Since the future of the society depends upon the role of students, so suitable career selection methods for the students are considered to be an important problem to explore. It is assumed that if a student has the required capability and positive attitudes towards a subject, then the student will achieve more in that subject. To consider the uncertain issues involved with students’ career selection, picture fuzzy set (PFS) and rough set based approaches are proposed in this study as they are found to be appropriate due to their inherent characteristics to deal with incomplete and imprecise information. For the purpose of selecting a suitable career, the article analyzes student's features in terms of career, memory, interest, knowledge, environment and attitude. We propose two hybridized distance measures using Hausdorff, Hamming and Euclidian distances under picture fuzzy environment where the evaluating information regarding students, subjects and student's features are given in picture fuzzy numbers. Then we present an algorithmic approach using the proposed distance measures and rough set theory. We apply rough set theory to determine whether a particular subject is suitable for a student even if there is controversy to select a stream. Lower and higher approximation with boundary region of rough set theory is used to manage the inconsistent situations. Finally, two case studies are demonstrated to validate the applicability of the proposed idea.

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Allotment of nurses to patients is a critical task in terms of better treatment. Nurses should be appointed according to a patient’s health condition, type of disease & financial condition. Again understaffing of nurses may hamper patient health & condition. Similarly, overstaffing of nurses is a waste of man powers. Adequate staffing of nurses is crucial. We propose a technique using game theory to meet over staffing and under staffing of nurses. Game theory plays a vital role to meet the exact requirement. Nash equilibrium can be used for taking all possible decisions, like appointment of nurses in different categories for smooth treatment of patients. However, final & most suitable decision can be taken using perfect Nash equilibrium. This technique is a perfect technique to implement in case of vital & critical decision points.

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