a novel approach based on FuzzyFCA and probability theory for learning and classification problems. LearnFCA uses an enhanced version of FuzzyLattice which has been developed to store class labels and probability vectors and has the capability to be used for classifying instances with encoded and unlabelled features. We evaluate LearnFCA on encodings from three datasets - mnist, omniglot and cancer images with interesting results and varying degrees of success. Adviser: Jitender Deogu

LearnFCA: A Fuzzy FCA and Probability Based Approach for Learning and Classification

Formal concept analysis(FCA) is a mathematical theory based on lattice and order theory used for data analysis and knowledge representation. Over the past several years, many of its extensions have been proposed and applied in several domains including data mining, machine learning, knowledge management, semantic web, software development, chemistry ,biology, medicine, data analytics, biology and ontology engineering. This thesis reviews the state-of-the-art of theory of Formal Concept Analysis(FCA) and its various extensions that have been developed and well-studied in the past several years. We discuss their historical roots, reproduce the original definitions and derivations with illustrative examples. Further, we provide a literature review of it’s applications and various approaches adopted by researchers in the areas of dataanalysis, knowledge management with emphasis to data-learning and classification problems. We propose LearnFCA, a novel approach based on FuzzyFCA and probability theory for learning and classification problems. LearnFCA uses an enhanced version of FuzzyLattice which has been developed to store class labels and probability vectors and has the capability to be used for classifying instances with encoded and unlabelled features. We evaluate LearnFCA on encodings from three datasets - mnist, omniglot and cancer images with interesting results and varying degrees of success. Adviser: Dr Jitender Deogu

Preference Learning

This report documents the program and the outcomes of Dagstuhl Seminar 14101 “Preference Learning”. Preferences have recently received considerable attention in disciplines such as machine learning, knowledge discovery, information retrieval, statistics, social choice theory, multiple criteria decision making, decision under risk and uncertainty, operations research, and others. The motivation for this seminar was to showcase recent progress in these different areas with the goal of working towards a common basis of understanding, which should help to facilitate future synergies

ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

B

Operational Decision Making under Uncertainty: Inferential, Sequential, and Adversarial Approaches

Modern security threats are characterized by a stochastic, dynamic, partially observable, and ambiguous operational environment. This dissertation addresses such complex security threats using operations research techniques for decision making under uncertainty in operations planning, analysis, and assessment. First, this research develops a new method for robust queue inference with partially observable, stochastic arrival and departure times, motivated by cybersecurity and terrorism applications. In the dynamic setting, this work develops a new variant of Markov decision processes and an algorithm for robust information collection in dynamic, partially observable and ambiguous environments, with an application to a cybersecurity detection problem. In the adversarial setting, this work presents a new application of counterfactual regret minimization and robust optimization to a multi-domain cyber and air defense problem in a partially observable environment

Fuzzy Logic

Fuzzy Logic is becoming an essential method of solving problems in all domains. It gives tremendous impact on the design of autonomous intelligent systems. The purpose of this book is to introduce Hybrid Algorithms, Techniques, and Implementations of Fuzzy Logic. The book consists of thirteen chapters highlighting models and principles of fuzzy logic and issues on its techniques and implementations. The intended readers of this book are engineers, researchers, and graduate students interested in fuzzy logic systems