Abstract
Allowing various forms of fuzzy numbers to be adopted in fuzzy multi criteria decision making (FMCDM) problems adds more flexibility to decision makers to represent their own opinions to handle uncertainty. For most cases uncertain numbers of the forms of: interval, triangle, or trapezoidal are used. In this paper, polygon fuzzy numbers (PFNs) are introduced so as to allow decision makers to adopt other forms of numbers such as: pentagon, hexagon, heptagon, octagon, etc, to provide more flexibility to represent uncertainty. A case study is given to illustrate the way of manipulation of the proposed PFN.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Hong, D.H.: Strong laws of large numbers for t-norm-based addition of fuzzy set-valued random variables. Fuzzy Sets and Systems 223, 449–728 (2013)
Chen, S.-M., Wang, C.-Y.: Fuzzy decision making systems based on interval type-2 fuzzy sets. Applied Mathematical Modeling Science Direct 424, 1–21 (2013)
Herrera, F., Herrera-Viedma, E.: Spain Linguistic decision analysis: steps for solving decision problems under linguistic information. Computer Science and Artificial Intelligence 115, 67–82 (2000)
Chen, S.-J., Chen, S.-M.: Fuzzy Risk Analysis Based on Similarity Measures of Generalized Fuzzy Numbers. IEEE Transaction on Fuzzy Systems 11(1), 45–56 (2003)
Yong, D., Wenkang, S., Feng, D., Qi, L.: A new similarity measure of generalized fuzzy numbers and its application to pattern recognition. Pattern Recognition Letters 25, 875–883 (2004)
Chen, S.-M., Chen, J.-H.: Fuzzy risk analysis based on ranking generalized fuzzy numbers with different heights and different spreads. Expert Systems with Applications 36, 6833–6842 (2009)
Sun, C.-C.: A performance evaluation model by integrating fuzzy AHP and fuzzy TOPSIS methods. Expert Systems with Applications 37, 7745–7754 (2010)
Anisseh, M., Piri, F., Shahraki, M.R., Agamohamadi, F.: Fuzzy extension of TOPSIS model for group decision making under multiple criteria 38(4), 325–338 (2011)
Roghanian, E., Rahimi, J., Ansari, A.: Comparison of first aggregation and last aggregation in fuzzy group TOPSIS. Applied Mathematical Modelling 34, 3754–3766 (2010)
Chang, Y.-C., Chen, S.-M., Liau, C.-J.: Fuzzy Interpolative Reasoning for Sparse Fuzzy-Rule-Based Systems Based on the Areas of Fuzzy Sets. IEEE Transaction on Fuzzy Systems 16(5), 1285–1301 (2008)
Cheng, C.H.: A new approach for ranking fuzzy numbers by distance method. Fuzzy Sets and Systems 95, 307–317 (1998)
Wang, Y.M., Yang, J.B., Xu, D.L., Chin, K.S.: On the centroids of fuzzy numbers. Fuzzy Sets and Systems 157, 919–926 (2006)
Hassanien, A.E., Suraj, Z., Slezak, D., Lingras, P.: Rough computing: Theories, technologies and applications. IGI Publishing Hershey, PA (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Bekheet, S., Mohammed, A., Hefny, H.A. (2014). A Generalized Polygon Fuzzy Number for Fuzzy Multi Criteria Decision Making. In: Hassanien, A.E., Tolba, M.F., Taher Azar, A. (eds) Advanced Machine Learning Technologies and Applications. AMLTA 2014. Communications in Computer and Information Science, vol 488. Springer, Cham. https://doi.org/10.1007/978-3-319-13461-1_39
Download citation
DOI: https://doi.org/10.1007/978-3-319-13461-1_39
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-13460-4
Online ISBN: 978-3-319-13461-1
eBook Packages: Computer ScienceComputer Science (R0)