Fuzzy algebraic systems (I): Direct products

Tu, Lu; Gu, Wei

doi:10.1016/0165-0114(94)90174-0

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2005

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Cited by 4 publications

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“…This notion was introduced by Schweizer and Sklar 8 , in order to generalize the ordinary triangle inequality in a metric space to the more general probabilistic metric space. Since then many researchers are engaged in extending the concepts and results of abstract algebra to broader framework of the fuzzy setting, for example see [9][10][11][12] . Also, based on the concept of falling shadow 13 , a theoretical approach of the fuzzy algebraic systems is established in 14 .…”

Section: Introductionmentioning

confidence: 99%

On Connection Between Uncertainty Algebraic Hypersystems and Probability Spaces

Davvaz

2005

Int. J. Unc. Fuzz. Knowl. Based Syst.

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Using the concept of triangular norm, we define T-fuzzy subalgebraic hypersystems, we examine a number of extended uncertainty algebraic hypersystems and study a few results in this respect. In fact, we define a probabilistic version of algebraic hypersystems using random sets. We show that fuzzy algebraic hypersystems defined in triangular norms are consequences of probabilistic algebraic hypersystems under certain conditions.

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