Neutrosophic Shortest Path Problem

Neutrosophic set theory provides a new tool to handle the uncertainties in shortest path problem (SPP). This paper introduces the SPP from a source node to a destination node on a neutrosophic graph in which a positive neutrosophic number is assigned to each edge as its edge cost. We define this problem as neutrosophic shortest path problem (NSSPP). A simple algorithm is also introduced to solve the NSSPP. The proposed algorithm finds the neutrosophic shortest path (NSSP) and its corresponding neutrosophic shortest path length (NSSPL) between source node and destination node. Our proposed algorithm is also capable to find crisp shortest path length (CrSPL) of the corresponding neutrosophic shortest path length (NSSPL) which helps the decision maker to choose the shortest path easily. We also compare our proposed algorithm with some existing methods to show efficiency of our proposed algorithm. Finally, some numerical experiments are given to show the effectiveness and robustness of the new model. Numerical and graphical results demonstrate that the novel methods are superior to the existing method

A Multi Objective Programming Approach to Solve Integer Valued Neutrosophic Shortest Path Problems

Neutrosophic (NS) set hypothesis gives another way to deal with the vulnerabilities of the shortest path problems (SPP). Several researchers have worked on fuzzy shortest path problem (FSPP) in a fuzzy graph with vulnerability data and completely different applications in real world eventualities. However, the uncertainty related to the inconsistent information and indeterminate information isn't properly expressed by fuzzy set. The neutrosophic set deals these forms of uncertainty. This paper presents a model for shortest path problem with various arrangements of integer-valued trapezoidal neutrosophic (INVTpNS) and integer-valued triangular neutrosophic (INVTrNS). We characterized this issue as Neutrosophic Shortest way problem (NSSPP). The established linear programming (LP) model solves the classical SPP that consists of crisp parameters

A fuzzy mathematics approach in measuring air pollution from motor vehicles

Air pollution from motor vehicle in cities specially in developing countries has been a major source of urban air pollution and hence a cause of concern for the administrators of the cities as well as for researchers in the field of ecology and mathematics. In the present work, the fuzzy membership functions for some of the attributes regarding air pollution from motor vehicle are proposed. To study the index of air pollution in different area of a city, the air pollution index is proposed, which takes into account the membership function for the attributes of pollution. By applying a suitable interpolation formula (in our case Lagrange's interpolation formula) a polynomial curve is obtained, which gives the measure of air pollution at any point of the city under certain assumptions. The effectiveness and suitability of the method is established by taking an example

Paediatric non-endemic nasopharyngeal carcinoma: our experience at an Indian tertiary teaching hospital

Introduction: Nasopharyngeal carcinoma (NPC) is a very uncommon malignant tumour in children under the age of 20. The diagnosis of paediatric NPC is challenging due to its relative rarity. This unusual occurrence is frequently linked to delayed diagnosis, which can result in advanced loco-regional illness. Here, we investigate the clinical manifestations, investigations, and treatment of paediatric nasopharyngeal carcinoma in a nonendemic region. Method: The data from children and adolescents who had been diagnosed with nasopharyngeal cancer served as the basis for this study, which was carried out at the Cardiology and Pathology Departments of a tertiary teaching hospital in the eastern region of India. Result: In this retrospective analysis, 17 paediatric patients under the age of 18 were enrolled. Between December 2020 and January 2022, they were treated at a tertiary teaching hospital. 17 kids with nasopharyngeal cancer between the ages of 6 and 18 took part in this study. In this study, there were 7 girls (41.1%) and 10 boys (58.8%). NPC diagnosis occurred at a median age of 14 years (interquartile range: 6–18 years). In 15 (88.2%) individuals, neck swelling was the most frequent clinical manifestation, followed by nasal bleeding, nasal block, and hearing impairment in 10 (58.8%), 12 (70.5%), and 11 (64.7%) of cases, respectively.  Conclusion: With the exception of individuals who have distant metastatic disease, children with NPC have a very good prognosis. NPC in children is typically not clinically suspected until the patient is in a late stage. The most important prognostic factor is the TNM staging. Unfortunately, NPC frequently has distant metastases at the time of diagnosis in the paediatric age range and has a tendency to be locally progressed