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