Equivalent finite fuzzy sets and Stirling numbers

Authors:
V. Murali
Affiliations:
Department of Mathematics (Pure & Applied), Rhodes University, Grahamstown, South Africa
Venue:
Information Sciences: an International Journal
Year:
2005

Citing 3
Cited 1

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Fuzzy points of equivalent fuzzy subsets

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I-Fuzzy equivalence relations and I-fuzzy partitions

Information Sciences: an International Journal

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Abstract

In this paper we study the number of k-level equivalence classes of fuzzy subsets of a finite set of n elements under a natural equivalence. This number is related to Stirling numbers. Viewing fuzzy subsets as functions from a set into the unit interval, we also associate a kernel partition with every equivalence class of fuzzy subsets. After some elementary properties of the equivalence, we provide a recurrence relation and a generating function concerning the number of k-level fuzzy subsets using Stirling numbers.