508 research outputs found
Left and right compatibility of strict orders with fuzzy tolerance and fuzzy equivalence relations
The notion of extensionality of a fuzzy relation w.r.t. a fuzzy equivalence was first introduced by Hohle and Blanchard. Belohlavek introduced a similar definition of compatibility of a fuzzy relation w.r.t. a fuzzy equality. In [14] we generalized this notion to left compatibility, right compatibility and compatibility of arbitrary fuzzy relations and we characterized them in terms of left and right traces introduced by Fodor. In this note, we will again investigate these notions, but this time we focus on the compatibility of strict orders with fuzzy tolerance and fuzzy equivalence relations
Hyperspace of a fuzzy quasi-uniform space
[EN] The aim of this paper is to present a fuzzy counterpart method of constructing the Hausdorff quasi-uniformity of a crisp quasi-uniformity. This process, based on previous works due to Morsi [25] and Georgescu [9], allows to extend probabilistic and Hutton [0, 1]-quasi-uniformities on a set X to its power set. In this way, we obtain an endofunctor for each one of the categories of those objects. We will demonstrate the commutativity of these endofunctors with Lowen and Katsaras' functors. Furthermore, we will prove the compatibility of our construction with the Hausdorff fuzzy quasi-pseudometric introduced in [33].The second author is supported by the grant MTM2015-64373-P (MINECO/FEDER, UE). The authors are grateful to the reviewers for useful comments which have improved the first version of the paperPedraza Aguilera, T.; RodrĂguez LĂłpez, J. (2020). Hyperspace of a fuzzy quasi-uniform space. Iranian Journal of Fuzzy Systems. 17(2):97-114. https://doi.org/10.22111/IJFS.2020.5222S9711417
Quantale Modules, with Applications to Logic and Image Processing
We propose a categorical and algebraic study of quantale modules. The results
and constructions presented are also applied to abstract algebraic logic and to
image processing tasks.Comment: 150 pages, 17 figures, 3 tables, Doctoral dissertation, Univ Salern
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Unbiased Boolean analysis of public gene expression data for cell cycle gene identification.
Cell proliferation is essential for the development and maintenance of all organisms and is dysregulated in cancer. Using synchronized cells progressing through the cell cycle, pioneering microarray studies defined cell cycle genes based on cyclic variation in their expression. However, the concordance of the small number of synchronized cell studies has been limited, leading to discrepancies in definition of the transcriptionally regulated set of cell cycle genes within and between species. Here we present an informatics approach based on Boolean logic to identify cell cycle genes. This approach used the vast array of publicly available gene expression data sets to query similarity to CCNB1, which encodes the cyclin subunit of the Cdk1-cyclin B complex that triggers the G2-to-M transition. In addition to highlighting conservation of cell cycle genes across large evolutionary distances, this approach identified contexts where well-studied genes known to act during the cell cycle are expressed and potentially acting in nondivision contexts. An accessible web platform enables a detailed exploration of the cell cycle gene lists generated using the Boolean logic approach. The methods employed are straightforward to extend to processes other than the cell cycle
Quantitative Graded Semantics and Spectra of Behavioural Metrics
Behavioural metrics provide a quantitative refinement of classical two-valued
behavioural equivalences on systems with quantitative data, such as metric or
probabilistic transition systems. In analogy to the classical
linear-time/branching-time spectrum of two-valued behavioural equivalences on
transition systems, behavioural metrics come in various degrees of granularity,
depending on the observer's ability to interact with the system. Graded monads
have been shown to provide a unifying framework for spectra of behavioural
equivalences. Here, we transfer this principle to spectra of behavioural
metrics, working at a coalgebraic level of generality, that is, parametrically
in the system type. In the ensuing development of quantitative graded
semantics, we discuss presentations of graded monads on the category of metric
spaces in terms of graded quantitative equational theories. Moreover, we obtain
a canonical generic notion of invariant real-valued modal logic, and provide
criteria for such logics to be expressive in the sense that logical distance
coincides with the respective behavioural distance. We thus recover recent
expressiveness results for coalgebraic branching-time metrics and for trace
distance in metric transition systems; moreover, we obtain a new expressiveness
result for trace semantics of fuzzy transition systems. We also provide a
number of salient negative results. In particular, we show that trace distance
on probabilistic metric transition systems does not admit a characteristic
real-valued modal logic at all
Borderline vs. unknown: comparing three-valued representations of imperfect information
International audienceIn this paper we compare the expressive power of elementary representation formats for vague, incomplete or conflicting information. These include Boolean valuation pairs introduced by Lawry and González-RodrĂguez, orthopairs of sets of variables, Boolean possibility and necessity measures, three-valued valuations, supervaluations. We make explicit their connections with strong Kleene logic and with Belnap logic of conflicting information. The formal similarities between 3-valued approaches to vagueness and formalisms that handle incomplete information often lead to a confusion between degrees of truth and degrees of uncertainty. Yet there are important differences that appear at the interpretive level: while truth-functional logics of vagueness are accepted by a part of the scientific community (even if questioned by supervaluationists), the truth-functionality assumption of three-valued calculi for handling incomplete information looks questionable, compared to the non-truth-functional approaches based on Boolean possibility–necessity pairs. This paper aims to clarify the similarities and differences between the two situations. We also study to what extent operations for comparing and merging information items in the form of orthopairs can be expressed by means of operations on valuation pairs, three-valued valuations and underlying possibility distributions
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