A Nonlinear Functional Analytic Framework for Modeling and Processing Fuzzy Sets

2007 ◽  
pp. 171-191 ◽  
Author(s):  
Rui J.P. de Figueiredo
Keyword(s):  
Fuzzy Sets ◽  
Analytic Framework ◽  
Nonlinear Functional

Analysis of Variance For Crisp Data with Membership Grades of Fuzzy Sets

2012 ◽  
Vol 2 (12) ◽  
pp. 548-552
Author(s):  
P. Pandian P. Pandian ◽  
◽  
D. Kalpanapriya D. Kalpanapriya
Keyword(s):  
Fuzzy Sets ◽  
Analysis Of Variance

Fuzzy Sets Theory in Comparison with Stochastic Methods to Analyse Nonlinear Behaviour of a Steel Member under Compression

2005 ◽  
Vol 10 (1) ◽  
pp. 65-75 ◽  
Author(s):  
Z. Kala
Keyword(s):  
Fuzzy Sets ◽  
Carrying Capacity ◽  
Stochastic Methods ◽  
Nonlinear Behaviour ◽  
Load Carrying Capacity ◽  
Load Carrying ◽  
Input Parameters ◽  
Stochastic Solution ◽  
Fuzzy Solution ◽  
Sets Theory

The load-carrying capacity of the member with imperfections under axial compression is analysed in the present paper. The study is divided into two parts: (i) in the first one, the input parameters are considered to be random numbers (with distribution of probability functions obtained from experimental results and/or tolerance standard), while (ii) in the other one, the input parameters are considered to be fuzzy numbers (with membership functions). The load-carrying capacity was calculated by geometrical nonlinear solution of a beam by means of the finite element method. In the case (ii), the membership function was determined by applying the fuzzy sets, whereas in the case (i), the distribution probability function of load-carrying capacity was determined. For (i) stochastic solution, the numerical simulation Monte Carlo method was applied, whereas for (ii) fuzzy solution, the method of the so-called α cuts was applied. The design load-carrying capacity was determined according to the EC3 and EN1990 standards. The results of the fuzzy, stochastic and deterministic analyses are compared in the concluding part of the paper.

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