A new online updating framework for constructing monotonicity-preserving Fuzzy Inference Systems

In this paper, a new online updating framework for constructing monotonicity-preserving Fuzzy Inference Systems (FISs) is proposed. The framework encompasses an optimization-based Similarity Reasoning (SR) scheme and a new monotone fuzzy rule relabeling technique. A complete and monotonically-ordered fuzzy rule base is necessary to maintain the monotonicity property of an FIS model. The proposed framework attempts to allow a monotonicity-preserving FIS model to be constructed when the fuzzy rules are incomplete and not monotonically-ordered. An online feature is introduced to allow the FIS model to be updated from time to time. We further investigate three useful measures, i.e., the belief, plausibility, and evidential mass measures, which are inspired from the Dempster-Shafer theory of evidence, to analyze the proposed framework and to give an insight for the inferred outcomes from the FIS mode

Examining the Modelling Capabilities of Defeasible Argumentation and non-Monotonic Fuzzy Reasoning

Knowledge-representation and reasoning methods have been extensively researched within Artificial Intelligence. Among these, argumentation has emerged as an ideal paradigm for inference under uncertainty with conflicting knowledge. Its value has been predominantly demonstrated via analyses of the topological structure of graphs of arguments and its formal properties. However, limited research exists on the examination and comparison of its inferential capacity in real-world modelling tasks and against other knowledge-representation and non-monotonic reasoning methods. This study is focused on a novel comparison between defeasible argumentation and non-monotonic fuzzy reasoning when applied to the representation of the ill-defined construct of human mental workload and its assessment. Different argument-based and non-monotonic fuzzy reasoning models have been designed considering knowledge-bases of incremental complexity containing uncertain and conflicting information provided by a human reasoner. Findings showed how their inferences have a moderate convergent and face validity when compared respectively to those of an existing baseline instrument for mental workload assessment, and to a perception of mental workload self-reported by human participants. This confirmed how these models also reasonably represent the construct under consideration. Furthermore, argument-based models had on average a lower mean squared error against the self-reported perception of mental workload when compared to fuzzy-reasoning models and the baseline instrument. The contribution of this research is to provide scholars, interested in formalisms on knowledge-representation and non-monotonic reasoning, with a novel approach for empirically comparing their inferential capacity

Pointwise construction of Lippschitz aggregation operators with specific properties

This paper describes an approach to pointwise construction of general aggregation operators, based on monotone Lipschitz approximation. The aggregation operators are constructed from a set of desired values at certain points, or from empirically collected data. It establishes tight upper and lower bounds on Lipschitz aggregation operators with a number of different properties, as well as the optimal aggregation operator, consistent with the given values. We consider conjunctive, disjunctive and idempotent n-ary aggregation operators; p-stable aggregation operators; various choices of the neutral element and annihilator; diagonal, opposite diagonal and marginal sections; bipolar and double aggregation operators. In all cases we provide either explicit formulas or deterministic numerical procedures to determine the bounds. The findings of this paper are useful for construction of aggregation operators with specified properties, especially using interpolation schemata.<br /

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

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Evaluating the Impact of Defeasible Argumentation as a Modelling Technique for Reasoning under Uncertainty

Limited work exists for the comparison across distinct knowledge-based approaches in Artificial Intelligence (AI) for non-monotonic reasoning, and in particular for the examination of their inferential and explanatory capacity. Non-monotonicity, or defeasibility, allows the retraction of a conclusion in the light of new information. It is a similar pattern to human reasoning, which draws conclusions in the absence of information, but allows them to be corrected once new pieces of evidence arise. Thus, this thesis focuses on a comparison of three approaches in AI for implementation of non-monotonic reasoning models of inference, namely: expert systems, fuzzy reasoning and defeasible argumentation. Three applications from the fields of decision-making in healthcare and knowledge representation and reasoning were selected from real-world contexts for evaluation: human mental workload modelling, computational trust modelling, and mortality occurrence modelling with biomarkers. The link between these applications comes from their presumptively non-monotonic nature. They present incomplete, ambiguous and retractable pieces of evidence. Hence, reasoning applied to them is likely suitable for being modelled by non-monotonic reasoning systems. An experiment was performed by exploiting six deductive knowledge bases produced with the aid of domain experts. These were coded into models built upon the selected reasoning approaches and were subsequently elicited with real-world data. The numerical inferences produced by these models were analysed according to common metrics of evaluation for each field of application. For the examination of explanatory capacity, properties such as understandability, extensibility, and post-hoc interpretability were meticulously described and qualitatively compared. Findings suggest that the variance of the inferences produced by expert systems and fuzzy reasoning models was higher, highlighting poor stability. In contrast, the variance of argument-based models was lower, showing a superior stability of its inferences across different system configurations. In addition, when compared in a context with large amounts of conflicting information, defeasible argumentation exhibited a stronger potential for conflict resolution, while presenting robust inferences. An in-depth discussion of the explanatory capacity showed how defeasible argumentation can lead to the construction of non-monotonic models with appealing properties of explainability, compared to those built with expert systems and fuzzy reasoning. The originality of this research lies in the quantification of the impact of defeasible argumentation. It illustrates the construction of an extensive number of non-monotonic reasoning models through a modular design. In addition, it exemplifies how these models can be exploited for performing non-monotonic reasoning and producing quantitative inferences in real-world applications. It contributes to the field of non-monotonic reasoning by situating defeasible argumentation among similar approaches through a novel empirical comparison

Heuristic design of fuzzy inference systems: a review of three decades of research

This paper provides an in-depth review of the optimal design of type-1 and type-2 fuzzy inference systems (FIS) using five well known computational frameworks: genetic-fuzzy systems (GFS), neuro-fuzzy systems (NFS), hierarchical fuzzy systems (HFS), evolving fuzzy systems (EFS), and multi-objective fuzzy systems (MFS), which is in view that some of them are linked to each other. The heuristic design of GFS uses evolutionary algorithms for optimizing both Mamdani-type and Takagi–Sugeno–Kang-type fuzzy systems. Whereas, the NFS combines the FIS with neural network learning systems to improve the approximation ability. An HFS combines two or more low-dimensional fuzzy logic units in a hierarchical design to overcome the curse of dimensionality. An EFS solves the data streaming issues by evolving the system incrementally, and an MFS solves the multi-objective trade-offs like the simultaneous maximization of both interpretability and accuracy. This paper offers a synthesis of these dimensions and explores their potentials, challenges, and opportunities in FIS research. This review also examines the complex relations among these dimensions and the possibilities of combining one or more computational frameworks adding another dimension: deep fuzzy systems

From inference to design: A comprehensive framework for uncertainty quantification in engineering with limited information

In this paper we present a framework for addressing a variety of engineering design challenges with limited empirical data and partial information. This framework includes guidance on the characterisation of a mixture of uncertainties, efficient methodologies to integrate data into design decisions, and to conduct reliability analysis, and risk/reliability based design optimisation. To demonstrate its efficacy, the framework has been applied to the NASA 2020 uncertainty quantification challenge. The results and discussion in the paper are with respect to this application