Neutrosophic Number Optimization Models and Their Application in the Practical Production Process

Abstract

In order to simplify the complex calculation and solve the difficult solution problems of neutrosophic number optimization models (NNOMs) in the practical production process, this paper presents two methods to solve NNOMs, where Matlab built-in function “fmincon()” and neutrosophic number operations (NNOs) are used in indeterminate environments. Next, the two methods are applied to linear and nonlinear programming problems with neutrosophic number information to obtain the optimal solution of the maximum/minimum objective function under the constrained conditions of practical productions by neutrosophic number optimization programming (NNOP) examples. Finally, under indeterminate environments, the fit optimal solutions of the examples can also be achieved by using some specified indeterminate scales to fulfill some specified actual requirements. The NNOP methods can obtain the feasible and flexible optimal solutions and indicate the advantage of simple calculations in practical applications.

Confidence Neutrosophic Number Linear Programming Methods Based on Probability Distributions and Their Applications in Production Planning Problems

“…It is known that the general NN-LP methods [23,[25][26][27][28][29][30] are composed of the NN objective function and the NN constraint equations to reflect the uncertainty in the actual PPPs. en, the optimal feasible solutions of the decision variables and the objective function [23,[25][26][27][28][29][30] cannot reflect some distribution and confidence level/interval of sample datasets/multivalued sets from a probabilistic point of view, the optimal feasible solutions cannot ensure their credibility and reliability. e proposed CNN-LP methods are composed of the CNN objective function and the CNN constraint equations corresponding to some distribution and confidence level/interval of product sample datasets to deal with uncertain PPPs.…”

“…erefore, the proposed CNN-LP methods can guarantee the credibility/reliability and rationality of their optimal interval feasible solutions from a probabilistic point of view. In this situation, the proposed CNN-LP methods demonstrate obvious superiority over the general NN-LP methods [23,[25][26][27][28][29][30] and show their effectiveness and rationality in handling the indeterminate PPPs.…”

“…In nonlinear programming problems, Ye et al [24] introduced the concepts of NN nonlinear functions, NN constraint inequalities, and NN nonlinear programming models, gave optimal interval solutions of the NN nonlinear programming models with various constraint problems, and then verified the efficiency of the proposed methods by numerical examples. Furthermore, Tu et al [25] introduced NN optimization models and solution methods based on the Matlab built-in function "fmincon()" and NN operations and then applied them to actual production problems to obtain optimal interval solutions under an uncertain environment. Furthermore, Pramanik and Dey [26] presented a NN multilevel linear programming approach to perform linear programming problems.…”

Synthesis and characterization of polypyrrole composites: Optimization strategies for tailored material qualities and enhanced applications

“…Advanced techniques such as spectroscopy, microscopy, and thermal analysis are employed to scrutinize the molecular and morphological aspects of the materials. This comprehensive characterization enables researchers to gain insights into the electronic structure, conductivity, and thermal stability, which are critical factors influencing the materials' applicability in different contexts (Chemistry, 2023;Ono, 2023;Saliba & Barnes, 2022;Sonika et al, 2022) [4,16,17,19] . The versatility of polypyrrole is further enhanced through the incorporation of various composites.…”

“…The exceptional conductivity of polypyrrole, coupled with the tailored properties of its composites, positions these materials as promising candidates for nextgeneration technologies. This investigation into conducting polypyrrole and its composites is poised to contribute significantly to the expanding realm of advanced materials (Guan et al [9,10,19,23,25] . The precision in preparation, thorough characterization, and exploration of diverse applications underscore the multifaceted nature of these materials.…”