TOPSIS Approach for Solving Bi-Level Non-Linear Fractional MODM Problems
Journal Title: JOURNAL OF ADVANCES IN MATHEMATICS - Year 2017, Vol 13, Issue 4
Abstract
TOPSIS (technique for order preference similarity to ideal solution) is considered one of the known classical multiple criteria decision making (MCDM) methods to solve bi-level non-linear fractional multi-objective decision making (BL-NFMODM) problems, and in which the objective function at each level is considered nonlinear and maximization type fractional functions. The proposed approach presents the basic terminology of TOPSIS approach and the construction of membership function for the upper level decision variable vectors, the membership functions of the distance functions from the positive ideal solution (PIS) and of the distance functions from the negative ideal solution (NIS). Thereafter a fuzzy goal programming model is adopted to obtain compromise optimal solution of BL-NFMODM problems. The proposed approach avoids the decision deadlock situations in decision making process and possibility of rejecting the solution again and again by lower level decision makers. The presented TOPSIS technique for BL-NFMODM problems is a new fuzzy extension form of TOPSIS approach suggested by Baky and Abo-Sinna (2013) (Applied Mathematical Modelling, 37, 1004-1015, 2013) which dealt with bi -level multi-objective decision making (BL-MODM) problems. Also, an algorithm is presented of the new fuzzy TOPSIS approach for solving BL-NFMODM problems. Finally, an illustrative numerical example is given to demonstrate the approach.
Authors and Affiliations
MAHMOUD A ABO-SINNA, AZZA H AMER
Norms Of Hankel-Hessenberg and Toeplitz-Hessenberg Matrices Involving Pell and Pell-Lucas Numbers
We derive some sum formulas for the squares of Pell and Pell-Lucas numbers. We construct Hankel-Hessenberg andToeplitz-Hessenberg matrices whose entries in the first column are HHP = aij , ij i j a Pï€ = ; Q HH =...
Some local Forms of Known Convergences of Sequence of Real Valued Functions
Using the notions of local uniform and strong local uniform con-vergence for the sequence of real valued functions or with value in metric space, the class of locally equally and strong locally equally convergences are s...
MATHEMATICAL ANALYSIS OF THE ROLE OF DETECTION RATE IN THE DYNAMICAL SPREAD OF HIV-TB CO-INFECTION
Human Immunodeficiency Virus (HIV) co-existing with Tuberculosis (TB) in individuals remains a major global health challenges, with an estimated 1.4 million patients worldwide. These two diseases are enormous public heal...
Robust H1 control for a class of switched nonlinear systems
This article is concerned with the robust H1 control problem of a class of switched nonlinear systems with norm-bounded time-varying uncertainties. The system considered in this class is composed of two parts: a uncertai...
An n-order (F,a,p,d)- Convex Function and Duality Problem
A class of n-order (F,a,p, d)-convex function and their generalization on functions is introduced. Using the assumption on the functions involved,weak, strong ,and converse duality theorems are established for the n-orde...