Shale gas energy is the most prominent and dominating source of power across the globe. The processes for the extraction of shale gas from shale rocks are very complex. In this study, a multiobjective optimization framework is presented for an overall water management system that includes the allocation of freshwater for hydraulic fracturing and optimal management of the resulting wastewater with different techniques. The generated wastewater from the shale fracking process contains highly toxic chemicals. The optimal control of a massive amount of contaminated water is quite a challenging task. Therefore, an on-site treatment plant, underground disposal facility, and treatment plant with expansion capacity were designed to overcome environmental issues. A multiobjective trade-off between socio-economic and environmental concerns was established under a set of conflicting constraints. A solution method—the neutrosophic goal programming approach—is suggested, inspired by independent, neutral/indeterminacy thoughts of the decision-maker(s). A theoretical computational study is presented to show the validity and applicability of the proposed multiobjective shale gas water management optimization model and solution procedure. The obtained results and conclusions, along with the significant contributions, are discussed in the context of shale gas supply chain planning policies over different time horizons.

In any decision-making process, it is often observed that due to some doubt or hesitation, it is quite difficult for decision maker(s) to specify the precise/crisp value of any parameters which results in the existence of uncertainty among parameter. In this study, a multiobjective nonlinear transportation problem (MO-NTP) has been formulated with fuzzy parameters. The nonlinearity occurs in cost function due to the existence of extra cost in the fixed cost which has been discussed briefly. The solution method, neutrosophic compromise programming approach (NCPA), based on neutrosophic decision set has been investigated which contains the concept of indeterminacy degree along with membership and non-membership degree of different objectives. It also provides an effective framework which reflects the reality involved in any decision making process. In order to show the validity and suitability of NCPA, a numerical example has been presented. The superiority of the NCPA has been shown by doing a comparative study with other existing approaches.

Transportation problems inherently involve uncertainty in real life. The uncertain framework for optimization of transportation models depends on various aspects. Therefore the effective modeling and optimization configuration is needed to solve such transportation problems. In this study, we have considered a multiobjective transportation problem with fuzzy parameters and developed a new Pythagorean-hesitant fuzzy computational algorithm to solve the problem under uncertainty. The proposed approach is based on Pythagorean-hesitant fuzzy decision set which captures a set of possible values for membership and non-membership degrees of each objective function under the Pythagorean-hesitant fuzzy environment. To show the applicability and validity of the proposed approach a numerical example has been presented. The efficiency performance of the proposed approach has also been discussed along with the comparative study with other existing approaches.

The existence of neutral /indeterminacy degrees reflects the more practical aspects of decision-making scenarios. Thus, this paper has studied the intuitionistic fuzzy multiobjective linear programming problems (IFMOLPPs) under neutrosophic uncertainty. To highlight the degrees of neutrality in IFMOLPPs, we have investigated the neutrosophic optimization techniques with intuitionistic fuzzy parameters. The marginal evaluation of each objective is determined by three different membership functions, such as truth, indeterminacy, and falsity membership degrees under the neutrosophic environment. The marginal evaluation of each objective function is elicited by various sorts of membership functions such as linear, exponential, and hyperbolic types of membership functions, which signifies an opportunity for decision-makers to select the desired membership functions. The developed neutrosophic optimization technique is implemented on existing numerical problems that reveal the validity and applicability of the proposed methods. A comparative study is also presented with other approaches. At last, conclusions and future research directions are addressed based on the proposed work.

This study presents the modeling of the multiobjective optimization problem in an intuitionistic fuzzy environment. The uncertain parameters are depicted as intuitionistic fuzzy numbers, and the crisp version is obtained using the ranking function method. Also, we have developed a novel interactive neutrosophic programming approach to solve multiobjective optimization problems. The proposed method involves neutral thoughts while making decisions. Furthermore, various sorts of membership functions are also depicted for the marginal evaluation of each objective simultaneously. The different numerical examples are presented to show the performances of the proposed solution approach. A case study of the cloud computing pricing problem is also addressed to reveal the real-life applications. The practical implication of the current study is also discussed efficiently. Finally, conclusions and future research scope are suggested based on the proposed work.