A heuristic statisticalmethod for testing intuitionistic fuzzy hypotheses of onefactor and two factor ANOVA model using intuitionistic fuzzy data samples is proposed. In this method, the decision rules to accept or reject the null and alternative hypotheses are given. The idea of the proposed procedure has been clarified with the help of numerical examples using R studio.

The development in the industries has necessitated the growth of transportation methods. Due to the variation in the transportation systems, many problems seem to arise in the present times. One such problem is the stochastic fuzzy transportation problem (SFTP). The SFTP is a chance‐constrained programming (CCP) problem with probabilistic constraints where supply and demand are randomness, and the objective function is in fuzzy nature. In this paper, we have developed three models for the SFTP, where the constraints are mixed type following Weibull distribution (WD). The aim of the research work is to optimize the transportation cost in FTP under probabilistic mixed constraints. In order to achieve this, the cost coefficient of the fuzzy objective function is converted to alpha cut representation, and the probabilistic mixed constraints are converted to deterministic form by using the WD. The proposed models are illustrated by providing a numerical example, and the problem is solved using Lingo software. It is worth pointing out that these models are constructed from different points of view. The decision‐maker’s (DM’s) preference has the final say in the usage of the models. A sensitivity analysis (SA) is performed to explore the sensitivity of the parameters in the proposed model.

The transportation problem (TP) is an important type of linear programming problem. The aim of TP is to optimize the objective function by allocating product shipments from various sources to multiple destinations. When limitations exist during transportation in the number of products transported from a source to destination due to a variety of factors, such as storage limitations, budgetary constraints, and so on, then TP becomes the capacitated transportation problem (CTP). The business entrepreneurs are keen on transporting multiple items with multiple objectives to generate maximum revenue for an organization, which leads to the development of a multi-objective bi-item capacitated transportation problem (MOBICTP). If a supplier's resources significantly increase or decrease, and the demand needs also significantly increase or decrease, the MOBICTP transforms into a MOBICTP with mixed constraints. Most real-world problems have uncertain parameters due to insufficient data, fluctuating market costs for an item, variation in weather conditions, and so on. Such uncertain parameters are addressed using fuzzy, multi-choice, or stochastic programming. In this article, we examined a novel integrated model for a multi-objective bi-item capacitated transportation problem, which includes a fermatean fuzzy multi-choice stochastic mixed constraint that follows normal distribution. First, the Fermatean fuzzy multi-choice stochastic parameter in the constraints is transformed into a multi-choice stochastic parameter in the constraints by using the (α, β )-cut technique and accuracy function. Then the improved chance-constrained method is developed using Newton divided difference interpolation polynomial. The improved chance-constrained method is used to transform the multi-choice stochastic parameter in the constraints into its equivalent deterministic constraints. Secondly, we propose a novel approach, the improved global weighted sum method, which transforms a multi-objective problem into a single objective problem and utilizes Lingo 18.0 software to find the optimal compromise solution to the equivalent deterministic problem. The main aim of this paper is to help business entrepreneurs improve their profit margins by optimizing the quantity of multiple items while minimizing damage costs, labor costs, transportation time, and transportation costs, and maximizing discounts. To show the model’s validity and significance, a numerical example is solved using the Lingo 18.0 software. In order to emphasize the proposed method, a comparative analysis is conducted with other existing methods. The final component includes a sensitivity analysis and conclusions with future research directions.

An uncertain transportation problem is a transportation problem in which the parameters are fuzzy numbers. This paper presents a survey on single objective fuzzy transportation problem (SOFTP) and multi-objective fuzzy transportation problem (MOFTP) with its mathematical models.

This paper presents intuitionistic fuzzy multi-objective nonlinear programming problem (IFMONLPP). All the coefficients of the multi-objective nonlinear programming problem (MONLPP) and the constraints are taken to be intuitionistic fuzzy numbers (IFN). The IFMONLPP has been transformed into crisp one and solved by using Kuhn-Tucker condition. Numerical example is provided to illustrate the approach.

In today's competitive world, entrepreneurs cannot argue for transporting a single product. It does not provide much profit to the entrepreneur. Due to this reason, multiple products need to be transported from various origins to destinations through various types of conveyances. Real-world decision-making problems are typically phrased as multi-objective optimization problems because they may be effectively described with numerous competing objectives. Many real-life problems have uncertain objective functions and constraints due to incomplete or uncertain information. Such uncertainties are dealt with in fuzzy/interval/stochastic programming. This study explored a novel integrated model bi-objective bi-item solid transportation problem with fuzzy stochastic inequality constraints following a normal distribution. The entrepreneur's objectives are minimizing the transportation cost and duration of transit while maximizing the profit subject to constraints. The chance-constrained technique is applied to transform the uncertainty problem into its equivalent deterministic problem. The deterministic problem is then solved with the proposed method, namely, the global weighted sum method (GWSM), to find the optimal compromise solution. A numerical example is provided to test the efficacy of the method and then is solved using the Lingo 18.0 software. To highlight the proposed method, comparisons of the solution with the existing solution methods are performed. Finally, to understand the sensitivity of parameters in the proposed model, sensitivity analysis (SA) is conducted.