Commutative monoids and their corresponding affine $$\Bbbk $$-schemes

2019 ◽  
Vol 101 (2) ◽  
pp. 421-434
Author(s):  
Alberto Navarro ◽  
José Navarro ◽  
Ignacio Ojeda
Keyword(s):  
2021 ◽  
pp. 1-21
Author(s):  
Muhammad Shabir ◽  
Rimsha Mushtaq ◽  
Munazza Naz

In this paper, we focus on two main objectives. Firstly, we define some binary and unary operations on N-soft sets and study their algebraic properties. In unary operations, three different types of complements are studied. We prove De Morgan’s laws concerning top complements and for bottom complements for N-soft sets where N is fixed and provide a counterexample to show that De Morgan’s laws do not hold if we take different N. Then, we study different collections of N-soft sets which become idempotent commutative monoids and consequently show, that, these monoids give rise to hemirings of N-soft sets. Some of these hemirings are turned out as lattices. Finally, we show that the collection of all N-soft sets with full parameter set E and collection of all N-soft sets with parameter subset A are Stone Algebras. The second objective is to integrate the well-known technique of TOPSIS and N-soft set-based mathematical models from the real world. We discuss a hybrid model of multi-criteria decision-making combining the TOPSIS and N-soft sets and present an algorithm with implementation on the selection of the best model of laptop.


2019 ◽  
Vol 100 (3) ◽  
pp. 732-742
Author(s):  
Bijan Davvaz ◽  
Zahra Nazemian

Mathematics ◽  
2015 ◽  
Vol 3 (4) ◽  
pp. 1001-1031 ◽  
Author(s):  
María Calvo-Cervera ◽  
Antonio Cegarra

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