in this paper the solution of a second order linear dierential equations with intu-itionistic fuzzy boundary value is described. it is discussed for two dierent cases: coecientis positive crisp number and coecient is negative crisp number. here fuzzy numbers aretaken as generalized trapezoidal intutionistic fuzzy numbers (gtrifns). further a numericalexample is illustrated.

In recent years, Fuzzy differential equations are very useful indifferent sciences such as physics, chemistry, biology and economy. It should be noted, that if the equations that appear to be uncertain, then take help of fuzzy logic at these equations. Considering that most of the time analytic solution of such equations and finding an exact solution has either high complexity or cannot be solv...

this paper presents an efficient hybrid method, namely fuzzy particleswarm optimization (fpso) and fuzzy c-means (fcm) algorithms, to solve the fuzzyclustering problem, especially for large sizes. when the problem becomes large, thefcm algorithm may result in uneven distribution of data, making it difficult to findan optimal solution in reasonable amount of time. the pso algorithm does find ago...