An Investigation Into the Distribution of Membership Grades for Non-Stationary Fuzzy Sets

Gajjar, Pragnesh A.; Garibaldi, Jonathan M.

doi:10.5220/0002321400790084

Proceedings of the International Joint Conference on Computational Intelligence 2009

DOI: 10.5220/0002321400790084

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An Investigation Into the Distribution of Membership Grades for Non-Stationary Fuzzy Sets

Pragnesh A. Gajjar

Jonathan M. Garibaldi

Abstract: Abstract:In this paper we study some properties related to the distribution of membership grades for non-stationary fuzzy sets. We obtain the formulation for the distribution, where the non-stationary fuzzy sets are obtained by generating instantiations about the center values. The two cases considered are for the underlying membership functions as Triangular and Gaussian. The analytical results obtained are then compared with computer generated results, for completeness.

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2013

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Modelling distributions of the temporal membership grades for non-stationary fuzzy sets

Tsagris

Garibaldi

2013

2013 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

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Non-stationary fuzzy sets have been introduced to model variation in human reasoning. While they have some similarities to type-2 fuzzy sets, there are many detailed differences. One of these differences is that they may feature horizontal random perturbations of membership functions, which result in distributions across the membership grades over time, termed temporal membership grades, which are somewhat akin to secondary membership grades of type-2 fuzzy sets. In this paper we study the distribution of the temporal membership grades of non-stationary fuzzy sets with Gaussian underlying membership functions. We derive the distribution of these grades when the non-stationary fuzzy sets are obtained by variations in location using a normal distribution. We show how to estimate the parameters of the derived distribution using numerical optimisation. In addition, we investigate the changes in the distributions obtained when using variations in location using a uniform distribution. Finally, we exhibit the performance of the beta and logistic normal distribution using examples of simulated data. In doing so, we further explore the relationships between non-stationary and type-2 fuzzy sets.

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Modelling distributions of the temporal membership grades for non-stationary fuzzy sets

Tsagris

Garibaldi

2013

2013 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

View full text Add to dashboard Cite

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An Investigation Into the Distribution of Membership Grades for Non-Stationary Fuzzy Sets

Cited by 1 publication

References 12 publications

Modelling distributions of the temporal membership grades for non-stationary fuzzy sets

Modelling distributions of the temporal membership grades for non-stationary fuzzy sets

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