Applied Mathematics

In conventional assignment problem, cost is always certain. In this paper, Assignment problem with crisp, fuzzy and intuitionistic fuzzy numbers as cost coefficients is investigated. There is no systematic approach for finding an optimal solution for mixed intuitionistic fuzzy assignment problem. This paper develops an approach to solve a mixed intuitionistic fuzzy assignment problem where cost is not in deterministic numbers but imprecise ones. The solution procedure of mixed intuitionistic fuzzy assignment problem is proposed to find the optimal assignment and also obtain an optimal value in terms of triangular intuitionistic fuzzy numbers. Numerical examples show that an intuitionistic fuzzy ranking method offers an effective tool for handling an intuitionistic fuzzy assignment problem.

In this paper the symmetry classification of third order quasi-linear PDE's containing arbitrary function have been studied with derailed examples.

The main objective of present investigation is to introduce the magnetohydrodynamic peristaltic transport with porous medium through a coaxial asymmetric vertical tapered channel and Joule heating with radiation. Effects of sundry parameters on the temperature and heat transfer coefficient at the wall y = h1 are studied through graphs. It is noted that the temperature increases when increase in Radiation parameter (N), Prandtl number (Pr), heat source/sink parameter (?), Brinkman number (Br), Hartmann number (M), non-uniform parameter (K1) and non-dimensional amplitude (?) in entire tapered channel. Further, we observe that the heat transfer coefficient decreases when non-uniform parameter (K1) is assigned higher values.

Let G be a graph with n vertices. Prime labeling of G is the labeling of the vertices using first n positive integers such that labeling of each pair of adjacent vertices are relatively prime. This work is a generalization of [2] which was analogous to [1] in which prime labeling for complete bipartite graphs were considered. In [2] conditions for the existence of prime labeling of complete tripartite graphs of the form K_(1,m,n) was given where m,n?Z^+. In our work, we have proved that prime labeling of K_(2,m,n) and K_(3,m,n) exists for some values of m and n where m,n?Z^+. Further, few non-existance cases have been discussed.

We consider a singular Sturm-Liouville differential expression with an indefinite weigh and present a sufficient condition for similarity of indefinite Sturm-Liouville operators to self- adjoint operators. Using this result, we construct a example of operator and prove that it is similar to a self-adjoint one.

The aim of this paper is to develop a methodology for solving matrix games with fuzzy payoffs. Here, a fuzzy matrix game has been considered and its solution method has been proposed using interval parametric technique. This technique is based on parametric representation of interval number. In this technique, the fuzzy number has been converted into interval number using interval approximation of fuzzy number and the interval number has been presented to its parametric interval functional form. Then the corresponding matrix game has been converted into crisp game using the said technique. The value of the matrix game for each player is obtained by solving corresponding crisp game problems using the existing method. Finally, a numerical example has been considered and solved in support of the solution method.

Mean labeling of graphs was discussed in [10] and the concept of odd mean labeling was introduced in [9].  k-odd mean labeling and (k, d) - odd mean labeling are introduced and discussed in [5], [6], [7]. In this paper, we introduce the concept of k-even mean labeling and investigate k-even mean labeling of C_n È P_m.

In this paper we formulate a new local function called ?-closure local function and we construct ?-closure compatible spaces using ?-open sets. Further we introduce an operator ?_?(A) for each A ? P(X) by utilizing ?(A). Moreover we characterize the properties of ?-closure local function and investigate their relationship with other types of similar functions.

In this paper, the author has studied performance of a three unit redundant system with the impact of switch and human failure. A system with three identical unit has been considered for assessment of performance under 2-out –of -3: G; policy. In the system, a switch is used to transfer load from one unit to another unit. All three units of system are connected in parallel configuration and working under 2-out-of-3: G; policy. The system can have two types of failure partial failure and complete failure. Partial failure degrades the efficiency of system but the complete failure breakdown the system and stop functioning of the system. Switch failure and human failure are considered as complete failure. The system has two types of failure and two types of repair. General repair is employed to the partially failed system and Gumbel-Hougaard family copula distribution complete failed system. The system is studied by supplementary variable technique and various measures of reliability, such as availability, reliability, MTTF and profit functions have been discussed. Some particular cases have been discussed by taking different failure rates.

Let G be a simple connected graph of order n. Let Dct(G, i) be the family of connected total dominating sets of G with cardinality i. The polynomial Dct (G, x) = dct (G, i) xi is called the connected total domination polynomial of G. In this paper, we study some properties of connected total domination polynomials of the Extended grid graph Gn. We obtain a recursive formula for dct (Gn, i). Using this recursive formula, we construct the connected total domination polynomial Dct (Gn, x) = dct(Gn, i) xi , of Gn, where dct(Gn, i) is the number of connected total dominating sets of Gn with cardinality i and some properties of this polynomial have been studied.