In this paper, we introduce the concept of neutrosophic number from different viewpoints. We define different types of linear and non-linear generalized triangular neutrosophic numbers which are very important for uncertainty theory. We introduced the de-neutrosophication concept for neutrosophic number for triangular neutrosophic numbers. This concept helps us to convert a neutrosophic number into a crisp number. The concepts are followed by two application, namely in imprecise project evaluation review technique and route selection problem.

In this paper, authors disclose a new concept of pentagonal neutrosophic (PN) approach to solve linear programming (LP) problem. To best of our insight, there is no approach for solving PNLP problem. For the first time, we take up the PNLP problem where the objectives, constraints are considered as pentagonal neutrosophic numbers (PNN). To deign our algorithm, we described the PN arithmetic operation laws and mathematical computation in PNN environment. This proposed method is based on ranking function and convert to its equivalent crisp LP (CrLP) problem. The obtained CrLP issue is presently being tackled by any LP method which is effectively accessible. To legitimize the proposed technique, some numerical tests are given to show the adequacy of the new model.

American scientific publishing group

In this article, the concept of parametric interval valued Pythagorean number (PIVPN) has been introduced, which is an extended version of Pythagorean number (PN). Here, a new score and accuracy function have been innovated in the PIVPN environment along with the De-Pythagorean value concept. The new tool and techniques have been fruitfully applied to two realistic problems, namely the networking critical path model (CPM) problem and the multicriteria group decision making problem (MCGDM) problem. In order to solve the MCGDM problem, we have prepared Parametric Interval valued Pythagorean Weighted Arithmetic Mean Operator (PIVPWAMO) and Parametric Interval valued Pythagorean Weighted Geometric Mean Operator (PIVPWGMO) operator in PIVPN environment. Finally, sensitivity analysis and industrious comprehensive numerical simulations have been performed to identify the reliability, efficiency, and usefulness of this novel work. In this article, we have shown that PIVPNs are a more well-organized representation to grip a real-life problem, and they can handle inconsistent conditions in a better compatible way in comparison to the other existing methods.