According to fuzzy arithmetic, general dual fuzzy linear system (GDFLS) cannot be replaced by a fuzzy linear system (FLS). In this paper, we use new notation of fuzzy numbers and convert a GDFLS to two linear systems in crisp case, then we discuss complexity of the proposed method. Conditions for the existence of a unique fuzzy solution to n× n GDFLS are derived. AMS Subject Classification: 34K...

Ordered fuzzy numbers (OFN) invented by the second author and his two coworkers in 2002 make possible to utilize the fuzzy arithmetic and to construct the Abelian group of fuzzy numbers and then an ordered ring. The definition of OFN uses the extension of the parametric representation of convex fuzzy numbers. Fuzzy implication is proposed with the help of algebraic operations and a lattice stru...

In this paper we propose the extension of some aggregation or arithmetic operations between discrete fuzzy numbers to discrete fuzzy number-valued multisets such as the addition, the union and the intersection and, even, the order. For this reason, we prove or recall some properties of discrete fuzzy numbers and we undertake their study on multisets.

In this paper, we propose a new approach to critical path analysis in a project network whose activity times are uncertain. The uncertain parameters in the project network are represented by fuzzy numbers. We use fuzzy arithmetic and a fuzzy ranking method to determine the fuzzy critical path of the project network without converting the fuzzy activity times to classical numbers. The proposed m...

A fuzzy number intuitionistic fuzzy set (FNIFS) is a generalization of intuitionistic fuzzy set. The fundamental characteristic of FNIFS is that the values of its membership function and non-membership function are trigonometric fuzzy numbers rather than exact numbers. In this paper, we define some operational laws of fuzzy number intuitionistic fuzzy numbers, and, based on these operational la...

Type-2 (T2) fuzzy variable is an extension of an ordinary fuzzy variable. In fuzzy possibility theory, T2 fuzzy variable is defined as a measurable map from the universe to the set of real numbers, and the possibility of a T2 fuzzy variable takes on a real number is a regular fuzzy variable (RFV). T2 fuzziness, which is usually used to handle linguistic uncertainties, can be described as T2 fuz...

If all we know about normalized fuzzy sets is which set is a subset of which, will we be able to detect crisp sets? It is known that we can do it if we allow all possible fuzzy sets, including non-normalized ones. In this paper, we show that a similar detection is possible if we only allow normalized fuzzy sets. We also show that we can detect type-1 fuzzy sets based on the subsethood ordering ...

In this paper we focus on a kind of quadratic programming with fuzzy numbers and variables. First by using a fuzzy ranking and arithmetic operations, we transform these problems to crisp model with non-linear objective and linear constraints, then by solving this problem we obtain a fuzzy optimal solution. Finally, we give an illustrative example. 2000 Mathematics Subject Classification: 90C70,...