An Inclusion Measure of Fuzzy Sets and its Properties

Jing Wang; Zhong Wei Chen

doi:10.4028/www.scientific.net/AMM.229-231.2667

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 229-231An Inclusion Measure of Fuzzy Sets and its...

An Inclusion Measure of Fuzzy Sets and its Properties

Abstract:

The inclusion measure between two fuzzy sets can promote fuzzy logic methods to play their full roles and has been widely used in numerous areas. In this paper, we propose a new inclusion measure of fuzzy sets. At first, we select an axiomatic definition included three axioms. Then, we give a computation formula under the constraint of three axioms, and discuss two properties of the new measure. At last, two examples are given to verify its performance. The results show that the proposed inclusion measure is reliable and rational for fuzzy sets.

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Periodical:

Applied Mechanics and Materials (Volumes 229-231)

Pages:

2667-2670

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.229-231.2667

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Online since:

November 2012

Authors:

Jing Wang, Zhong Wei Chen

Keywords:

Fuzzy Logic, Fuzzy Measure, Fuzzy Set, Inclusion Measure

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References

[1] L.A. Ladeh: Fuzzy sets. Information and Control Vol. 8 (1965), pp.338-353.

Google Scholar

[2] C.S. Chiu: Mixed feed forward/feedback based adaptive fuzzy control for a class of MIMO nonlinear systems. IEEE Transactions on Fuzzy Systems Vol. 14 (2006), pp.716-727.

DOI: 10.1109/tfuzz.2006.877357

Google Scholar

[3] W. Zeng and H. Li: Inclusion measures, similarity measures, and the fuzziness of fuzzy sets and their relations. International Journal of Intelligent Systems Vol. 21 (2006), pp.639-653.

DOI: 10.1002/int.20152

Google Scholar

[4] D. Sinha and E.R. Dougherty: Fuzzification of set inclusion: theory and applications. Fuzzy Sets and Systems Vol. 55 (1993), pp.15-42.

DOI: 10.1016/0165-0114(93)90299-w

Google Scholar

[5] C. Cornelis, V. Donck and E.E. Kerre: Sinha-Dougherty approach to the fuzzification of set inclusion revisited. Fuzzy Sets and Systems Vol. 134 (2003), pp.283-295.

DOI: 10.1016/s0165-0114(02)00225-7

Google Scholar

[6] A. Kehagias and M. Konstantinidou: L-fuzzy valued inclusion measure, L-fuzzy similarity and L-fuzzydistance. Fuzzy Sets and Systems Vol. 136 (2003), pp.313-332.

DOI: 10.1016/s0165-0114(02)00407-4

Google Scholar

[7] J. Fan, W. Xie and J. Pei: Subsethood measure: new defnitions. Fuzzy Sets and Systems Vol. 106 (1999), pp.201-209.

DOI: 10.1016/s0165-0114(97)00275-3

Google Scholar