SUPPLIER SELECTION USING FUZZY INTERFACE SYSTEM

Transcription

1 International Journal of Marketing and Finance Vol. 1 No. 1 (January-June 2011) pp SUPPLIER SELECTION USING FUZZY INTERFACE SYSTEM 1 C. Elanchezhian Research Scholar, Department of Production Technology, M.I.T. Campus, Anna University, Chrompet, Chennai , Tamilnadu, India, elanchezhian_c@yahoo.co.in. 2 B. Vijaya Ramnath, Research Scholar, Department of Production Technology, M.I.T. Campus, Anna University, Chrompet, Chennai , Tamilnadu, India. 3 R. Kesavan Asst. Professor, Department of Production Technology, M.I.T. Campus, Anna University, Chrompet, Chennai , Tamilnadu, India. Abstract: Traditionally, marketing, distribution, planning, manufacturing, and the purchasing organizations along the supply chain operated independently. These organizations have their own objectives and these are often conflicting. Marketing s objective of high customer service and maximum sales dollars conflict with manufacturing and distribution goals. Many manufacturing operations are designed to maximize throughput and lower costs with little consideration for the impact on inventory levels and distribution capabilities. Purchasing contracts are often negotiated with very little information beyond historical buying patterns. The result of these factors is that there is not a single, integrated plan for the organization there were as many plans as businesses. Clearly, there is a need for a mechanism through which these different functions can be integrated together. Supply chain management is a strategy through which such integration can be achieved. A supply chain consists of three types of entities: customers, a producer, and the producer s suppliers. The extended supply chain includes customers customers and suppliers suppliers. Supply chain management oversees and optimizes the processes of acquiring inputs from suppliers (purchasing), converting those inputs into a finished product and delivering those products or outputs - to customer s fulfillment.

2 C. Elanchezhian B. Vijaya Ramnath & R. Kesavan In general, this paper intends to provide empirical evidence of the criteria and the procedures for the supplier selection process used in different corporate environment. It plans also evaluate rigorous regulations as per ISO 9001 standards. Finally identify the suitability of the Fuzzy Inference system to assist in decision making to resolve the supplier selection problem. Keywords: Supply chain, supplier selection process, Fuzzy Inference System. 1. INTRODUCTION There has been an evolution in the role and structure of the purchasing function through the nineties. The purchasing function has gained great importance in the supply chain management due to globalization. Purchasing involves buying the raw materials, supplies and components for the organization. The activities also associated with selecting a supplier. Supplier rating is the result of a formal supplier evaluation system. Suppliers are given a title according to their attainment of some level of performance, such as delivery, lead time, quality, price, or some combination of variables. The motivation for the establishment of such a rating system is part of the effort of manufacturers and service firms to ensure that the desired characteristics of a purchased product or service is built in and not determined later by some after-the-fact indicator. The supplier rating may take the form of a hierarchical ranking from poor to excellent and whatever rankings the firm chooses to insert in between the two. For some firms, the supplier rating may come in the form of some sort of award system or as some variation of certification. Much of this attention to vender rating is a direct result of the widespread implementation of the just-in-time concept in the United States and its focus on the critical role of the buyer-supplier relationship. Most firms want vendors that will produce all of the products and services defect-free and deliver them just in time (or as close to this ideal as reasonably possible). Some type of vehicle is needed to determine which supplying firms are capable of coming satisfactorily close to this and thus to be retained as current suppliers. One such vehicle is the vendor rating. 2

3 Supplier Selection using Fuzzy Interface System Some authors have identified several criteria for supplier selection such as net price, quality, delivery, capacity, previous experience, communication system, service, geographical location, financial capability, cost reduction programme, capacity to train the buyer s engineers, ability to provide maintenance contract, credit availability. In general, this paper intends to provide empirical evidence of the criteria and the procedures for the supplier selection process used in different corporate environment. It plans also evaluate rigorous regulations as per ISO 9001 standards. Finally identify the suitability of the Fuzzy Inference system to assist in decision making to resolve the supplier selection problem. 2. LITERATURE SURVEY This chapter provides the literature that has been studied to understand the basic concepts of supply chain management. One of the most important process performed in organization today is the evaluation, selection and continuous improvement of suppliers. It is understood from different literature that there is no standard procedure to evaluate and select a right vendor. There are several criteria to evaluate and select the vendor. This review first includes the general frame work used in supplier selection process. Next, some of the methods currently available are attached discussed. Supply chain management (SCM) is the management of a network of interconnected businesses involved in the ultimate provision of product and service packages required by end customers (Harland, 1996). Supply Chain Management spans all movement and storage of raw materials, work-in-process inventory, and finished goods from point-of-origin to point-of-consumption (supply chain). Barla (2003) did a case study of vendor selection and evaluation for a manufacturing company under lean philosophy. In order to reduce the vendor base, the vendor selection and evaluation study is conducted using the multi-attribute selection model. 3

4 C. Elanchezhian B. Vijaya Ramnath & R. Kesavan According to Chiphon (1996) supply chain management is the process of strategically managing the movement and storage of material, parts and finished goods inventory from suppliers through the firm and to the customer. Choy and Lee (2002) proposed a case-based supplier management tool (CBSMT) using the case-based reasoning (CBR) technique in the areas of intelligent supplier selection and management that will enhance performance, compared with the traditional approach. Dickson (1966) in his seminal paper identified 23 supplier selection criteria, which deeply influenced later researches in this area reviewed, annotated, and classified 74 related articles which had appeared since OBJECTIVE OF THIS WORK The major objective of this paper is to evaluate suppliers in a corporate environment using Fuzzy Inference system and to develop a software model using MatLab software which will accept the input values as input parameters such as primary criteria like source of material, manufacturing facility, turnover, income tax clearance and final criteria like price, performance, quality, delivery schedule and returns the output values through output parameter, overall ranking of different supplier and the maximum overall ranking value can be picked, which will enable us to identify the most effective supplier. 4. FUZZY INFERENCE SYSTEM Fuzzy inference is the process of formulating the mapping from a given input to an output using fuzzy logic. The mapping then provides a basis from which decisions can be made, or patterns discerned. The process of fuzzy inference involves all of the pieces that are described in the previous sections: Membership Functions, Logical Operations, and If-Then Rules. IT can implement two types of fuzzy inference systems in the toolbox: FIS have been successfully applied in fields such as automatic control, data classification, decision analysis, expert systems, and 4

5 Supplier Selection using Fuzzy Interface System computer vision. Because of its multidisciplinary nature, FIS are associated with a number of names, such as fuzzy-rule-based systems, fuzzy expert systems, fuzzy modeling, fuzzy associative memory, fuzzy logic controllers, and simply fuzzy systems The Fuzzy Inference Diagram The fuzzy inference system consists of main five steps. They are Fuzzifier, Rule base, Fuzzy inference engine, Defizzifier and output quantity. The fuzzy inference system in shown by a simple diagram in Figure 1. Figure 1: Block Diagram of FIS In this figure, the flow proceeds up from the inputs in the lower left, then across each row, or rule, and then down the rule outputs to finish in the lower right. This compact flow shows everything at once, from linguistic variable fuzzification all the way through defuzzification of the aggregate output. The Figure 2 shows the actual full-size fuzzy inference diagram. There is a lot to see in a fuzzy inference diagram For instance, from this diagram with these particular inputs, it is understand that the implication method is truncation with the min function. The max function is being used for the fuzzy OR operation. Rule 3 (the bottom- 5

6 C. Elanchezhian B. Vijaya Ramnath & R. Kesavan most row in the diagram shown previously) is having the strongest influence on the output. and so on. The Rule Viewer described in The Rule Viewer is a MATLAB implementation of the fuzzy inference diagram is shown in Figure 2. Dinner for Two a 2 input, 1 output, 3 rule system Input 1 Service (0-10) Input 2 Food (0-10) Rule 1 If service is poor or food as rancid, then 6p is cheap. Rule 2 If service is good, then 6p is average. Rule 3 If service is excellent or food is delicious. then 6p is generous. Output Tip (5-25%) The inputs are crisp (non-fuzzy) numbers limited to a specific range. All rules are evaluated in parallel using fuzzy reasoning. The results of the rules are combined and distilled (defuzzified). The result is a crisp (nonfuzzy) number. Figure 2: Block Diagram of Rule Based FIS In Figure 2 it is stated that fuzzy inference system consisting of five steps. The input value (crips value) to be fired in the system and that will be converted in the form of output by the following mentioned steps. Step 1. Fuzzify Inputs The first step is to take the inputs and determine the degree to which they belong to each of the appropriate fuzzy sets via membership functions. In Fuzzy Logic Toolbox software, the input is always a crisp numerical value limited to the universe of discourse of the input variable (in this case the interval between 0 and 10) and the output is a fuzzy degree of membership in the qualifying linguistic set (always the interval between 0 and 1). Fuzzification of the input amounts to either a table lookup or a function evaluation. 6

7 Supplier Selection using Fuzzy Interface System Step 2. Apply Fuzzy Operator After the inputs are fuzzified, you know the degree to which each part of the antecedent is satisfied for each rule. If the antecedent of a given rule has more than one part, the fuzzy operator is applied to obtain one number that represents the result of the antecedent for that rule. This number is then applied to the output function. The input to the fuzzy operator is two or more membership values from fuzzified input variables. The output is a single truth value. Step 3. Apply Implication Method Before applying the implication method, you must determine the rule s weight. Every rule has a weight (a number between 0 and 1), which is applied to the number given by the antecedent. Generally, this weight is 1 (as it is for this example) and thus has no effect at all on the implication process. From time to time you may want to weight one rule relative to the others by changing its weight value to something other than 1. Step 4. Aggregate All Outputs Because decisions are based on the testing of all of the rules in a FIS, the rules must be combined in some manner in order to make a decision. Aggregation is the process by which the fuzzy sets that represent the outputs of each rule are combined into a single fuzzy set. Aggregation only occurs once for each output variable, just prior to the fifth and final step, defuzzification. The input of the aggregation process is the list of truncated output functions returned by the implication process for each rule. The output of the aggregation process is one fuzzy set for each output variable. Step 5. Defuzzify The input for the defuzzification process is a fuzzy set (the aggregate output fuzzy set) and the output is a single number. As much as fuzziness helps the rule evaluation during the intermediate steps, the final desired output for each variable is generally a single number. However, the aggregate of a fuzzy set encompasses a range 7

8 C. Elanchezhian B. Vijaya Ramnath & R. Kesavan of output values, and so must be defuzzified in order to resolve a single output value from the set Application of Fuzzy Inference System The fuzzy inference system is a flexible decision making tool which is applicable in the following system. Control Systems The fuzzy inference system is applicable for concept of map, traffic control system, Self adjusting washing machines (size of wash adjusts amount of detergent, water temperature, wash cycle, TV adjusts sharpness, brightness, color, contrast Elevators for controlling elevators for peak and slack times etc. Decision Systems For the case of decision making it is applicable in Bank decision support system for securities trading, New product pricing, Credit granting, How to allocate resources to an enterprise s paper pool, What constitutes safety and suitability in an investment portfolio and Share market Fuzzy Set Theory The premise of fuzzy modeling is that an uncertainty approach is more consistent with human information processing, because humans have an ability to analyze imprecise concepts. This imprecise knowledge is essential to human-cognitive processes and it is effectively modeled through the use of linguistic values and degrees of membership in fuzzy set theory. To understand the mathematical definition of fuzzy sets, consider a finite set of objects X. The finite set is described as: X = x1, x2, x3,..., xn. where xi are the elements in the set X. Each element xi has a membership value (u), which represents its grade of membership in a fuzzy set. The set of membership values associated with the fuzzy set occur along the continuous [0, 1]; the interval over a fuzzy 8

9 Supplier Selection using Fuzzy Interface System set applies. A fuzzy set A can be represented as a linear combination of the following form: A = u1(x1), u2(x2), u3(x3),..., un(xn) A fuzzy set can be expressed as a vector, a table, or a standard function whose parameters can be adjusted to fit a given system. The nature of fuzzy set theory makes it useful for handling a variety of imprecise or inexact The Fuzzy Rule Base consists of fuzzy if then (also called Antecedent-Consequence ) rules which are generated based on the concept of the dominant rule of a data sample. Exemplifying, assume we have a rule. Conditions. if x1 is A and x2 is B, then y is C. where x1 and x2 are variables, y is a solution variable, and A, B, and C are fuzzy terms. For a data sample, if its belief value for variable x1 in fuzzy term A is larger than the belief value for x1 in any other fuzzy terms, and its belief for value variable x2 in fuzzy term B is larger than its belief value for x2 in any other fuzzy terms, then the fuzzy rule is called the dominant rule of the data sample. The Fuzzy Inference Engine takes all possible combinations of the previously determined fuzzy sets, compares them with the fuzzy rule base, and assigns to each combination the corresponding fuzzy region of influence. The Defuzzifier uses all information about the input and output fuzzy sets and determines, using the information in terms of fuzzy sets, a numerical output value. Several defuzzification strategies exist, but the methodology use in this paper is mom (Mean of Maximum the average of the maximum Membership Function A membership function (MF) is a curve that defines how each point in the input space is mapped to a membership value (or degree of membership) between 0 and 1. The input space is sometimes referred to as the universe of discourse, a fancy name for a simple concept. The only condition a MF must really satisfy is that it must vary between 0 and 1. The function itself can be an arbitrary curve whose 9

10 C. Elanchezhian B. Vijaya Ramnath & R. Kesavan shape we can define as a function that suits us from the point of view of simplicity, convenience, speed, and efficiency. A classical set might be expressed as A = {x x > 6}. A fuzzy set is an extension of a classical set. If X is the universe of discourse and its elements are denoted by x, then a fuzzy set A in X is defined as a set of ordered pairs. A = {x, µa(x) x X}. The general form of a membership function is in Figure 3. Figure 3: General form of Membership Function The simplest membership functions are formed using straight lines. Of these, the simplest is the triangular membership function, and it has the function name trim. It is nothing more than a collection of three points forming a triangle. The trapezoidal membership function has a flat top and really is just a truncated triangle curve. These straight line membership functions have the advantage of simplicity. The two type used membership function are shown in Fig 4 and Fig 5. Figure 4: Triangular MF 10

11 Supplier Selection using Fuzzy Interface System Figure 5: Trapezoidal MF 5. MATLAB SOFTWARE MATLAB is a numerical computing environment and programming language. Created by The MathWorks, MATLAB allows easy matrix manipulation, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs in other languages. Although it is numeric only, an optional toolbox uses the MuPAD symbolic engine, allowing access to computer algebra capabilities. 6. METHODOLOGY To maximize performance of supply chains, companies must ensure that they have an actualized picture of suppliers and demand issues. They must ensure the efficient, timely, and cost-effective procurement of goods, starting at the product integration stage. We also noted in the Factors and models for supplier selection section that there were too many variables to cope with, most of which not suited for quantifcation. Therefore, fuzzy logic concepts could better represents the cognitive processes of the specialists Supplier Selection Process The supplier selection is a complex process which is required to follow the following steps: 11

12 C. Elanchezhian B. Vijaya Ramnath & R. Kesavan Formalize the Process is one of the techniques in supplier selection process. The product and vendor review process must be formalized. To be thorough and fair, the requirements need to be identified for the tooling and the vendor. There should be a formal request for proposal or at least a checklist by which evaluations are performed so the various prospective solutions can be understood, documented and reviewed. Identify the Stakeholders is necessary in supplier selection process. The correct stakeholders need to be identified and involved in the tool selection process. All too often purchases are done in a vacuum without the involvement of all stakeholders and thus only a partial set of requirements are identified Supplier Selection Criteria The block diagram of supplier selection criteria are shown in Fig 6. Figure 6: Block Diagram of Supplier Selection Criteria 12

13 Supplier Selection using Fuzzy Interface System 6.3. Supplier Selection Preliminary Criteria The preliminary criteria for supplier selection process are listed below. General Information Financial Status Sales Tax & Income Tax Clearance Organization structure Approval from Consultants Past Records Available product quality Product Development Activity Manufacturing Facilities Experience, knowledge and capability of production Technical collaboration Adequacy of plant & machineries Raw Material Source Storage of material Material handling Facilities Quality Control Management Experience, knowledge and capability of QC manager Availability of suitable measurement tool Calibration of measuring tools System of written down work/qc instruction Raw material identification and issue procedure Acceptance and rejection record System for control of non conforming product. 13

14 C. Elanchezhian B. Vijaya Ramnath & R. Kesavan 6.4. Supplier Selection Method A large number of methods using quality, quantity, price, and delivery schedule and service factor has been developed for the purpose of rating the supplier. The weightages vary from item to item depending upon cost criticality, availability of the item and market conditions of demand of supply. In this context, the Indian Institute of Technology at Madras has complied a supplier rating index using 300 parameters to assess the supplier performance. Several supplier selection methods are available as follows. Weighted Point Plan is quantified to the above method points allocated for quality, delivery and price. The nos of factors and points can be altered to suit individual products. An addition of weighted average of the performance parameters is known as weighted point plan. Categorical Method depends primarily on the experience and judgment of the buyer and hence this is my subjective. The buyer makes out a list of all relevant parameters and annual performance. Cost Ratio method system involves computing the actual cost incurred in procurement, cashing transportation, packaging etc. costs relating to quality may include factory visit, approval of samples inspection. Key Questions Approach involves many questions, what, where, how, why, when, what for and who are asked about the item in this method. When these questions are answered, subsidiary question arise. This question should include issues on management, labour etc. Table 1 Various Data About Suppliers Supplier-A Supplier-B Supplier-C Supplier-D Price (Rs) Quality Average Standard Below Above Average Average Service Good Normal Good Excellent Delivery 5 months 6 months 4 months 7 months 14

15 Supplier Selection using Fuzzy Interface System From the above data the best supplier shall be selected as per customer requirement. The proposed inference system applies triangular and trapezoidal membership functions to define the shape of both input and output variables. The values of the are drawn for each value of the inputs from x1 to x4. Analyzing vector a, we have four tangible input parameters (x1, x2, x3, x4) and an output, defined as follows: Price (x 1 ): This aspect of the evaluation refers to the cost of the product which can be supplied to manufacturer. It is evaluated as low, medium, or high than the mean industry level in the same commodity. Quality Level (x 2 ): This is the actual rejection rate of defective incoming material detected by the customer s Incoming Quality and Production Departments. The characteristic is defined in comparison with the average in the industry as below average, average, above average, and standard in class depending on customer s perception. Service (x 3 ): it is important for the customer to have servicing facility of the product. After purchasing the product, if the customer faces any difficulties, the supplier should rectify the problem. Service can be divided into three categories depending on its own performance: poor, average, and good when customer expectations. Delivery Rate ( x 4 ): it is the supplier s compliance with the predetermined order quantity, mix, and delivery dates to support customer s production requirements. MF can be divided into three categories depending on its own performance: poor, average, and good when customer expectations have been completely achieved Fuzzy Inference System Model It shows that input variables Price (x 1 ), Quality (x 2 ), Delivery schedule (x 3 ) and Service (x 4 ) which shall be used as input in inference system and the out put shall be a numerical value of all the input as supplier selection rating. The fuzzy inference model for the above example is shown in Figure 7. 15

16 C. Elanchezhian B. Vijaya Ramnath & R. Kesavan Figure 7: Fuzzy Inference System Model Price (x 1 ): This aspect of the evaluation refers to the cost of the product which can be supplied to manufacturer. It is evaluated as low, medium, or high than the mean industry level in the same commodity. The category has been created as follows and membership function is shown in Figure 8. Low = Less than Rs 1500 Medium = Between Rs 1300 & 1700 High = Rs 1500 and above Trapezoidal membership function Triangular membership function Trapezoidal membership function Figure 8: Price Membership Function Quality Level (x 2 ): This is the actual rejection rate of defective incoming material detected by the customer s Incoming Quality and Production Departments. The classification are in comparison with the average in the industry as below average, average, above average, and standard in class depending on customer s perception and membership function is shown in Figure 9. 16

17 Supplier Selection using Fuzzy Interface System Below average = Less than 40 point Average = between 30 to 50 Above Average = Between 45 to 65 Standard = Above 55 point Trapezoidal membership function Triangular membership function Triangular membership function Trapezoidal membership function Figure 9: Quality Membership Function Delivery Rate ( x 4 ): it is the supplier s compliance with the predetermined order quantity, mix, and delivery dates to support customer s production requirements. Figure 6.4 shows that the evaluation of the company can be divided into three categories depending on its own performance: poor, average, and good when customer expectations have been completely achieved as in Figure 10. Good = Less than 5 months Average = Between 4 to 7 month Poor = Above 6 month Trapezoidal membership function Triangular membership function Trapezoidal membership function Figure 10: Delivery Membership Function 17

18 C. Elanchezhian B. Vijaya Ramnath & R. Kesavan If-Then Rules for Above criteria If-Then Rules are created for the above criteria and the has been written in fuzzy toolbox as shown in Figure 10. (a) If Price low, quality below average, delivery poor and service poor then rejected. (b) If Price low, quality below average, delivery poor and service average then rejected. (c) If Price low, quality below average, delivery poor and service good then rejected. (d) If Price low, quality average, delivery poor and service good then rejected and So on. 7. RESULT AND DISCUSSION Fuzzy Inference Systems are employed in domains where decision makers must repeatedly have to make decisions, especially in complex situations. These systems must be judged on the basis of its ability to infer, from a set of given inputs, the same output a specialist would provide in any situation. Following this concept we have tested the reliability of the constructed FIS system, through a series of simulations, varying the value of one or several inputs simultaneously. Using the FIS Editor software from Matlab (Graphical User Interface) it constructed the commands to easily test the fuzzy system developed, observe its performance, and validate the model. As it can be seen in output graph that each variable allows the user to individually select from a range of values. The default value in each case is zero and the input changes when the scroll bar arrows are clicked. With the FIS model, it defined, the final stage was to implement these functions and made several evaluations. The input values for individual vendor s are fired in the constructed fuzzy inference system and the out of the individual vendors are shown in the form of graph. At the same time the composite rating of the individual supplier are also coming out at output. Finally the output rating of the supplier to be compared each other and the supplier shall be ranked from maximum rating to minimum rating. 18

19 Supplier Selection using Fuzzy Interface System The input values and composite score of Supplier-A is shown Figure 11. Input Variables of Supplier-A: Price: Rs 1286 Quality: Service: 50 Delivery: Output points of Supplier-A: Point 88.6 Result: Supplier-A is Selected 55 points 5 months Figure 11: Overall Rating of Supplier-A The input values and composite score of Supplier-B is shown Figure 12. Input Variables of Supplier-B: Price: Rs Quality: Service: 60 Delivery: Output points of Supplier-B: Point points 6 months

20 C. Elanchezhian B. Vijaya Ramnath & R. Kesavan Result: Supplier-B is Choice-1 Figure 12: Overall Rating of Supplier-B The input values and composite score of Supplier-C is shown Figure 13. Input Variables of Supplier-C: Price: Rs 1375 Quality: Service: 65 Delivery: Output points of Supplier-C: Point 70 Result: Supplier-C is Rejected 30 points 4 months Finally, from the above example it is concluded that the overall rating of the suppliers-a, B & C are 88.6, 87.7 and 70 respectively. Hence supplier-a is selected, Supplier-B is under consideration and Supplier-C is rejected. 20

21 Supplier Selection using Fuzzy Interface System Figure 13: Overall Rating of Supplier-C 8. CONCLUSION This paper has illustrated a modular Fuzzy Inference System for supplier selection. It has been also observed that fuzzy set theory can be applied to most of the traditional areas of production research using a language to model problems, which contain fuzzy relationships. Fuzzy set theory provides a proper language by which indefinite and imprecise factors can be handled and it is able to integrate qualitative and quantitative analysis with any type of numerical variable or input. The structures of fuzzy systems are often simple and more realistic than non-fuzzy models. In this report specific application of the fuzzy inference theory and modular approach that can help companies to make decisions about supplier selection. The methodology demonstrates that it can be easily translated to model the decision-making process of facilities and service purchases within the company. Additionally, it can be used for supplier benchmark studies, negotiation process, supply 21

22 C. Elanchezhian B. Vijaya Ramnath & R. Kesavan chain improvement, supplier performance feedback, metrics development, supplier rankings development, allocation of order quantities, and so on. Purchasing managers and buyers can have a better idea of their supply base characteristics, and also can compare any supplier to any other supplier during quotation. A strategic commitment from suppliers is a vital determinant of business success which helps directly and indirectly to improve companies performances and this model is beneficial as it incorporates strategic and operational measurements at the same time. REFERENCES Barbarosoglu. G, Yazgac T., An Application of the Analytic Hierarchy Process to the Supplier Selection Problem, Production and Inventory Management Journal, 1997, 38(1): Ding-zhong Feng, The Determinants of Vendor Selection: The Evaluation Function Approach, Journal of Purchasing and Materials Management, 2001, 4(3), pp Feng Dingzhong, Chen Leilei, Jiang Meixian, Vendor Selection in Supply Chain System: An Approach using Fuzzy Decision and AHP, In: International Conference on Services Systems and Services Management, Beijing, China, 2005, 5: pp Guiffrida, A., & Nagi, R., Fuzzy Set Theory Applications in Production Management Research: A Literature Survey, Journal of Intelligent Manufacturing, 1998, 9, pp Holland J. Adaptation, In Natural and Artificial Systems, Ann Arbor, USA: University of Michigan Press, 1995, pp Kasilingam R G, Lee C P., Selection of Vendors A Mixed-Integer Programming Approach, Computers & Industrial Engineering, 1996, 31(1): pp Kumar M, Vrat P., A Fuzzy Goal Programming Approach for Vendor Selection Problem in a Supply Chain, Computer & Industrial Engineering, 2004, 46(1): pp Kannan, V., & Tan, K., Supplier Selection and Assessment: Their Impact on Business Performance, The Journal of Supply Chain Management, 2002, 38 pp-4. Liu Baoding, Liu Yankui., Expected Value of Fuzzy Variable and Fuzzy Expected Value Model, IEEE Transactions on Fuzzy Systems, 2002, 10(4): pp Liu Baoding, Iwammura K., Chance Constrained Programming with Fuzzy Parameters, Fuzzy Sets and Systems, 1998, 94(2): pp

23 Supplier Selection using Fuzzy Interface System Li Xiang, Liu Baoding., A Sufficient and Necessary Condition for Credibility Measures, International Journal of Uncertainty, Fuzziness & Knowledge-Based Systems, 2006, 14(5): pp McCauley-Bell, P., Intelligent Agent Characterization and Uncertainty Management with Fuzzy Set Theory: A Tool to Support Early Supplier Integration, Journal of Intelligent Manufacturing, 1999, 10, pp Pan A., Allocation of Order Quantities Among Suppliers, Journal of Purchasing and Materials Management, 1997, 25(3): pp 36-39, Sarkis, J., & Talluri, S., A Model for Strategic Supplier Selection, Proceedings of the Third Worldwide Research Symposium on Purchasing and Supply Chain Management, Canada, 2001, 14(5): pp Sound and Vision Engineering Department, Gdansk University of Technology, (2006), Fundamentals of Fuzzy-Sets and Fuzzy-Reasoning. Talluri S., A Buyer-Seller Game Model for Selection and Negotiation of Purchasing Bids, European Journal of Operational Research, 2002, 143(1):