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Frontiers of Higher Order Fuzzy Sets pp 131–146Cite as

Modeling the Uncertainty of a Set of Graphs Using Higher-Order Fuzzy Sets

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Abstract

Recent advances in type-2 fuzzy sets (T2FS) have attracted considerable attention for applications in data mining and pattern recognition. In particular, there is an effort in designing granulation procedures able to generate, from raw input measurements, data, granules of information modeled as T2FS. From our viewpoint, the principal aim of those procedures is to embed into the generated T2FS model the key uncertainty characterizing the input data. However, to date there is no formal principle or guideline for the formal evaluation of such granulation procedures in these terms. In this paper, our aim is to define a framework to design and evaluate what we called uncertainty-preserving transformation procedures, which are basically computational procedures that generate, from raw input measurements, information granules modeled as T2FS. In particular, in this chapter, we deal with input measurements that are represented as graphs; hence, a set of graphs \(\mathcal{G}\) is seen as a set of raw input measurements sampled from an unknown data generating process P. The framework is, however, meant to be general and thus applicable to any input type. We motivate and explain the proposed framework by performing experimental evaluations on ad hoc synthetically generated datasets.

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Authors and Affiliations

  1. Department of Information Engineering, Electronics, and Telecommunications, SAPIENZA University of Rome, Via Eudossiana 18, 00184, Rome, Italy

    Lorenzo Livi & Antonello Rizzi

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  1. Lorenzo Livi
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  2. Antonello Rizzi
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Correspondence to Lorenzo Livi .

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  1. Ryerson University, Toronto, Ontario, Canada

    Alireza Sadeghian

  2. Ryerson University, Toronto, Ontario, Canada

    Hooman Tahayori

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Livi, L., Rizzi, A. (2015). Modeling the Uncertainty of a Set of Graphs Using Higher-Order Fuzzy Sets. In: Sadeghian, A., Tahayori, H. (eds) Frontiers of Higher Order Fuzzy Sets. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3442-9_7

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  • DOI: https://doi.org/10.1007/978-1-4614-3442-9_7

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