228 research outputs found
Fuzzy entropy from weak fuzzy subsethood measures
In this paper, we propose a new construction method for fuzzy and weak fuzzy subsethood measures based on the aggregation of implication operators. We study the desired properties of the implication operators in order to construct these measures. We also show the relationship between fuzzy entropy and weak fuzzy subsethood measures constructed by our method
Measuring Relations Between Concepts In Conceptual Spaces
The highly influential framework of conceptual spaces provides a geometric
way of representing knowledge. Instances are represented by points in a
high-dimensional space and concepts are represented by regions in this space.
Our recent mathematical formalization of this framework is capable of
representing correlations between different domains in a geometric way. In this
paper, we extend our formalization by providing quantitative mathematical
definitions for the notions of concept size, subsethood, implication,
similarity, and betweenness. This considerably increases the representational
power of our formalization by introducing measurable ways of describing
relations between concepts.Comment: Accepted at SGAI 2017 (http://www.bcs-sgai.org/ai2017/). The final
publication is available at Springer via
https://doi.org/10.1007/978-3-319-71078-5_7. arXiv admin note: substantial
text overlap with arXiv:1707.05165, arXiv:1706.0636
Subsethood Measures of Spatial Granules
Subsethood, which is to measure the degree of set inclusion relation, is
predominant in fuzzy set theory. This paper introduces some basic concepts of
spatial granules, coarse-fine relation, and operations like meet, join,
quotient meet and quotient join. All the atomic granules can be hierarchized by
set-inclusion relation and all the granules can be hierarchized by coarse-fine
relation. Viewing an information system from the micro and the macro
perspectives, we can get a micro knowledge space and a micro knowledge space,
from which a rough set model and a spatial rough granule model are respectively
obtained. The classical rough set model is the special case of the rough set
model induced from the micro knowledge space, while the spatial rough granule
model will be play a pivotal role in the problem-solving of structures. We
discuss twelve axioms of monotone increasing subsethood and twelve
corresponding axioms of monotone decreasing supsethood, and generalize
subsethood and supsethood to conditional granularity and conditional fineness
respectively. We develop five conditional granularity measures and five
conditional fineness measures and prove that each conditional granularity or
fineness measure satisfies its corresponding twelve axioms although its
subsethood or supsethood measure only hold one of the two boundary conditions.
We further define five conditional granularity entropies and five conditional
fineness entropies respectively, and each entropy only satisfies part of the
boundary conditions but all the ten monotone conditions
A bidirectional subsethood based similarity measure for fuzzy sets
Similarity measures are useful for reasoning about fuzzy sets. Hence, many classical set-theoretic similarity measures have been extended for comparing fuzzy sets. In previous work, a set-theoretic similarity measure considering the bidirectional subsethood for intervals was introduced. The measure addressed specific concerns of many common similarity measures, and it was shown to be bounded above and below by Jaccard and Dice measures respectively. Herein, we extend our prior measure from similarity on intervals to fuzzy sets. Specifically, we propose a vertical-slice extension where two fuzzy sets are compared based on their membership values.We show that the proposed extension maintains all common properties (i.e., reflexivity, symmetry, transitivity, and overlapping) of the original fuzzy similarity measure. We demonstrate and contrast its behaviour along with common fuzzy set-theoretic measures using different types of fuzzy sets (i.e., normal, non-normal, convex, and non-convex) in respect to different discretization levels
Workshop on Fuzzy Control Systems and Space Station Applications
The Workshop on Fuzzy Control Systems and Space Station Applications was held on 14-15 Nov. 1990. The workshop was co-sponsored by McDonnell Douglas Space Systems Company and NASA Ames Research Center. Proceedings of the workshop are presented
Strong fuzzy subsethood measures and strong equalities via implication functions
In this work we present the definition of strong fuzzy subsethood measure as a unifiying concept for the different notions of fuzzy subsethood that can be found in the literature. We analyze the relations of our new concept with the definitions by Kitainik ( [20]), Young ( [26]) and Sinha and Dougherty ( [23]) and we prove that the most relevant properties of the latter are preserved. We show also several construction methods. © 2014 Old City Publishing, Inc
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