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Comparative Advantages for Compromise Solution

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If condition is not satisfied, that means, Then alternatives all are the same compromise solution, there is no comparative advantage of from others. But for the case of maximum value, the corresponding alternative is the compromise (closeness) solution. If condition is not satisfied, the stability in decision making is deficient whilehas a comparative advantage. Therefore, and has the same compromise solution. Select the best alternative by choosing as a best compromise solution with the minimum value of and must have to satisfy with the above conditions (Park, Cho, & Kwun, 2011).

Fuzzy Set Theory

Fuzzy set theory has been introduced by Zadeh (1965) to overcome this vagueness, ambiguity and subjectivity of the human judgment process. Usually, it is very difficult to solve the problems due to the involvement of the subjectivity and uncertainty situation in the multi-criteria decision making process. Moreover, decision makers are frequently faced with confusions, and difficulties while dealing with this kind of decision making process. Decision makers express their opinions in terms of linguistic scales. Linguistic data’s are converted into fuzzy numbers with the help of different membership functions. Then, it becomes easy to solve multi-criteria decision making problems. Therefore, fuzzy set theory has become a helpful tool for mechanizing human activities with uncertainty-based information. This theory is incorporated with a paper because vagueness kind information related parameters present in this supplierselection problem.Fuzzy numbers are a fuzzy subset of real numbers, and represent the expansion of the idea of a confidence interval (Zadeh, 1965). Let be the classical set of objects (e.g. universe), whose elements are denoted by. The crisp value of a statement can be given by the membership function as from to {0, 1}, Here,is called an evaluation set and it is permitted to be a real intervalfor the continuous mapping membership function. Is called a fuzzy set and the function valueis termed as the degree of membership of in. Fuzzy membership function has more types.

Membership functions of the triangular fuzzy number.Based on the extension principle, the fuzzy sum and fuzzy subtractionof any two triangular fuzzy numbers are also triangular fuzzy numbers; but the multiplication of any two triangular fuzzy numbers is only an approximate triangular fuzzy number (Zadeh,1975). Let’s have a two positive triangular fuzzy numbers, such as, and, and a positive real number, some algebraic operations can be expressed as follows: The operations of are defined as: Here, Also, the crisp value of a triangular fuzzy number set can be determined by defuzzification which locates the Best Non-fuzzy Performance (BNP) value. Thus, the BNP values of a fuzzy number are calculated by using the center of area (COA)method as follows: (Moeinzadeh & Hajfathaliha, 2009). Every time, in every country, and for every sector, cost is very important. Especially in global supply chains, cost is one of the most important criteria which affect the supplier selection problem directly. Every company wants to work with the supplier who can serve the transportation activities with high quality and low cost because as all of us know, the condition for the profit maximization can be achieved with the cost minimization.

Tariff and Taxes

Each country has its own guidelines for the tariff imposed on the import-export of goods. A foreign government wants to attract buyers from other countries to boost its economy, whereas the importing country would like to impose high tariffs to protect its domestic industry. Therefore despite the general agreement on tariffs and trade (GATT), tariffs will be imposed on the goods and services purchased from foreign countries. The manufacturing firm (buyer) should carefully estimate these additional charges before choosing its global supplier since tariff and dumping duties can lead to a substantial increase in purchasing price. Those preferences are given to the nations with less duties and taxes, because it ultimately helps in reducing the final price of the product to the customers.

Transportation Cost

Transportation is an important part of the logistics and can be implemented in various modes. Road, railroad, sea road and air road are the main roads of transportation. Transportation cost is a substantial part of the sum of the general expenses which is highly dependent to the modes. It includes the cost of fuel or lubricants, penalties, driver salaries, maintenance costs, failure of the vehicle costs Services The performance of the supplier in providing service to the manufacturer is the prime criteria to decide its suitability for a particular product. The good service given by the supplier may help in increase the customer base and so this criterion Is important in global supplier selection. Flexibility and Responsiveness The ability of the supplier to change according to the customer’s demand, price structure, order frequency and current business scenario has a great importance in the selection of global suppliers. These things can affect the performance of the firm in case of urgent and uncertain demand. More flexible and responsive suppliers in terms of the demand constraints can be chosen for better performance towards the customer. Information Sharing The ease of communication and negotiability with the suppliers decides the long-term relation between the supplier and manufacturer and so this should be included in deciding the global supplier selection. Since languages, business customs, ethics and communication devices vary from country to country, the manufacturing firm should consider sub-criteria such as cultural similarity, ethical standard and electronic data interchange capabilities in order to ensure effective communication and negotiation with the foreign supplier. A good relationship can help to better understand their objectives and they can help each other to enhance their performance towards customers.


The manufacturers want to work with the supplier who can manage the supply chain system on time and has the ability for following the exact delivering schedule table. Lead Time Lead Time is referred to as the time between the moment of ordering and the moment of delivery of a product, also known as Total Lead Time. It includes the Order Processing Time, Production Lead Time and the Delivery Lead Time of the supplier. The lead times are indicated by the suppliers and can be dependent on the distance of the supplier to the new plant, the transportation mode, the supplier’s production planning, the number of outstanding order and stock levels. The criterion is expressed in days. Just in TimeDelivery The suppliers have to follow the predefined delivery schedule for achieving on-time delivery.


Environmentally friendly materials are the materials that protect the environment by using them severely. Reduced Emissions Control the improper waste disposal, use of hazardous material in operation. Organizations must consider reducing their carbon footprint to meet corporate objectives and reducing their carbon footprint when selecting global suppliers. Recycle Mainly refers to the ability of the supplier to handle the defective product, the recycling goods, etc Recycling is the process in which the waste material which is related to the product and its manufacturing phase is useful or can be used by reutilization of the waste rather solid or gas.

Risk factors

The global supplier selection decision is most strongly affected by the risks. This selection process is more complicated and riskier than domestic supplier selection process. Water risk Those companies whose customers may be affected by water issues. Companies indicating that water are important in their operations they are engaging with their value chain upstream and downstream to manage risks, take collective action, Control the unwanted use of water in business operation or facilitate the transition to a water secure future. Exchange rates andEconomic position Different countries have their own currency and relative value of the currencies changes frequently, so the exchange rate of the currency may also play an important role in deciding the product and transportation cost. This should also be properly discussed in the process of global supplier selection. The economic status of the supplier’s country can affect the currency exchange rate, local price control, inflation rate and so forth. This can result high hidden costs for international sourcing and so these should be factored into the global supplier selection decision.

Proposed Methodology

The concept of fuzzy set theory and VIKOR method, the proposed fuzzy VIKOR method has been applied to find the best compromise solution under the multi-person multi-criteria decision-making supplier selection problem. Usually, decision-making problems are dealing with some alternatives which can be ranked, with respect to distinct criteria. Ratings of the alternatives and the weights of each criterion are the two most significant data which can affect the results of decision-making problems. Therefore, the proposed methodology has been used here, to calculate the definite weight of criteria and ranking of the alternatives. In this paper, the importance weights of various criteria and ratings of qualitative criteria are measured as linguistic variables because linguistic assessment can only have the capability to approximate the subjective judgment through a decision maker’s opinion. Moreover, linear triangular membership functions are considered for capturing the vagueness of these linguistic assessments.

The proposed algorithm consists of the following steps:

  1. Step1. Make a list of feasible alternatives, find the evaluation criteria, and constitute a group of decision makers. Suppose, there aredecision makers who are responsible for assessingalternativeswith respect to the importance of each of thecriteria, (Bashiri & Badri, 2011)
  2. Step2. Identify appropriate linguistic variables and their positive triangular fuzzy numbers. Linguistic variables are used to calculate the importance weights of criteria and the ratings of the alternatives with respect to distinct criteria. Linguistic variables for weights Equally preferred (EP) (1, 1, 1)Weakly preferred (WP) (2/3, 1, 3/2)Fairly strongly preferred (FSP) (3/2, 2, 5/2)Very strongly preferred (VSP) (5/2, 3, 7/2)Absolutely preferred (AP) (7/2, 4, 9/2)
  3. Step3. Construct a fuzzy decision matrix by pulling the decision makers’ opinions to get the aggregated fuzzy weight of the criteria, and the aggregated fuzzy rating of alternatives. Let is the number of decision makers in a group and, the aggregated fuzzy weightwith respect to each criterion can be calculated as (Chen, 2000). And also the aggregated fuzzy ratingsof alternatives with respect to each criterion can be calculated as:In the supplier selection problem, the value of aggregated weights and ratings are expressed in matrix format as follows: (19) For alternatives, and for criteria.
  4. Step4. Defuzzify the fuzzy decision matrix and fuzzy weight of each criterion in to crisp values using the relation based on the COA defuzzification method proposed in section 3 (Relation 16).
  5. Step5. Determine best crisp valueand worst crisp valuefor all criterion ratings,by using the relations
  6. Step6. Compute the valuesandusing the relations respectively.
  7. Step7. Compute the values using the relation (6) described in section 2.
  8. Step8. Rank the alternatives by sorting each values in ascending order.
  9. Step9. Select the best alternatives as a compromise solution by referring step 5 of section.

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Comparative Advantages For Compromise Solution. (2019, September 13). GradesFixer. Retrieved July 4, 2022, from
“Comparative Advantages For Compromise Solution.” GradesFixer, 13 Sept. 2019,
Comparative Advantages For Compromise Solution. [online]. Available at: <> [Accessed 4 Jul. 2022].
Comparative Advantages For Compromise Solution [Internet]. GradesFixer. 2019 Sept 13 [cited 2022 Jul 4]. Available from:
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