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Issue:Modified ranking of intuitionistic fuzzy numbers

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Title of paper: Modified ranking of intuitionistic fuzzy numbers
Author(s):
V. Lakshmana Gomathi Nayagam
Department of Mathematics, National Institute of Technology, Thiruchirappalli, Tamil Nadu, India
venkateshwari.gandhi@gmail.com
Venkateshwari G.
Department of Mathematics, Sacs MAVMM Engineering College, Madurai, Tamil Nadu, India
Geetha Sivaraman
Department of Mathematics, Periyar Maniammai University, Thanjavur, Tamil Nadu, India
Published in: "Notes on Intuitionistic Fuzzy Sets", Volume 17 (2010) Number 1, pages 5—22
Download:  PDF (240  Kb, File info)
Abstract: The notion of fuzzy subsets was introduced by Zadeh [19] and it was generalised to intuitionistic fuzzy subsets by Atanassov [1]. After the invention of intuitionistic fuzzy subsets, many real life problems are studied accurately. The ranking of intuitionistic number plays a main role in modeling many real life problems involving intuitionistic fuzzy decision making, intuitionistic fuzzy clustering. In this paper, a new method of intuitionistic fuzzy scoring to intuitionistic fuzzy number has been introduced and studied. The significance of the proposed intuitionistic fuzzy scoring method has been discussed. The aim of this paper is to introduce a new technique for clustering based on intuitionistic fuzzy number. The proposed scoring method has been applied to clustering problem where the data collected is in terms of intuitionistic fuzzy linguistic term which is converted into intuitionistic fuzzy number. The intuitionistic fuzzy number is converted to intuitionistic fuzzy scoring using the defined scoring method. A distance measure has been applied to intuitionistic fuzzy score and the similarity measure can be calculated with the help of obtained distance measure. Now we find that the association matrix is tolerance relation. By using the algorithm, the tolerance relation is converted to fuzzy equivalence relation. By fixing alpha cut, the data are clustered in to different groups. The new intuitionistic fuzzy scoring method has wide application in various fields.


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