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 $$ \alpha ,\beta ,\gamma $$ -cut of single-valued triangular neutrosophic numbers and introduces the arithmetic operations of triangular neutrosophic numbers using $$ \alpha ,\beta ,\gamma $$ -cut. 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.
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