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Fuzzy random regression based multi-attribute evaluation and its application to oil palm fruit grading

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Abstract

Multi-attribute decision-making is usually concerned with weighting alternatives, thereby requiring weight information for decision attributes from a decision maker. However, the assignment of an attribute’s weight is sometimes difficult, and may vary from one decision maker to another. Additionally, imprecision and vagueness may affect each judgment in the decision-making process. That is, in a real application, various statistical data may be imprecise or linguistically as well as numerically vague. Given this coexistence of random and fuzzy information, the data cannot be adequately treated by simply using the formalism of random variables. To address this problem, fuzzy random variables are introduced as an integral component of regression models. Thus, in this paper, we proposed a fuzzy random multi-attribute evaluation model with confidence intervals using expectations and variances of fuzzy random variables. The proposed model is applied to oil palm fruit grading, as the quality inspection process for fruits requires a method to ensure product quality. We include simulation results and highlight the advantage of the proposed method in handling the existence of fuzzy random information.

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References

  • Abbas, Z., Yeow, Y. K., Shaari, A. H., Khalid, K., Hassan, J., & Saion, E. (2005). Complex permittivity and moisture measurements of oil palm fruits using an open-ended coaxial sensor. IEEE Sensors Journal, 5(6), 1281–1287.

    Article  Google Scholar 

  • Abdullah, M. Z., Guan, L. C., & Karim, A. A. (2004). The applications of computer vision system and tomographic radar imaging for assessing physical properties of food. Journal of Food Engineering, 61(1), 125–135.

    Article  Google Scholar 

  • Abdullah, M. Z., Guan, L. C., & Mohd Azemi, B. M. N. (2001). Stepwise discriminant analysis for colour grading of oil palm using machine vision system. Transactions of the Institution of Chemical Engineers, 79(C), 223–231.

    Google Scholar 

  • Alfatni, M. S. M., Shariff, A. R. M., Shafri, H. Z. M., Saaed, O. B., & Eshanta, O. M. (2008). Oil palm fruit bunch grading system using red, green, and blue digital number. Journal of Applied Sciences, 8(8), 1444–1452.

    Article  Google Scholar 

  • Basiron, Y. (2007). Palm oil production through sustainable plantations. European Journal of Lipid Science and Technology, 109(4), 289–295.

    Article  Google Scholar 

  • Basiron, Y., & Chan, K. W. (2004). The oil palm and its sustainability. Journal of Palm Oil Research, 16(1), 1–10.

    Google Scholar 

  • Bellman, R. E., & Zadeh, L. A. (1970). Decision making in a fuzzy environment. Management Science, 17B(4), 141–164.

    Article  Google Scholar 

  • Brans, J. P., Vincke, Ph., & Mareschal, B. (1986). How to rank and how to select projects: the PROMETHEE method. Journal of Operational Research, 24(2), 228–238.

    Article  Google Scholar 

  • Cardoso, D. M., & de Sousa, J. F. (2005). A Multi-attribute ranking solutions confirmation procedure. Annals of Operations Research, 138(1), 127–141.

    Article  Google Scholar 

  • Ismail, A., Simeh, M. A., & Noor, M. M. (2003). The production cost of oil palm fresh fruit bunches: the case of independent smallholders in Johor. Oil Palm Industry Economic Journal, 3(1), 1–7.

    Google Scholar 

  • Jalani, B. S., Yusof, B., Ariffin, D., Chan, K. W., & Rajanaidu, N. (2002). Prospects of elevating national oil palm productivity: a Malaysian perspective. Oil Palm Industry Economic Journal, 2(2), 1–9.

    Google Scholar 

  • Katagiri, H., & Sakawa, M. (2003). A study on fuzzy random linear programming problems based on possibility and necessity measure. In T. Bilgic, B. D. Baets, & O. Kaynak (Eds.), Lecture notes in computer science. Fuzzy sets and systems—IFSA 2003 (pp. 725–732). Berlin: Springer.

    Chapter  Google Scholar 

  • Keeney, R. L., & Raiffa, H. (1976). Decisions with multi-objectives. New York: Wiley.

    Google Scholar 

  • Kwakernaak, H. (1978). Fuzzy random variables-I. Definitions and theorems. Information Sciences, 15(1), 1–29.

    Article  Google Scholar 

  • Kwakernaak, H. (1979). Fuzzy random variables-II. Algorithm and examples. Information Sciences, 17(3), 253–278.

    Article  Google Scholar 

  • Li, D.-F., & Sun, T. (2007). Fuzzy linear programming approach to multi-attribute decision-making with linguistic variables and incomplete information. Advances in Complex Systems (ACS), 10(4), 505–525.

    Article  Google Scholar 

  • Li, Y., Chen, S., & Nie, X. (2005). Fuzzy pattern recognition approach to construction contractor selection export. Fuzzy Optimization and Decision Making, 4(2), 103–118.

    Article  Google Scholar 

  • Liu, B., & Liu, Y.-K. (2002). Expected value of fuzzy variable and fuzzy expected value models. IEEE Transactions on Fuzzy Systems, 10(4), 445–450.

    Article  Google Scholar 

  • Liu, Y.-K., & Liu, B. (2003). Fuzzy random variable: a scalar expected value operator. Fuzzy Optimization and Decision Making, 2(2), 143–160.

    Article  Google Scholar 

  • Lu, I.-Y., Chen, C.-B., & Wang, C.-H. (2007). Fuzzy multi-attribute analysis for evaluating firm technological innovation capability. International Journal of Technology Management, 40(1–3), 114–130.

    Article  Google Scholar 

  • Malczewski, J. (1997). Propagation of errors in multicriteria location analysis: a case study. Multiple criteria decision making. In G. Fandel & T. Gal (Eds.), Proc. of the twelfth international conference (pp. 154–165), Hagen (Germany), 1995. Berlin: Springer.

    Google Scholar 

  • Mavrotas, G., Diakoulaki, D., & Capros, P. (2003). Combined MCDA–IP approach for project selection in the electricity market. Annals of Operations Research, 120(1-4), 159–170.

    Article  Google Scholar 

  • Ming, K.K., & Chandramohan, D. (2002). Malaysian palm oil industry at crossroads and its future direction. Kuala Lumpur: Malaysian Palm Oil Board Publisher.

    Google Scholar 

  • MPOB (2003). Oil palm fruit grading manual (2nd edn.). Malaysia: Malaysian Palm Oil Board Publisher.

    Google Scholar 

  • Nahmias, S. (1978). Fuzzy variables. Fuzzy Sets and Systems, 1(2), 97–111.

    Article  Google Scholar 

  • Nguyen, H. T. (1978). A note on the extension principle for fuzzy sets. Journal of Mathematical Analysis and Applications, 64(2), 369–380.

    Article  Google Scholar 

  • Nureize, A., & Suradi, Z. (2007). Staff performance appraisal using fuzzy evaluation. In C. Boukis, L. Pnevmatikakis, & L. Polymenakos (Eds.), Artificial intelligence and innovations 2007: from theory to applications: Vol. 247. IFIP international federation for information processing (pp. 195–203). Boston: Springer.

    Google Scholar 

  • Nureize, A., & Watada, J. (2010). A fuzzy regression approach to hierarchical evaluation model for oil palm grading. Fuzzy Optimization Decision Making, 9(1), 105–122.

    Article  Google Scholar 

  • Ogryczak, W. (2000). Multiple criteria linear programming model for portfolio selection. Annals of Operations Research, 97(1), 143–162.

    Article  Google Scholar 

  • Roy, B. (1968). Classement et choix en présence de points de vue multiples (la méthode ELECTRE). la Revue d’Informatique et de Recherche Opérationelle (RIRO), 8, 57–75.

    Google Scholar 

  • Ribeiro, R. A. (1996). Fuzzy multiple attribute decision making: a review and new preference elicitation techniques. Fuzzy Sets and Systems, 78(2), 155–181.

    Article  Google Scholar 

  • Saaty, T. L. (1980). The analytic hierarchy process. New York: McGraw-Hill.

    Google Scholar 

  • Tanaka, H., Hayashi, I., & Watada, J. (1989). Possibilistic linear regression for fuzzy data. European Journal of Operational Research, 40(3), 389–396.

    Article  Google Scholar 

  • Tanaka, H., Uejima, S., & Asai, K. (1982). Linear regression analysis with fuzzy model. IEEE Transactions on Systems, Man and Cybernetics SMC, 12(6), 903–907.

    Article  Google Scholar 

  • Tavana, M., Sodenkamp, M. A., & Suhl, L. (2010). A soft multi-criteria decision analysis model with application to the European Union enlargement. Annals of Operations Research, 181(1), 393–421.

    Article  Google Scholar 

  • Watada, J., & Tanaka, H. (1987). Fuzzy quantification methods. In Proceedings, the 2nd IFSA congress (pp. 66–69), Tokyo.

    Google Scholar 

  • Watada, J. (1994). Applications in business; multi-attribute decision making. In T. Terano, K. Asai, & M. Sugeno (Eds.), Applied fuzzy system. AP professional (pp. 244–252).

    Google Scholar 

  • Watada, J. (1996). Possibilistic time-series analysis and its analysis of consumption. In D. Dubois & M. M. Yager (Eds.), Fuzzy information engineering (pp. 187–200). New York: Wiley.

    Google Scholar 

  • Watada, J., & Toyoura, Y. (2002). Formulation of fuzzy switching auto-regression model. International Journal of Chaos Theory and Applications, 7(1–2), 67–76.

    Google Scholar 

  • Watada, J., Wang, S., & Pedrycz, W. (2009). Building confidence-interval-based fuzzy random regression model. IEEE Transactions on Fuzzy Systems, 17(6), 1273–1283.

    Article  Google Scholar 

  • Yager, R. (1988). On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Transactions on Systems, Man, and Cybernetics, 18(1), 183–190.

    Article  Google Scholar 

  • Zadeh, L. A. (1975a). The concept of a linguistic variable and its application to approximate reasoning-I. Information Sciences, 8(3), 199–249.

    Article  Google Scholar 

  • Zadeh, L. A. (1975b). The concept of a linguistic variable and its application to approximate reasoning-II. Information Sciences, 8(4), 301–357.

    Article  Google Scholar 

  • Zadeh, L. A. (1975c). The concept of a linguistic variable and its application to approximate reasoning-III. Information Sciences, 9(1), 43–80.

    Article  Google Scholar 

  • Zimmermann, H.-J. (1985). Fuzzy sets theory and its application. Norwell: Kluwer, pp. 49–60.

    Book  Google Scholar 

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Authors and Affiliations

  1. Graduate School of Information, Production and Systems, Waseda University, 2-7 Hibikino, Wakamatsu, Kitakyushu, 808-0135, Japan

    A. Nureize, J. Watada & S. Wang

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  1. A. Nureize
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  2. J. Watada
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  3. S. Wang
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Correspondence to A. Nureize.

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Nureize, A., Watada, J. & Wang, S. Fuzzy random regression based multi-attribute evaluation and its application to oil palm fruit grading. Ann Oper Res 219, 299–315 (2014). https://doi.org/10.1007/s10479-011-0979-z

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