Pentadecagonal Fuzzy Number and its Applications

Abstract

The pentadecagonal Fuzzy number is an extension of dodecagonal and triskadecagonal fuzzy number which is developed under an uncertain linguistic environment which would be simplified to illustrate with pentadecagonal fuzzy linguistic scale values. Alpha cut method is the standard method performing different arithmetic operations include addition, subtraction, multiplication and division. This was applied in Operation Research, lathe machine, computer system and Fourier series. For a computer system, mainly power is required for the total operation which is provided by the mains or if the mains fail, then power will be generated from an auxillary genset. A fault tree is constructed having the top event as the failure of the computer system. By using intuitionistic pentadecagonal fuzzy number, we analyse the fault rate of the entire computer system with forbearance level of acceptance and forbearance of rejection. For a lathe machine, we use the fuzzy reliability to find the fault rate using the fault tree analysis by Interval-valued pentadecagonal fuzzy number, the defuzzification strategy used are centroid method and Euclidean distance which helps to evaluate the lower and upper bound of the maximum percentage of ineffectual of lathe machine. Fourier analysis is one of the powerful tool for many problems in which we can define the membership function for the closed interval. It helps us in time frequency analysis. The Fourier series periodic function for pentadecagonal fuzzy number is defined and it found to be symmetric. The reverse order pentadecagonal fuzzy number for Fourier series fuzzy valued function is also defined and is illustrated with an example which is found to be symmetric When uncertainty, imprecise, incomplete, inconsistent information arises in a philosophical viewpoint, there emerge the neutrosophic set which leads to the integral part of the framework.