Arithmetic Behaviors of P-Norm Generalized Trapezoidal Intuitionistic Fuzzy Numbers with Application to Circuit Analysis

Arithmetic Behaviors of P-Norm Generalized Trapezoidal Intuitionistic Fuzzy Numbers with Application to Circuit Analysis

Sanhita Banerjee (IIEST, Shibpur, Howrah, India) and Tapan Kumar Roy (IIEST, Shibpur, Howrah, India)
Copyright: © 2017 |Pages: 53
DOI: 10.4018/IJFSA.2017070102

Abstract

P-norm Generalized Trapezoidal Intuitionistic Fuzzy Number is the most generalized form of Fuzzy as well as Intuitionistic Fuzzy Number. It has a huge application while solving various problems in imprecise environment. In this paper the authors have discussed some basic arithmetic operations of p-norm Generalized Trapezoidal Intuitionistic Fuzzy Numbers using two different methods (extension principle method and vertex method) and have solved a problem of circuit analysis taking the given data as p-norm Generalized Trapezoidal Intuitionistic Fuzzy Numbers.
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2. Mathematical Preliminaries

  • Definition-2.1: Intuitionistic Fuzzy Set (IFS) (Atanassov, 1999): Let IJFSA.2017070102.m03 be a finite universal set. An Intuitionistic Fuzzy Set IJFSA.2017070102.m04 in a given universal set U is an object having the form IJFSA.2017070102.m05 where the functions IJFSA.2017070102.m06; i.e., IJFSA.2017070102.m07 and IJFSA.2017070102.m08; i.e., IJFSA.2017070102.m09 define the degree of membership and the degree of non-membership of an element IJFSA.2017070102.m10, such that they satisfy the following conditions:

    IJFSA.2017070102.m11

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