Abstract
The transportation problems (TPs) support the optimal management of the transport deliveries. In classical TPs the decision maker has information about the crisp values of the transportation costs, availability and demand of the products. Sometimes in the parameters of TPs in real life there is ambiguity and vagueness caused by uncontrollable market factors.Uncertain values can be represented by fuzzy sets (FSs) of Zadeh. The FSs have the degrees of membership and non-membership. The concept of intuitionistic fuzzy sets (IFSs) originated in 1983 as an extension of FSs. Atanasov’s IFSs also have a degree of hesitansy to representing the obscure environment.In this paper we formulate the TP, in which the transportation costs, supply and demand values are intuitionistic fuzzy pairs (IFPs), depending on the diesel prices, road condition, weather and other factors. Additional constraints are included in the problem: limits for the transportation costs. Its main objective is to determine the quantities of delivery from producers to buyers to maintain the supply and demand requirements at the cheapest transportation costs. The aim of the paper is to extend the fuzzy zero point method (FZPM [35]) to the intuitionistic FZPM (IFZPM) to find an optimal solution of the intuitionistic fuzzy TP (IFTP) using the IFSs and index matrix (IM) concepts, proposed by Atanassov. The solution algorithm is demonstrated by a numerical example. Its optimal solution is compared with that obtained by the intuitionistic fuzzy zero suffix method (IFZSM).
Highlights
T HE transportation problems (TPs) originally proposed by Hitchcock in 1941 [12]
In [49], we have proposed for the first time the intuitionistic fuzzy zero suffix method (IFZSM) to determine an optimal solution of the intuitionistic fuzzy TP (IFTP), interpreted by the intuitionistic fuzzy sets (IFSs) and index matrix (IM) [18] concepts
The reliability of the proposed approach is demonstrated by an example in Section 4 and the results are compared with those obtained after application of IFZSM
Summary
Μkm,ln , νkm,ln where for i = 1, ..., m; j = 1, ..., n: we recall some basic definitions on intuitionistic fuzzy pairs from (see [10], [19], [21], [23], [46]) and on index matrix apparatus from (see [20], [48]). Index type operations: AGIndex{(min / max)/(min✷ / max✷)/(min⋄ / max⋄)(minR / maxR)}(⊥) (A). AGIndex{(min / max)/(min✷ / max✷)/(min⋄ / max⋄)(minR / maxR)}(⊥)(∈/F) (A) = ki, l j presents the index of the minimum/ maximum element between the elements of A, whose indexes ∈/ F, with no empty value in accordance with the relations (2).
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