Papers

Decision making preferences to certain criteria usually focus on positive degrees without considering the negative degrees. However, in real life we came across more frequently with problems related to our Car, valuation of faults becomes more comprehensive if negative degrees are considered concurrently. Preference is expected to be more effective when considering both positive and negative degrees of preference to evaluate the best decision. Therefore, the aim of this paper is to propose the conflicting bi-fuzzy preference relations in decision making by utilization of a modified novel score function. The conflicting bi fuzzy preference relation is obtained by intuitionistic fuzzy preference relations. Releasing the intuitionistic condition by taking into account positive and negative degrees simultaneously and utilizing the novel score function are the main modifications to establish the proposed preference model. The proposed model is tested with a numerical example and proved to be simple and practical.

In this paper we have proved a theorem on generalized Nörlund summability of infinite series, which generalizes various known results. However, our theorem is as follows.

Theorem : Let {p_n} be a positive non-increasing sequence, {e_n} is a positive non-decreasing sequence and {l_n} is a non-negative, non-increasing such that

as n®¥

n Dl_n = O(l_n )

Sp_n l_n < ¥

and then the series Sa_ne_nl_n is summable by G(N, p, l).

In this paper we shall study theorem with the function pFq for p=q+1 and p=q. Also we relate Barnes integral with the pFq which will help us to solve the problems related to typical integrals and its related integrals.

Sufficient optimality conditions and duality results for a class of minimax nonlinear parametric programming problems are obtained under V-r - Invexity.

In this paper we find the n^th power of GM Matrix on a set of distinct positive integers in terms of the matrix and its power of trace.

The aim of the present paper, we have studied almost hyperbolic Hermite manifolds and also obtain a few interesting results. Almost contact hyperbolic (f,g,h,x) structures have been defined by M.D. Upadhyay and K.K. Dube⁷ and others. Vanzara⁸ studied almost r-contact structures. The paper is organized as fallows. Section1, contains a brief introduction to hyperbolic Hermite and Nijenhuis tensor, while in section 2 some necessary details about some results of manifolds are presented. In section 3, we define affine connections of D in mⁿ and a vector valued bilinear function of torsion tensor.

A relationship exists between the algebraic sum of the coefficients in the nth rising diagonals of the left justified Tchebychef polynomials and Lucas numbers.

A relationship exists between the algebraic sum of the coefficients in the nth rising diagonals of the left justified Tchebychef polynomials and Lucas numbers.

In this short note, the concept of s-singular values of a given matrix is introduced. Also, we present two simple results on s-normal matrices.

A fuzzy system can uniformly approximate any real continuous function on a compact domain to any degree of accuracy. Such results can be viewed as an existence of optimal fuzzy systems. Li-Xin Wang discussed a similar problem using Gaussian membership function and Stone-Weierstrass Theorem. He established that fuzzy systems with product inference, centroid defuzzification and Gaussian membership functions are capable of approximating any real continuous function on a compact set to arbitrary accuracy. In this paper we study a similar approximation problem by using exponential membership functions.