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A computational method for normalization of Trapezoidal Fuzzy Numbers

Authors: G. Mahender Reddy; Sameena Afreen; V. Shyam Prasad; Abdul Majeed;

A computational method for normalization of Trapezoidal Fuzzy Numbers

Abstract

{"references": ["Abhinav Bansal, Trapezoidal Fuzzy Numbers (a, b, c, d): Arithmetic Behavior, International Journal of Physical and Mathematical Sciences, International Journal of Physical and Mathematical Sciences, Vol. No. 2, 2011, pp. 39-44", "Buckley. J. J.,1985a, Ranking Alternatives using Fuzzy Numbers, Fuzzy Sets and Systems, Vol. 15, pp. 21-31.", "Buckley. J. J., Fuzzy Hierarchical Analysis, Fuzzy Sets and Systems, Vol. 15, 1985b, pp. 233-242", "C.Carlsson and R. Fuller, Fuzzy Multi criteria Decision Making: Recent Developments, Fuzzy Sets and Systems, Vol. No. 78, 1996, pp. 139-153.", "D.-Y. Chang, Applications of Extent Analysis method On Fuzzy AHP, European Journal of Operational Research 95 , 1996, 649-655.", "D. Dubois and H. Prade, The use of Fuzzy Numbers in Decision Analysis, Fuzzy information and Decision Process, 1982, pp. 309-321.", "Evangelos Triantaphyllou and Stuart H. Mann, \"Using the analytic Hierarchy Process for decision making in engineering applications\", International Journal of Industrial engineering:Applications and Practice, Vol.2, No.1, 1995, pp 35-44.", "Fathema G and Lewis W, A case study comparison of the Analytical Hierarchy Process and a Fuzzy Decision Methodology, The Engineering Economist, Vol. No.40, No. 3, 1995, pp. 233-246.", "Laarhoven, P. J. M. and W. Pedrycz, A fuzzy extension of Saaty's priority theory, Fuzzy Sets and Systems, Vol. 11, 1983, pp. 229-241.", "Liang G. S. and Wang M. J. J., A Fuzzy Multi Criteria Decision-Making Method for Facility Site Selection, International Journal of Production Research, Vol. No.29, No.11, 1991, pp. 2313-2330."]}

In multi criteria decision making, if the judgments are expressed as fuzzy numbers, the normalization process is necessary in obtaining the rank of alternatives. Extent analysis method on Fuzzy Analytical Hierarchy Process is a popular decision making method introduced by D.Y. Chang(1996). This method was applied on various applications to obtain the rank of alternatives. The normalization method is to normalize Triangular Fuzzy Numbers, it has some flaws according to Wang and Elhag (2006). This paper presents the modified extent analysis method with accurate normalization procedure and an extent analysis method was introduced to find the weights of alternatives when the judgments are provided as Trapezoidal Fuzzy Numbers.

Keywords

Analytical Hierarchy Process, Fuzzy Analytical Hierarchy Process, Extent Analysis Method, Trapezoidal Fuzzy Numbers.

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This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
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