The Indus River Basin covers an area of around 1 million square kilometers and connects four countries: Afghanistan, China, India, and Pakistan. More than 300 million people depend to some extent on the basin's water, yet a growing population, increasing food and energy demands, climate change, and shifting monsoon patterns are exerting increasing pressure. Under these pressures, a ''business as usual'' (BAU) approach is no longer sustainable, and decision makers and wider stakeholders are calling for more integrated and inclusive development pathways that are in line with achieving the UN Sustainable Development Goals. Here, we propose an integrated nexus modeling framework co-designed with regional stakeholders from the four riparian countries of the Indus River Basin and discuss challenges and opportunities for developing transformation pathways for the basin's future.

Many problems of practical interest can be modeled and solved by using graph algorithms. In general, graph theory has a wide range of applications in diverse fields. In this paper, the intuitionistic fuzzy organizational and neural network models, intuitionistic fuzzy neurons in medical diagnosis, intuitionistic fuzzy digraphs in vulnerability assessment of gas pipeline networks, and intuitionistic fuzzy digraphs in travel time are presented as examples of intuitionistic fuzzy digraphs in decision support system. We have also designed and implemented the algorithms for these decision support systems.

A Fermatean fuzzy set is a more powerful tool to deal with uncertainties in the given information as compared to intuitionistic fuzzy set and Pythagorean fuzzy set and has energetic applications in decision-making. Aggregation operators are very helpful for assessing the given alternatives in the decision-making process, and their purpose is to integrate all the given individual evaluation values into a unified form. In this research article, some new aggregation operators are proposed under the Fermatean fuzzy set environment. Some deficiencies of the existing operators are discussed, and then, new operational law, by considering the interaction between the membership degree and nonmembership degree, is discussed to reduce the drawbacks of existing theories. Based on Hamacher’s norm operations, new averaging operators, namely, Fermatean fuzzy Hamacher interactive weighted averaging, Fermatean fuzzy Hamacher interactive ordered weighted averaging, and Fermatean fuzzy Hamacher interactive hybrid weighted averaging operators, are introduced. Some interesting properties related to these operators are also presented. To get the optimal alternative, a multiattribute group decision-making method has been given under proposed operators. Furthermore, we have explicated the comparison analysis between the proposed and existing theories for the exactness and validity of the proposed work.