scholarly journals Subtraction of soft matrices

2021 ◽  
Vol 2106 (1) ◽  
pp. 012028
Author(s):  
S Abdurrahman ◽  
Thresye ◽  
R R Lula ◽  
R A Rachman ◽  
Y Evina
Keyword(s):  
Set Theory ◽  
Soft Matrix ◽  
Distributive Law

Abstract In this paper, we introduce subtraction operation notation on the soft matrix of size m×n with its entry on the set {0, 1}. In addition, we studied the characteristics of subtraction operations over intersection and union operations on soft matrices. The result shows the distributive law of subtraction operations over intersection and union operations on the soft matrix. Finally, we discuss the characteristics of De Morgan’s law analogous to set theory.

scholarly journals From Boolean Valued Analysis to Quantum Set Theory: Mathematical Worldview of Gaisi Takeuti

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 397
Author(s):  
Masanao Ozawa
Keyword(s):  
Quantum Mechanics ◽  
Quantum Logic ◽  
Set Theory ◽  
World View ◽  
Open Problems ◽  
Boolean Valued Analysis ◽  
Mathematical World ◽  
Distributive Law ◽  
And Algebra ◽  
Adjoint Operators

Gaisi Takeuti introduced Boolean valued analysis around 1974 to provide systematic applications of the Boolean valued models of set theory to analysis. Later, his methods were further developed by his followers, leading to solving several open problems in analysis and algebra. Using the methods of Boolean valued analysis, he further stepped forward to construct set theory that is based on quantum logic, as the first step to construct "quantum mathematics", a mathematics based on quantum logic. While it is known that the distributive law does not apply to quantum logic, and the equality axiom turns out not to hold in quantum set theory, he showed that the real numbers in quantum set theory are in one-to-one correspondence with the self-adjoint operators on a Hilbert space, or equivalently the physical quantities of the corresponding quantum system. As quantum logic is intrinsic and empirical, the results of the quantum set theory can be experimentally verified by quantum mechanics. In this paper, we analyze Takeuti’s mathematical world view underlying his program from two perspectives: set theoretical foundations of modern mathematics and extending the notion of sets to multi-valued logic. We outlook the present status of his program, and envisage the further development of the program, by which we would be able to take a huge step forward toward unraveling the mysteries of quantum mechanics that have persisted for many years.

scholarly journals Application of Repeated Average Method on Generalized Fuzzy Soft Matrix for Decision Making

2019 ◽  
Vol 45 (2) ◽  
pp. 249-259
Author(s):  
MK Hasan ◽  
MM Rahman ◽  
Abeda Sultana
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Fuzzy Set ◽  
Average Method ◽  
Soft Set ◽  
Mathematical Approach ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Soft Matrix

Molodtsov introduced the theory of soft sets, which can be seen as a new mathematical approach to vagueness. Maji and his associates have further initiated several basic notions of soft set theory. They have also introduced the concept of fuzzy soft set, a more generalized concept, which is a combination of fuzzy set and soft set. In this paper, Repeated Average Method has been used in Generalized Fuzzy Soft Matrix for prompt decision making. Asiat. Soc. Bangladesh, Sci. 45(2): 249-259, December 2019

scholarly journals Soft matrix product and soft cryptosystem

Filomat ◽  
2018 ◽  
Vol 32 (19) ◽  
pp. 6519-6530
Author(s):  
Emin Aygün
Keyword(s):  
Set Theory ◽  
Soft Set ◽  
Matrix Product ◽  
Mathematical Tool ◽  
Soft Matrix

Soft set theory, proposed by Molodtsov, has been regarded as an effective mathematical tool to deal with uncertainties. In this work, we define two new operations on the set of soft matrices, called inverse production and characteristic production and give their properties. We introduce soft cryptosystem as a new cryptosystem method by using inverse production and characteristic production of soft matrices. We finally define soft encryption and soft decryption. Some applications are given

The free one-generated left distributive algebra: basics and a simplified proof of the division algorithm

2013 ◽  
Vol 11 (12) ◽  
Author(s):  
Richard Laver ◽  
Sheila Miller
Keyword(s):  
Normal Form ◽  
Set Theory ◽  
Large Cardinal ◽  
Braid Groups ◽  
Division Algorithm ◽  
Free Left ◽  
Distributive Law ◽  
The Law

AbstractThe left distributive law is the law a· (b· c) = (a·b) · (a· c). Left distributive algebras have been classically used in the study of knots and braids, and more recently free left distributive algebras have been studied in connection with large cardinal axioms in set theory. We provide a survey of results on the free left distributive algebra on one generator, A, and a new, simplified proof of the existence of a normal form for terms in A. Topics included are: the confluence of A, the linearity of the iterated left division ordering <L of A, the connections of A to the braid groups, and an extension P of A obtained by freely adding a composition operation. This is followed by a simplified proof of the division algorithm for P, which produces a normal form for terms in A and is a powerful tool in the study of A.

A Course on Set Theory

2009 ◽  
Author(s):  
Ernest Schimmerling
Keyword(s):  
Set Theory

Set Theory

2016 ◽  
Author(s):  
Daniel W. Cunningham
Keyword(s):  
Set Theory
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