In many real life problems, the parameters used to characterize the uncertainty or vagueness or impreciseness in information are either triangular or trapezoidal fuzzy numbers. But it is not always possible to restrict the membership function to either triangular or trapezoidal form. In this paper, a new form of non-normal fuzzy number named as Heptagonal fuzzy number is introduced and its arit...

The fuzzy representation of the edges has been widely studied in different works. Generally, for each pixel, the authors use membership degrees linearly proportional to the magnitude of the gradient at that position of the image. This would be equivalent to using a triangular membership functions on the gradient magnitude. In this work we study the use of parametric functions in the transformat...

In this paper we study some properties related to the distribution of membership grades for non-stationary fuzzy sets. We obtain the formulation for the distribution, where the non-stationary fuzzy sets are obtained by generating instantiations about the center values. The two cases considered are for the underlying membership functions as Triangular and Gaussian. The analytical results obtaine...

Slowly but surely, intuitionistic fuzzy sets are giving away their secrets. By tracing them back to the underlying algebraic structure that they are defined on (a complete lattice), they can be embedded in the well– known class of L–fuzzy sets, whose formal treatment allows the definition and study of order–theoretic concepts such as triangular norms and conorms, negators and implicators, as we...

the notion of a probabilistic metric  space  corresponds to thesituations when we do not know exactly the  distance.  probabilistic metric space was  introduced by karl menger. alsina, schweizer and sklar gave a general definition of  probabilistic normed space based on the definition of menger [1]. in this note we study the pn spaces which are  topological vector spaces and the open mapping an...

The VHDL-AMS based genetic optimization of fuzzy logic controller for movement control systems is discussed here. The designs have been carried out in the digital domain with HDL. The basic components of the fuzzy logic controller are designed using VHDL-AMS. The proposed work focuses on control of speed with respect to input parameter such as Alignment & distance with triangular membership fun...

Fuzzy control is one of the most important parts of fuzzy theory for which several approaches exist. Mamdani uses $alpha$-cuts and builds the union of the membership functions which is called the aggregated consequence function. The resulting function is the starting point of the defuzzification process. In this article, we define a more natural way to calculate the aggregated consequence funct...

In this paper, we introduce the new definition of rough membership function using continuous and discuss several concepts properties set value functions as results on function. Moreover, extend to topology spaces by substituting an equivalence class prove some theorems certain types more general fundamental generalized sets. Our result concept valued theory.

This paper presents three new methodologies for the basic operations, which aim at finding new ways of computing union (maximum) and intersection (minimum) membership values by taking into effect the entire membership values in a fuzzy set. The new methodologies are conceptually simple and easy from the application point of view and are illustrated with a variety of problems such as Cartesian p...