fuzzy rule-based

Integrated and coordinated planning of the main functions of the supply chain (procurement, production and distribution) often leads to economic efficiency and, as a result, more profit for the entire supply chain. On the other hand, the financial flow and the flow of goods and information are crucial and influential flows in any supply chain. In this paper, the main contribution is to integrated planning of procurement, production and distribution for a multi-product supply chain in order to maximize the producer's profit and also minimize the deviations of the producer's financial indicators by considering both the physical and financial flow. In this regard, the studded supply chain includes several suppliers, one producer and several customers. One of the prominent features of the proposed model is the use of mathematical programming to model the financial flow and achieve the producer's financial goals. Since the presented model is a bi-objective one, two fuzzy multi-objective interactive methods, Selim and Ozkarahan (SO) and Torabi and Hassini (TH) can adjust the degree of satisfaction of the objective functions have been applied. Next, the model is optimized using the goal programming method. Finally, the numerical results in optimizing the proposed fuzzy model show the proposed model's efficiency and the high quality of performance and applicability of the proposed model. The core achievement in the numerical results is that the total value of the distribution in the two models is equal. However, the SO method obtains more unbalanced solutions when the decision maker pays more attention to the first objective function.

Multi-Attribute Decision Making (MADM) process is the most well-known branch of decision making and it is one of the most important tasks that have received a lot of attention in many areas. In solving MADM issues, the parameters of decision-making are often faced with problems, such as imprecise, vague, uncertain, or incomplete information which lead to inaccurate decision-making. To cope with these problems, the researchers apply fuzzy set theory as the best-developed approach. Among different fuzzy methods, the fuzzy rule-based system (FRBS) due to its flexibility, simplicity, and experts' knowledge modeling is an adequate technique for solving MADM problems. The main objective of this study is to apply experts' opinions by Z-numbers in MADM issues to enhance the accuracy of the decision-making process. The fundamental issue in solving MADM problems is that inadequate information in the experts' opinions leads to some degree of uncertainty in decisions. Indeed, in FRBS research to ranking, the reliability level (Z-numbers) in experts' opinions within the decision-making process has not been taken into account. Whereas, the Z-numbers play a key role in the decision-making process to reach more precise decisions affecting the final ranking results. In the proposed approach (Z-FRBS), by considering experts' opinions in the form of Z-numbers to deal with inadequate information and modeling experts' knowledge through FRBS, the process of making a decision is performed without using conventional techniques which resulted in a more accurate solving MADM problems. The effectiveness and validity of the proposed method was approved with an illustrative example, sensitivity analysis, and comparison with three other validated method.