Vitiligo is a problem due to the destruction of melanocytes which is present in 1% of people all over the world. The origin of this disease is unknown and difficult to cure. Absence of melanin in the body causes lesions which will ooze out all over the body. Phototherapy and surgical therapy are the two types of treatment available in the existing world. The Cytotoxic CD8 + T lymphocytes act as a major factor for the abovesaid disease. The main objective of this work is to treat patients with different methods according to the severity of vitiligo, which can be identified with the help of out ranking based on hesitant fuzzy relation. Multi-criteria and multi-objective hesitant fuzzy are applied in this work to find out the ranking through which the severity of the disease is detected. This method helps in identifying the vitiligo lesions, which can be treated effectively in a short period of time. During the application of vitiligo treatment, FQA-TOPSIS (Fuzzy Quantified Attribute-TOPSIS) hesitant fuzzy relation methodology is deployed with three decision maker’s support using linguistic and intuitionistic values. The decision maker’s fuzzy values will be normalized and aggregated in this work with improved methodologies. The two objectives are deployed with their own fuzzy values and are implemented in the decision maker’s values. In the article fuzzy weightage has been calculated in two ways. One is every linguistic like low, medium, high and very high has got its significant intuitionistic values that all will be available with the scale of 1 to 10. The same has given as triplets. In our research work the above said has applied with the objective based weightage. So the accuracy has been increased through the work. The outcome of this methodology is to find out the coefficient closeness of the alternatives and to out rank the decision alternatives. The difference between the Final +ve Ideal Solution (FPIS) and Final -ve Ideal Solution (FNIS) is determined and FQA-TOPSIS Hesitant Fuzzy is ranked in the result.
In this paper, we give an algorithm that enables us to compute the neighbourhood of vertices of generalized tree obtained from a family of n stars having number of branches of those stars form an arithmetic progression (geometric progression) with common difference (ratio) j and one of the branches of each of those stars merged with one different point of a common path on n vertices successively in increasing order.
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