Comp. Appl. Math.
An intuitionistic fuzzy (δ, γ )-norm entropy with its
application in supplier selection problem
· Satish Kumar
Received: 24 December 2017 / Revised: 20 April 2018 / Accepted: 23 May 2018
© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2018
Abstract In this communication, based on the concept of (δ, γ )-norm entropy, an (δ, γ )-
norm intuitionistic fuzzy entropy measure is introduced in the settings of intuitionistic fuzzy
set theory. Some of its major properties are also proved. The performance of the proposed
entropy measure is demonstrated using numerical examples. Based on the proposed intu-
itionistic fuzzy (IF) entropy, a new multiple-attribute decision-making method (MADM)
considering the merits of subjective and objective weights has been introduced. Two meth-
ods of ﬁnding the weights of attributes are discussed. The proposed MADM method is
effectively explained with the help of supplier selection example.
Keywords δ-Norm entropy · (δ, γ )-Norm entropy · Intuitionistic fuzzy entropy ·
Multi-attribute decision-making · VIKOR
Mathematics Subject Classiﬁcations 94A15 · 94A24 · 26D15
Discovery of fuzzy set (FS) by Zadeh (1965) attracted the researchers worldwide. Before
this invention, probability was the only way to measure uncertainty. However, the vague
terms like fast speed, very intelligent, etc. could not be represented using probability theory.
To quantify the vagueness involved in such terms, the fuzzy set theory proposed by Zadeh
(1965) has proved to be very useful. With the evolution of FSs, many theories and approaches
generalizing the concept of FS came into existence, for example, Type-2 FSs (1975)etc.
Communicated by Anibal Tavares de Azevedo.
Department of Mathematics, Maharishi Markandeshwar University, Mullana, Ambala 133207, India