Title: Intuitionistic fuzzy zero point method for solving type-2 intuitionistic fuzzy transportation problem
Authors: P. Senthil Kumar
Addresses: PG and Research Department of Mathematics, Jamal Mohamed College (Autonomous), Tiruchirappalli, Tamilnadu, India
Abstract: In conventional transportation problem, supply, demand and costs are fixed crisp numbers. Therefore, in this situation, the decision maker (DM) can predict transportation cost exactly. On the contrary, in real world transportation problems the costs are in uncertain quantities with hesitation due to various factors like variation in rates of fuels, traffic jams, weather in hilly areas, etc. In such situations, the DM cannot predict transportation cost exactly and it will force the DM to hesitate. So, to counter these uncertainties, in this article, the author designed a transportation problem in which supplies, demands are crisp numbers and cost is intuitionistic fuzzy number. This type of problem is termed as type-2 intuitionistic fuzzy transportation problem (type-2 IFTP). Hence to deal with uncertainty and hesitation in transportation problem, intuitionistic fuzzy zero point method is proposed to find out optimal solution to the type-2 IFTP. Moreover, special kind of type-2 IFTP is proposed and its related theorems are proved. Finally, the ideas of the proposed method are illustrated with the help of numerical example which is followed by the results and discussion.
Keywords: intuitionistic fuzzy set; triangular intuitionistic fuzzy number; TIFN; trapezoidal intuitionistic fuzzy number; TrIFN; type-2 intuitionistic fuzzy transportation; intuitionistic fuzzy zero point method; optimal solution.
International Journal of Operational Research, 2020 Vol.37 No.3, pp.418 - 451
Received: 06 Sep 2016
Accepted: 17 Apr 2017
Published online: 21 Feb 2020 *