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Membership modification and level sets

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Abstract

We introduce the concept of a membership modification function and describe its role in transforming one fuzzy set into another. We discuss the related idea of a membership modification program consisting of a collection of related membership modification functions and show how the concept of level sets is an example of a membership modification program. Using this idea of membership modification allows us to consider other transformations of fuzzy sets that soften the idea of level sets. Using these ideas we provide an extension of the Jaccard similarity index.

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Acknowledgments

This work has been supported by a Multidisciplinary University Research Initiative (MURI) grant (Number W911NF-09-1-0392) for “Unified Research on Network-based Hard/Soft Information Fusion”, issued by the US Army Research Office (ARO) under the program management of Dr. John Lavery. This work has also been supported by an ONR grant for "Human Behavior Modeling Using Fuzzy and Soft Technologies", award number N000141010121. We gratefully appreciate this support.

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  1. Iona College, Machine Intelligence Institute, New Rochelle, NY, 10801, USA

    Ronald R. Yager

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  1. Ronald R. Yager
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Correspondence to Ronald R. Yager.

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Technical Report No.: MII-3206R.

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Yager, R.R. Membership modification and level sets. Soft Comput 17, 391–399 (2013). https://doi.org/10.1007/s00500-012-0914-5

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