This paper deals with Gärdenfors’ theory of conceptual spaces. Let \({\mathcal {S}}\) be a conceptual space consisting of 2-type fuzzy sets equipped with several kinds of metrics. Let a finite set of prototypes \(\tilde{P}_1,\ldots,\tilde{P}_n\in \mathcal {S}\) be given. Our main result is the construction of a classification algorithm. That is, given an element \({\tilde{A}}\in \mathcal {S},\) our algorithm classifies it into the conceptual field determined by one of the given prototypes \(\tilde{P}_i.\) The construction of our algorithm uses some physical analogies (...) and the Newton potential plays a significant role here. Importantly, the resulting conceptual fields are not convex in the Euclidean sense, which we believe is a reasonable departure from the assumptions of Gardenfors’ original definition of the conceptual space. A partitioning algorithm of the space \(\mathcal {S}\) is also considered in the paper. In the application section, we test our classification algorithm on real data and obtain very satisfactory results. Moreover, the example we consider is another argument against requiring convexity of conceptual fields. (shrink)

This paper approaches the interaction of a health professional with an AI system for diagnostic purposes as a hybrid decision making process and conceptualizes epistemo-ethical constraints on this process. We argue for the importance of the understanding of the underlying machine epistemology in order to raise awareness of and facilitate realistic expectations from AI as a decision support system, both among healthcare professionals and the potential benefiters. Understanding the epistemic abilities and limitations of such systems is essential if we are (...) to integrate AI into the decision making processes in a way that takes into account its applicability boundaries. This will help to mitigate potential harm due to misjudgments and, as a result, to raise the trust—understood here as a belief in reliability of—in the AI system. We aim at a minimal requirement for AI meta-explanation which should distinguish machine epistemic processes from similar processes in human epistemology in order to avoid confusion and error in judgment and application. An informed approach to the integration of AI systems into the decision making for diagnostic purposes is crucial given its high impact on health and well-being of patients. (shrink)

A new approach to semantics, based on ordered Banach spaces, is proposed. The Banach spaces semantics arises as a generalization of the four particular cases: the Giles' approach to belief structures, its generalization to the non-Boolean case, and fuzzy extensions of Boolean as well as of non-Boolean semantics.

ype-2 fuzzy sets and complex fuzzy sets are both three dimensional extensions of type-1 fuzzy sets. Complex fuzzy sets come in two forms, the standard form, postulated in 2002 by Ramot et al., and the 2011 innovation of pure complex fuzzy sets, proposed by Tamir et al.. In this paper we compare and contrast both forms of complex fuzzy set with type-2 fuzzy sets, as regards their rationales, applications, definitions, and structures. In addition, pure complex fuzzy sets are compared with (...) type-2 fuzzy sets in relation to their inferencing operations. Complex fuzzy sets and type-2 fuzzy sets differ in their roles and applications; complex fuzzy sets are pertinent to inferencing where there is seasonality, and type-2 fuzzy sets are applicable to reasoning under uncertainty. Their definitions differ also, though there is equivalence between those of a pure complex fuzzy set and a type-2 fuzzy set. Structural similarity is evident between these three-dimensional sets. Complex fuzzy sets are represented by a 3–D line, and type-2 fuzzy sets by a 3–D surface, but a surface is simply a generalisation of a line. This similarity is particularly apparent between pure complex fuzzy sets and type-2 fuzzy sets, which are both mappings from the domain onto the unit square. However type-2 fuzzy sets were found not to be isomorphic to pure complex fuzzy sets. The mechanisms by which complex fuzzy sets model and quantify periodicity, and type-2 fuzzy sets model and quantify uncertainty are discussed. A type-2 fuzzy set can be represented as the union of its type-2 embedded set. An embedded type-2 fuzzy set is a type-2 fuzzy set in itself, whose geometrical representation is a 3-D line. Thus, geometrically an embedded type-2 fuzzy set can be seen as equivalent to a pure complex fuzzy set and therefore a type-2 fuzzy set can be represented as the union of a collection pure complex fuzzy sets, which in turn can be regarded as embedded complex fuzzy sets of a type-2 fuzzy set. This relationship is exploited to provide a complex definition of a type-2 fuzzy set. (shrink)

Utilities of health states are often estimated to support public decisions in health care. People’s preferences may be imprecise, for lack of actual trade-off experience. We show how to elicit the utilities accounting for imprecision, discover the main drivers of imprecision, and compare several approaches to modelling health state utility data in the fuzzy setting. We extended the time trade-off questionnaire, to elicit utilities of states defined in the EQ-5D-3L descriptive system in184 respondents. Our study demonstrates that respondents are capable (...) of assessing their own imprecision and rigorous mathematical modelling is possible. The imprecision is larger than as inferred from the standard TTO method and is larger than estimation error, even in our smallish sample. Non-trading in TTO often results from imprecision, rather than lexicographic preferences for longevity over quality. People are especially imprecise in assessing the impact of usual activities on utility; also, the internal inconsistency of a health state increases the imprecision. Fuzzy least squares method seems best suited to assign disutilities to individual dimensions, while separately modelling the location of utility and amount of imprecision seems best to produce value sets. If crisp parameters are estimated, accounting for imprecision changes the results little. (shrink)

The main problem discussed in this paper is: Why and how did animal cognition abilities arise? It is argued that investigations of the evolution of animal cognition abilities are very important from an epistemological point of view. A new direction for interdisciplinary researches – the creation and development of the theory of human logic origin – is proposed. The approaches to the origination of such a theory (mathematical models of ``intelligent invention'' of biological evolution, the cybernetic schemes of evolutionary progress (...) and purposeful adaptive behavior) as well as potential interdisciplinary links of the theory are described and analyzed. (shrink)

Various semantics for studying the square of opposition have been proposed recently. So far, only [14] studied a probabilistic version of the square where the sentences were interpreted by (negated) defaults. We extend this work by interpreting sentences by imprecise (set-valued) probability assessments on a sequence of conditional events. We introduce the acceptability of a sentence within coherence-based probability theory. We analyze the relations of the square in terms of acceptability and show how to construct probabilistic versions of the square (...) of opposition by forming suitable tripartitions. Finally, as an application, we present a new square involving generalized quantifiers. (shrink)

This paper briefly surveys several prominent modeling approaches to knowledge-based intelligent systems design and, especially, expert systems and the breakthroughs that have most broadened and improved their applications. We argue that the implementation of technology that aims to emulate rudimentary aspects of human intelligence has enhanced KBIS design, but that weaknesses remain that could be addressed with existing research in cognitive science. For example, we propose that systems based on representational plasticity, functional dynamism, domain specificity, creativity, and concept learning, with (...) their theoretical and experimental rigor, can best characterize the problem-solving capabilities of humans and can best overcome five key limitations currently exhibited by knowledge-based intelligent systems. We begin with a brief survey of the relevant work related to KBIS design and then discuss these five shortcomings with new suggestions for how to integrate results from cognitive science to resolve each of them. Our ultimate goal is to increase awareness and direct attention to areas of theoretical and experimental cognitive research that are fundamentally relevant to the goals underlying KBISes. (shrink)

This paper aims to briefly introduce the main idea behind the fuzzy approach and to identify the areas and problems encountered in the humanities that might profit from using this approach. Based on a short overview of selected applications of fuzzy in psychology we identify key areas in which the fuzzy approach has already been applied, and propose a list of general types of problems that the fuzzy approach may provide solutions for in psychology and the humanities in general. These (...) types of problems are illustrated using practical examples. The benefits and possible shortcomings of using the fuzzy approach compared to classical approaches in use today are discussed. The goal of this paper is to indicate areas in research and practice in the humanities, where modern mathematical tools—in this case linguistic fuzzy modeling—have already been used or might prove promising. (shrink)