This paper deals with the study of generalizations of fuzzy subalgebras and fuzzy ideals in BCK/BCI-algebras. In fact, the notions of ∈ , ∈ ∨ κ ~ ∗ , q κ ~ -fuzzy subalgebras, ∈ , ∈ ∨ κ ~ ∗ , q κ ~ -fuzzy ideals, and ∈ ∨ κ ~ ∗ , q κ ~ , ∈ ∨ κ ~ ∗ , q κ ~ -fuzzy ideals in BCK/BCI-algebras are introduced. Some examples are provided to demonstrate the logic of the concepts used in this paper. Moreover, some characterizations of these notions are discussed. In addition, the concept of ∈ , ∈ ∨ κ ~ ∗ , q κ ~ -fuzzy commutative ideals is introduced, and several significant characteristics are discussed. It is shown that for a BCK-algebra A , every ∈ , ∈ ∨ κ ~ ∗ , q κ ~ -commutative ideal of a BCK-algebra is an ∈ , ∈ ∨ κ ~ ∗ , q κ ~ -fuzzy ideal, but the converse does not hold in general; a counter example is constructed.

The study scrutinizes the effects of thermal radiation, heat generation, and induced magnetic field on steady, fully developed hydromagnetic free convection flow of an incompressible viscous and electrically conducting couple stress fluid in a vertical channel. The channel walls are maintained at an isoflux-isothermal condition, such that the left channel wall is maintained at a constant heat flux. In contrast, the right channel wall is maintained at a constant temperature. The governing simultaneous equations are solved analytically utilizing the method of undetermined coefficient, and closed form solutions in dimensionless form have been acquired for the velocity field, the induced magnetic field, and the temperature field. The expression for the induced current density has been also obtained. A parametric study for the velocity, temperature, and induced magnetic field profiles, as well as for the skin-friction coefficient, Nusselt number, and induced current density, is conducted and discussed graphically.

Megnetohydrodynamic (MHD) convection flow of two immiscible fluids in an inclined channel in the presence of an applied magnetic field is investigated. Both fluids are assumed to be Newtonian and heat generating or absorbing and having constant transport properties. The channel walls are maintained at different temperature. The resulting coupled and nonlinear equations of momentum and energy are solved analytically by using the regular perturbation method valid for small value of ε=PrEc. The influence of various parameters on velocity field and temperature field for heat absorption and heat generation are discussed with the aid of the graphs.

Abstract:The problem of fully developed free convection flow of electrically conducting fluid in an inclined microchannel in the presence of transverse magnetic field and internal heat generation is investigated. The analytical solution for velocity profile and temperature profile have been obtained, considering the velocity slip and temperature jump conditions at the wall of the microchannel. The effect of different parameters involved in the problem on the velocity and temperature profile along with the skin friction parameter and Nusselt number has been discussed graphically.

In this paper, the notions of ∈ , ∈ ∨ q -fuzzy soft BCK / BCI -algebras and ∈ , ∈ ∨ q -fuzzy soft sub- BCK / BCI -algebras are introduced, and related properties are investigated. Furthermore, relations between fuzzy soft BCK / BCI -algebras and ∈ , ∈ ∨ q -fuzzy soft BCK / BCI -algebras are displayed. Moreover, conditions for an ∈ , ∈ ∨ q -fuzzy soft BCK / BCI -algebra to be a fuzzy soft BCK / BCI -algebra are provided. Also, the union, the extended intersection, and the “AND”-operation of two ∈ , ∈ ∨ q -fuzzy soft (sub-) BCK / BCI -algebras are discussed, and a characterization of an ∈ , ∈ ∨ q -fuzzy soft BCK / BCI -algebra is established.