Intuitionistic and Neutrosophic Fuzzy Logic: Basic Concepts and Applications

  • Amita JainEmail author
  • Basanti Pal Nandi
Part of the Studies in Computational Intelligence book series (SCI, volume 827)


Fuzzy set proposed by Zadeh states that belongingness of an element in a set is a matter of degree unlike classical set where membership is a matter of affirmation or denial. Fuzzy set theory provides more natural representation for real world problems. Intuitionistic fuzzy set (IFS) is the generalization of fuzzy set, proposed by Atanassov, in 1986 (Fuzzy Sets Syst 20(1):87–96, 1986 [1]). It assigns two values called membership degree and a non-membership degree respectively. Later Florentin Smarandache introduced an additional parameter for neutrality which generalise Intuitionistic Fuzzy Set as Neutrosophic Fuzzy Set (NFS). The speciality lies in the 3D Neutrosophic space where each logical statement is evaluated with 3 components namely truth, falsity and indeterminacy. IFS and NFS revolve around these divisions of degree of belongingness to their component structure and so generate different variations. In this chapter we discuss the properties of these two variants of fuzzy set based on their different extension, propositional calculus, predicate calculus, degree of dependence of each component, geometric representation and various application areas of both the sets.


Intuitionistic fuzzy Neutrosophic cube Neutrosophic fuzzy Predicate calculus Propositional calculus Research statistics 


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Ambedkar Institute of Advanced Communication Technologies and ResearchDelhiIndia
  2. 2.Guru Tegh Bahadur Institute of TechnologyNew DelhiIndia

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