International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No.4, October 2014
TWO NEW OPERATOR DEFINED OVER INTERVAL VALUED INTUITIONISTIC FUZZY SETS S. Sudharsan1, 2 and D. Ezhilmaran3 1
2
Research Scholar, Bharathiar University, Coimbatore -641046, India. Department of Mathematics, C. Abdul Hakeem College of Engineering & Technology, Melvisharam,Vellore – 632 509, Tamilnadu, India. 3 School of Advanced Sciences, VIT University, Vellore – 632 014, Tamilnadu, India.
ABSTRACT IVIFS with and Multiplication of an IVIFS with the natural number ”are proved.
In this paper, two new Operator defined over IVIFSs were introduced, which will be “Multiplication of an
Key Words: Intuitionistic fuzzy set, Interval valued Intuitionistic fuzzy sets, Operations over interval valued intuitionistic fuzzy sets.
AMS CLASSIFICATION: 03E72
1. INTRODUCTION In 1965, Fuzzy sets theory was proposed by L. A. Zadeh[18]. In 1986, the concept of intuitionistic fuzzy sets (IFSs), as a generalization of fuzzy set were introduced by K. Atanassov[1]. After the introduction of IFS, many researchers have shown interest in the IFS theory and applied in numerous fields, such as pattern recognition, machine learning, image processing, decision making and etc... In 1994, new operations defined over the intuitionistic fuzzy sets was proposed by K. Atanassov[3]. In 2000, Some operations on intuitionistic fuzzy sets were proposed by Supriya Kumar De, Ranjit Biswas and Akhil Ranjan Roy[12]. In 2001, an application of intuitionistic fuzzy sets in medical diagnosis were proposed by Supriya Kumar De, Ranjit Biswas and Akhil Ranjan Roy [13]. In 2006, n-extraction operation over intuitionistic fuzzy sets were proposed by B. Riecan and K. Atanassov[9]. In 2010, Operation division by n over intuitionistic fuzzy sets were proposed by B. Riecan and K. Atanassov [10]. In 2010, Remarks on equalities between intuitionistic fuzzy sets was K. Atanassov[4]. In 2008, properties of some IFS operators and operations were proposed by Liu Q, Ma C and Zhou X [7]. In 2008, Four equalities connected with intuitionistic fuzzy sets was proposed by T. Vasilev [14]. In 2011, Intuitionistic fuzzy sets: Some new results were proposed by R. K. Verma and B. D. Sharma[15]. In 1989, the notion of Interval-Valued Intuitionistic Fuzzy Sets which is a generalization of both DOI : 10.5121/ijfls.2014.4401
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