Multiplicative Type of Operations over Intuitionistic Fuzzy Pairs

  • Krassimir AtanassovEmail author
  • Eulalia SzmidtEmail author
  • Janusz KacprzykEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10333)


Intuitionistic Fuzzy Sets (IFSs) are an extension of fuzzy sets. Each element x of the IFS A has degrees of a membership (\(\mu _A(x)\)) and of a non-membership (\(\nu _A(x)\)) so that \(0 \le \mu _A(x) + \nu _A(x) \le 1\). The pair \(\langle \mu _A(x), \nu _A(x) \rangle \) is called an Intuitionistic Fuzzy Pair (IFP). A lot of operations, relations and operators are defined over IFPs. In the paper, novel operations over IFPs are introduced and some of their basic properties are studied. Geometrical interpretations of these operations are given. Open problems are formulated.


Intuitionistic fuzzy conjunction Intuitionistic fuzzy disjunction Intuitionistic fuzzy pair Multiplication Intuitionistic fuzzy negation 



The first author is thankful for the support provided by the Bulgarian National Science Fund under Grant Ref. No. DFNI-I-02-5.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical EngineeringBulgarian Academy of SciencesSofiaBulgaria
  2. 2.Intelligent Systems Laboratory Prof. Asen Zlatarov UniversityBurgasBulgaria
  3. 3.Systems Research InstitutePolish Academy of SciencesWarsawPoland
  4. 4.Warsaw School of Information TechnologyWarsawPoland

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