Basic theory and algorithms for fuzzy sets and logic

2011 ◽  
pp. 34-46 ◽  
Author(s):  
B. Postlethwaite
Keyword(s):  
Fuzzy Sets ◽  
Basic Theory

Interval Cut-Set of Generalized Interval-Valued Intuitionistic Fuzzy Sets

2012 ◽  
Vol 2 (3) ◽  
pp. 35-50 ◽  
Author(s):  
Amal Kumar Adak ◽  
Monoranjan Bhowmik ◽  
Madhumangal Pal
Keyword(s):  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Basic Theory ◽  
Intuitionistic Fuzzy ◽  
Different Types ◽  
Cut Set ◽  
Decomposition Theorems ◽  
Interval Valued

In this paper, some different types of interval cut-set of genaralized interval-valued intuitionistic fuzzy sets (GIVIFSs), complement of these cut-sets are introduced. Some properties of those cut-set of GIVIFSs are investigated. Also three decomposition theorems of GIVIFSs are obtained based on the different cut-set of GIVIFSs. These works can also be used in setting up the basic theory of GIVIFSs.

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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