The purpose of this research paper was to propose a method which can be utilized to determine the different types of performance measures on the basis of the crisp values for the fuzzy queuing model which has an unreliable server and where the rate of arrival, the rate of service, the rate of breakdown and the rate of repair are all expressed as the fuzzy numbers. In this case the inter arrival time, the time of service, the rates of breakdown and the rates of repair are all triangular functions and are also expressed as the Trapezoidal fuzzy numbers. The main intent is to transform the fuzzy inter arrival time, the time of service, the rates of breakdown and the rates of repair into the crisp values by using the Ranking function method. Then the crisp values are applied in the classical formulas for the performance measure. In the fuzzy environment the ranking fuzzy numbers are very helpful in making the decisions. The ranking function method is one of the most reliable method, is simpler to apply in comparison to other methods and can be utilized to solve the different types of queuing problems. In this research paper a numerical example is also provided for both the triangular and the trapezoidal fuzzy number so that a practical insight into the problem can be provided.

The present paper introduces a new class of separation axioms called α-generalized separation axioms using α-generalized open sets and also includes the study of the connections between these separation axioms and the existing α-separation axioms. Also, here, the concept of   -closed set has been coined and then   -separation axioms have been framed w.r.t   -open sets.

The aim of this paper is to elaborate the study of some nearly-open sets as p-open, s-open, α-open & β-open sets & the associated strongly continuity as well as compactness. Also the inter relationship of these nearly open sets has been discussed.

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In the present paper, we introduce, study and investigate the following separation axioms:-spaces (for i=0,1,2). Moreover, some of special results and properties, which belong to them, are studied.