An Interval Method for Ordering Fuzzy Numbers

• Main Authors: Sung-Wei Chuan, 宋偉銓
• Other Authors: Miin-Shen Yang
• Format: Others
• Language: en_US
• Published: 2000
• Online Access: http://ndltd.ncl.edu.tw/handle/05985883959033039613

碩士 === 中原大學 === 數學系 === 88 === Abstract Since Jain [10] proposed decision-making in the presence of fuzzy variables in 1976, various approaches to ranking fuzzy numbers are studied and applied in substantive areas(see Bortolan [3], Chen [4],Choobineh and Li [7], Kim and Park [12],Liou and Wang [14], Yager [18] etc.)Totally, these methods tend to defuzzify an intrinsically fuzzy rating into a crisp rating.Actually, because the nature of measurement is fuzzy very often,system evaluation in decision science could be made on the basis of fuzzy sets. Jain [10,11] first use fuzzy numbers to assess the decision system based on ranking these fuzzy numbers and making their decisions by decision makers. Now ordering fuzzy numbers play an important role on decision-making in a fuzzy environment. In this thesis, in Section 2 we have literature review. Jain [10,11] first presented decision-making in fuzzy environment on the basis of ranking fuzzy numbers. Then Chen [4] proposed the maximizing set and minimizing set for ranking fuzzy numbers to improve the ranking index of Jain [10,11]. However, the ranking method in Chen [4] is always influenced by x_max and x_min in the maximum and the minimum values of the data set. Therefore, Liou and Wang [14] proposed ranking method of total integral value. In general, Liou's method is better than Chen [4]. But the total integral value is still controlled by a choosen value of parameter. Although free choice of parameter brings flexible elasticity,when the choice value of parameter changes, the ranking results also change according to the choice.However,we do not know where the value is optimal.We propose a new method based on interval ranking.The proposed method will improve the weakness of Liou and Wang [14].The proposed method and its property are presented in Section 3. Finally, some numerical examples and comparisons are made in Section 4. \end{document}