Neutrosophic linear programming using possibilistic mean
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METHODOLOGIES AND APPLICATION
Neutrosophic linear programming using possibilistic mean Kiran Khatter1
Ó Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The paper discusses the concept of fuzzy set theory, interval-valued fuzzy set, intuitionistic fuzzy set, interval-valued intuitionistic fuzzy set, neutrosophic set and its operational laws. The paper presents the a; b; c-cut of single-valued triangular neutrosophic numbers and introduces the arithmetic operations of triangular neutrosophic numbers using a; b; ccut. Then, possibilistic mean of truth membership function, indeterminacy membership function and falsity membership function is defined. The proposed approach converts each triangular neutrosophic number in linear programming problem to weighted value using possibilistic mean to determine the crisp linear programming problem. The proposed approach also considers the risk attitude of expert while deciding the parameters of linear programming model. Keywords Neutrosophic set (NS) Neutrosophic number Single-valued neutrosophic set (SVNS) Alpha cut Beta cut Gamma cut Possibilistic mean Possibility mean Neutrosophic number linear programming (NNLP) Neutrosophic linear programming (NNLP) Neutrosophic optimization
1 Introduction Fuzzy set theory was proposed by Zadeh (1965) to deal the incompleteness, uncertainty and impreciseness with the help of grade of membership. Afterwards, the concept of interval-valued fuzzy set (IVFS) was presented by Zadeh (1975) if information is uncertain and is in the form of some intervals. Atanassov (1986) developed an intuitionistic fuzzy set (IFS) (Atanassov 1999, 2000) to describe the degree of membership and non-membership separately. Liu and Yuan (2007) presented the triangular intuitionistic fuzzy sets by generalizing the IFS with respect to triangular fuzzy numbers (TFN). Further, Atanassov and Gargov (1989) combined the concept of IFS and IVFS and introduced the interval-valued intuitionistic fuzzy set (IVIFS). Ye (2014a) extended the triangular intuitionistic fuzzy set and proposed the trapezoidal intuitionistic fuzzy set for representing the membership and non-membership values of trapezoidal information.
Communicated by V. Loia. & Kiran Khatter [email protected] 1
Department of Computer Science, BML Munjal University, Sidhrawali, India
In real-world scenario, we often encounter with incomplete and indeterminate information where it is not possible to represent the information only by the means of membership function and non-membership function. To deal with such situations, Smarandache (1998) proposed the neutrosophic set (NS) by combining the fuzzy set theory concept and intuitionistic fuzzy set (IFS) and introduced the indeterminacy membership function in addition to a truth membership and falsity membership functions. Later, Wang et al. (2010) proposed singlevalued neutrosophic set to make the use of NS in real-life situations. Ye (2015) introduced the trapezoidal neutrosoph
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