In this paper, a Stieltjes integral approximation method for uncertain variational inequality problem (UVIP) is studied. Firstly, uncertain variables are introduced on the basis of variational inequality. Since the uncertain variables are based on nonadditive measures, there is usually no density function. Secondly, the expected value model of UVIP is established after the expected value is discretized by the Stieltjes integral. Furthermore, a gap function is constructed to transform UVIP into an uncertain constraint optimization problem, and the optimal value of the constraint problem is proved to be the solution of UVIP. Finally, the convergence of solutions of the Stieltjes integral discretization approximation problem is proved.

Modern civilisation is increasingly prioritising sustainability to address environmental challenges like resource depletion and waste accumulation. Repurposing discarded materials such as vehicle tires and seashells into sustainable materials is vital for mitigating these issues. However, the mechanical properties of concrete may be weakened by including scraps of rubber. Similar problems related to the disposal of seashell waste include soil solidification and illegal dumping. This study looks at the possibility of using rubber powder (1%, 5%, 10%, and 15%) and clamshell powder (5%), respectively, as partial substitutes for sand and cement. Objectives include evaluating the physical and mechanical properties of mortar and determining the optimal percentage of rubber powder when combined with clamshell powder. After creating the mortar mixes, tests were conducted to determine flexural strength, density, and compression after 7, 14, and 28 days of curing. According to the results, compression strength decreases with increasing rubber powder percentages. 15% showed the lowest compression strength (20.163 MPa) and 1% the greatest (28.197 MPa). Furthermore, flexural testing showed that a 1% rubber powder combined with clamshell powder was best. By recycling waste materials, using 1% rubber powder and 5% clamshell powder in mortar can help solve environment challenges. However, it’s crucial to properly balance these amounts to ensure the strength of the mortar. Although this strategy contributes significantly to sustainability, it is not a comprehensive solution to the larger environmental problems; it is only one aspect of the picture. It can be concluded that the optimum percentage of rubber that can be used with 5% clam shell powder is 1%.

One of the significant by products of Malaysia's industrial sector is the generation of solid waste that does not biodegrade. Coir, along with other by products of industrialisation such as plastic bags, PET bottles, and pulverised waste LDPE, must be disposed of in an appropriate manner. Utilising discarded items contributes to pollution prevention and resource conservation. A few researchers have investigated the possibility of recycling waste materials to lessen pollution and preserve important resources. An experiment revealed that replacing fine particles (sand) with low-density polyethylene (LDPE) negatively affects the compressive strength of concrete cement. To solve this issue, steel fibre was included as an additional component after it was applied. This study investigated a variety of ratios of LDPE substitution for fine aggregates. These ratios ranged from 0% to 15%, with increments of 5%. Following 7, 14, and 28 days, the density, compressive strength, and flexural strength of the concrete were measured and analysed. The findings showed that adding 15% LDPE to concrete cement made it less dense (1840 kg/m3) and weaker in its compressive strength (32.87 MPa) and flexural strength (4.627 MPa) at 28 days. Based on this, it has been determined that a combination consisting of a 5% substitution of LDPE and an additional 2% of steel fibre is the most effective combination for further research endeavours.