Optimal Solution of Balanced and Unbalanced Fuzzy Transportation Problem Using Hexagonal Fuzzy Numbers

Abstract

A fuzzy transportation problem (FTP) includes cost, supply and demand of transportation problems. Its numbers are fuzzynumbers. Fuzzy transportation problem works to reduce transportation cost of some commodities through a capacitate network. Present research paper points out a technique with an alpha cut, optimal solution for solving transportation problem. We suggest a technique to find the fuzzy optimal solution on scales of transportation problem and propose a new hexagonal representation of fuzzy numbers. In general, the comparison of balanced fuzzy transportation problem (BFTP) and unbalanced fuzzy transportation problem (UFTP) shows that the optimal transportation cost of UFTP is less than BFTP.Keywords: Fuzzy transportation problem, Hexagonal fuzzy numbers, α-Optimal solution, Robust ranking method. Contribution/ OriginalityThis study contributes in networking for transportation. This study uses new estimation methodology. This study originates optimal solution and comparison between BFTP and UFTP. This study investigated comparatively. This paper contributes the first logical analysis that is minimizes or maximizes objective solution is an optimal solution in hexagonal fuzzy numbers.

Decision support system using Dhouib-Matrix-TP1 heuristic for pentagonal fuzzy transportation problem

“…A fuzzy set 𝐴 is defined on universal set of real number 𝑅, is said to be fuzzy number if its membership function has the following properties [38], [39]: -𝐴 must be normal and convex fuzzy set.…”

DA systematic approach for solving mixed constraint fuzzy balanced and unbalanced transportation problem

“…Unit cost of the product from each origin to each destination is represented by mixed trapezoidal fuzzy numbers shown in Table 6. (5,6,8,9) (1,5,6,7) 5.5 (1,3,5,7) Demand (1,2,4,6) (0,1,1,2) (3,5,7,8) Solution: The given mixed fuzzy transportation problem is a unbalanced fuzzy transportation problem. Here the cost matrix contains four real numbers and rest are trapezoidal fuzzy numbers.…”

“…They used mixed intuitionistic fuzzy transportation problem. Ghadle and Pathade [8] compare balanced and unbalanced fuzzy transportation problem by using hexagonal fuzzy numbers and robust ranking technique. Ahmed and Khan [9] developed a new algorithm for finding an initial basic feasible solution of a transportation problem with fuzzy approach.…”

Hexagonal fuzzy number inadvertences and its applications to MCDM and HFFLS based on complete ranking by score functions

“…A new membership function on HXFN is introduced in Dhurai and Karpagam (2016b) and fuzzy optimal solution for fully FLPP using HXFNs is studied in Dhurai and Karpagam (2016a). Moreover, optimal solution of balanced and unbalanced transportation problem using HXFNs is proposed in Ghadle and Pathade (2016) and new ranking method on HXFNs and Octagonal. There are many research papers present in the literature are (Chen 1999;Chi and Vincent 2018;Chu and Tsao 2002;Chutia and Chutia 2017;De Hierro et al 2020;Dombi and Jonas 2020;Ezzati et al 2012;Geetha et al 2014;Jeevaraj et al 2016;Nayagam et al 2016a, b;Ponnialagan et al 2018;Shakouri et al 2020;Velu et al 2017;Wang and Wang 2014) for ranking interval, triangular, trapezoidal FNs and intuitionistic fuzzy numbers as well as general fuzzy number and intuitionistic fuzzy numbers based on different parameters such as centroid, value, ambiguity, rank index, score functions, upper dense sequence etc.…”