Tolerance and weak tolerance of interval eigenvectors in fuzzy algebra

2020 ◽  
Author(s):  
M. Gavalec ◽  
J. Plavka ◽  
D. Ponce
Keyword(s):  
Fuzzy Algebra

scholarly journals M-Hazy Vector Spaces over M-Hazy Field

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1118
Author(s):  
Faisal Mehmood ◽  
Fu-Gui Shi
Keyword(s):  
Vector Space ◽  
Linear Transformation ◽  
Binary Operation ◽  
Vector Spaces ◽  
Fundamental Properties ◽  
Classical Algebra ◽  
Important Development ◽  
Fuzzy Algebra ◽  
Convex Spaces

The generalization of binary operation in the classical algebra to fuzzy binary operation is an important development in the field of fuzzy algebra. The paper proposes a new generalization of vector spaces over field, which is called M-hazy vector spaces over M-hazy field. Some fundamental properties of M-hazy field, M-hazy vector spaces, and M-hazy subspaces are studied, and some important results are also proved. Furthermore, the linear transformation of M-hazy vector spaces is studied and their important results are also proved. Finally, it is shown that M-fuzzifying convex spaces are induced by an M-hazy subspace of M-hazy vector space.

Semiring of Generalized Interval-Valued Intuitionistic Fuzzy Matrices

2017 ◽  
pp. 132-152
Author(s):  
Debashree Manna
Keyword(s):  
Vector Space ◽  
Distributive Lattice ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Algebra ◽  
Definition Of ◽  
Interval Valued

In this paper, the concept of semiring of generalized interval-valued intuitionistic fuzzy matrices are introduced and have shown that the set of GIVIFMs forms a distributive lattice. Also, prove that the GIVIFMs form an generalized interval valued intuitionistic fuzzy algebra and vector space over [0, 1]. Some properties of GIVIFMs are studied using the definition of comparability of GIVIFMs.

Artificial Neural Networks Equivalent to Fuzzy Algebra T-Norm Conjunction Operators

2007 ◽  
Author(s):  
L. S. Iliadis ◽  
S. I. Spartalis ◽  
Theodore E. Simos ◽  
George Maroulis
Keyword(s):  
Neural Networks ◽  
Artificial Neural Networks ◽  
Fuzzy Algebra ◽  
Artificial Neural

scholarly journals On Generalized Transitive Matrices

2011 ◽  
Vol 2011 ◽  
pp. 1-16
Author(s):  
Jing Jiang ◽  
Lan Shu ◽  
Xinan Tian
Keyword(s):  
Boolean Algebra ◽  
Distributive Lattice ◽  
Canonical Form ◽  
Transitive Closure ◽  
Fuzzy Algebra

Transitivity of generalized fuzzy matrices over a special type of semiring is considered. The semiring is called incline algebra which generalizes Boolean algebra, fuzzy algebra, and distributive lattice. This paper studies the transitive incline matrices in detail. The transitive closure of an incline matrix is studied, and the convergence for powers of transitive incline matrices is considered. Some properties of compositions of incline matrices are also given, and a new transitive incline matrix is constructed from given incline matrices. Finally, the issue of the canonical form of a transitive incline matrix is discussed. The results obtained here generalize the corresponding ones on fuzzy matrices and lattice matrices shown in the references.

Fuzzy sets, fuzzy algebra, and fuzzy statistics

1978 ◽  
Vol 66 (12) ◽  
pp. 1619-1639 ◽  
Author(s):  
A. Kandel ◽  
W.J. Byatt
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Algebra ◽  
Fuzzy Statistics
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