Constrained fuzzy arithmetic approach to fuzzy transportation problems with fuzzy decision variables

Most of the existing methods for solving fully fuzzy mathematical programs are based on the standard fuzzy arithmetic operations and/or Zadeh's extension principle. These methods may produce questionable results for many real-life applications. Due to this fact, this paper presents a novel method based on the constrained fuzzy arithmetic concept to solve fully fuzzy balanced/unbalanced transportation problems in which all of the parameters (source capacities, demands of destinations, transportation costs etc.) as well as the decision variables (transportation quantities) are considered as fuzzy numbers. In the proposed method, the requisite crisp and/or fuzzy constraints between the base variables of the fuzzy components are provided from the decision maker according to his/her exact or vague judgments. Thereafter, fuzzy arithmetic operations are performed under these requisite constraints by taking into account the additional information while transforming the fuzzy transportation model into crisp equivalent form. Therefore, various fuzzy efficient solutions can be generated by making use of the proposed method according to the decision maker's risk attitude. In order to present the efficiency/applicability of the proposed method, different types of fully fuzzy transportation problems are generated and solved as illustrative examples. A detailed comparative study is also performed with other methods available in the literature. The computational analysis have shown that relatively more precise solutions are obtained from the proposed method for “risk-averse” and “partially risk-averse” decision makers. The proposed method also successfully provided fuzzy acceptable solutions for “risk seekers” with high degree of uncertainty similar to the other existing methods in the literature.