International Journal of Fuzzy Logic Systems (IJFLS) Vol.5, No.1, January 2015
On Intuitionistic Fuzzy Transportation Problem Using Hexagonal Intuitionistic Fuzzy Numbers A.Thamaraiselvi1 and R.Santhi2 1
2
Research scholar, Department of Mathematics, NGM College, Pollachi, India-642001 Assistant Professor, Department of Mathematics, NGM College, Pollachi, India-642001
ABSTRACT In this paper we introduce Hexagonal intuitionistic fuzzy number with its membership and non membership functions. The main objective of this paper is to introduce an Intuitionistic Fuzzy Transportation problem with hexagonal intuitionistic fuzzy number. The arithmetic operations on hexagonal intuitionistic fuzzy numbers are performed. Based on this new intuitionistic fuzzy number, we obtain a initial basic feasible solution and optimal solution of intuitionistic fuzzy transportation problem. The solutions are illustrated with suitable example.
KEYWORDS Intuitionistic fuzzy number, Hexagonal Intuitionistic fuzzy number, Hexagonal Intuitionistic Fuzzy Transportation problem, Initial Basic Feasible Solution, Optimal Solution.
1. INTRODUCTION The classical transportation problem refers to a special type of linear programming problem in which a single homogeneous goods kept at various sources to various destinations in such a way that the total transportation cost is minimum. The basic transportation problem was introduced and developed by Hitchcock in 1941 in which the transportation costs, the supply and demand quantities are crisp values. But in the real, the parameters of a transportation problem may be uncertain due to many uncontrollable factors. To deal such fuzziness in decision making, Bellmann and Zadeh[3] and Zadeh[12] introduced the concept of fuzziness. Many authors discussed the solutions of fuzzy transportation problem(FTP) using various techniques. In 1982, O’heigeartaigh [8] proposed an algorithm to solve FTP with triangular membership function. In 1996, Chanas and Kutcha [4] proposed a method to find the optimal solution to the transportation problem with fuzzy coefficients. In 2010, Pandian and Natarajan [9] proposed a new algorithm namely fuzzy zero point method to find optimal solution of a FTP with trapezoidal fuzzy numbers. Sometimes the concept of fuzzy set theory is not enough to deal the vagueness in transportation problems. So intuitionistic fuzzy set (IFS) theory is introduced to deal the transportation problems. In 1986, the idea of intuitionistic fuzzy sets introduced by Atanassov [1,2] to deal vagueness or uncertainty. The main advantage of IFSs is that include both the degree of membership and non membership of each element in the set.
DOI : 10.5121/ijfls.2015.5102
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