In handing information regarding various aspects of uncertainty, non-classicalmathematics (fuzzy mathematics or great extension and development of classical mathematics) is considered to be a more powerful technique than classical mathematics. The non-classical mathematics, therefore, has now days become a useful tool in applications mathematics and computer science. The purpose of this paper is to apply the concept of the fuzzy sets to some algebraic structures such as an ideal, upper semilattice, lower semilattice, lattice and sub-algebra and gives some properties of these algebraic structures by using the concept of fuzzy sets. Finally, related properties are investigated in fuzzy BCK-algebras.
A theoretical design of a multi-layer for Nd:YAG mirrors resonator is described in this work. An output coupler was designed and fabricated by successive thin layers to achieve very high transmittance at optical wavelengths around 1064 nm for Nd:YAG mirrors resonator. The different film optical filters were used to control the transmittance and reflectance. The three samples of dielectric materials composed of HfO 2 /Y 2 O 3 , Sc 2 O 3 + MgO, and Ta 2 O 5 + TiO 2 were used and compared with each other in transmittance, reflectance, full width at half maximum (FWHM), physical thickness, optical thickness, geometric thickness, and incident angles by the software [1].
This paper aims to introduce new notions of (fuzzy) n-fold P-ideals and (fuzzy) n-fold weak P-ideals in BCI-algebras, and investigate several properties of the foldness theory of P-ideals in BCI-algebras. Finally, we construct a computer-program for studying the foldness theory of P-ideals in BCI-algebras.
In this article we introduce new notions of (fuzzy) n-fold positive implicative ideals, (fuzzy) n-fold weak positive implicative ideals, and (fuzzy) n-fold weak implicative (weak) ideals in BCK-algebras and investigate some of their properties.
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