Fuzzy sets and logic have been largely used for the treatment of the uncertainty, vagueness and ambiguity found in the modeling of real problems. However, there may exist also the case when there is uncertainty related to the membership functions to be used in the modeling of fuzzy sets and fuzzy numbers, as there are many ways to define the shape of this kind of number. Thus, one can use, for ...

In this paper, we investigate the existence of a positive solution of fully fuzzy linear equation systems. This paper mainly to discuss a new decomposition of a nonsingular fuzzy matrix, the symmetric times triangular (ST) decomposition. By this decomposition, every nonsingular fuzzy matrix can be represented as a product of a fuzzy symmetric matrix S and a fuzzy triangular matrix T.

The concept of duality plays an important role in optimization theory .In this paper, a new method is proposed to find the fuzzy optimal solution of fully fuzzy linear programming problems using breaking point and duality theory. By using the proposed method the fuzzy optimal solution of fully fuzzy linear programming problem with inequality constraints has been obtained. To illustrate the prop...

Statistical Quality Control is a valuable strategy that applies to the statistical technique for monitoring manufacturing system under particular situations. On other hand, fuzzy set theory an ideal instrument cope with unclear situation. The existing studies are restricted, and there still mystery behind data. This paper deals technique: namely, control chart based on process capability indice...

With respect to multiple attribute decision making problem with triangular fuzzy linguistic information, in which the attribute weights and expert weights take the form of real numbers, and the preference values take the form of triangular fuzzy linguistic variables, a operator for aggregating triangular fuzzy linguistic variables, such as the fuzzy linguistic weighted harmonic mean (FLWHM) ope...

The basic transportation problem was originally developed by Hitchcock. In the literature several methods are proposed for solving Fuzzy transportation problem. In this paper, we propose a new algorithm called Fuzzy Russell’s method for the initial basic feasible solution to a Fuzzy transportation problem. To examine the proposed method a numerical example is solved. Fuzzy numbers may be normal...

In this paper, for an arbitrary multiplicative functional f from the set of all upper triangular fuzzy matrices to the fuzzy algebra, we prove that there exist a multiplicative functional F and a functional G from the fuzzy algebra to the fuzzy algebra such that the image of an upper triangular fuzzy matrix under f can be represented as the product of all the images of its main diagonal element...

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...

DEA (Data Envelopment Analysis) is a technique for evaluating the relative effectiveness of decision-making units (DMU) with multiple inputs and outputs data based on non-parametric modeling using mathematical programming (including linear programming, multi-parameter programming, stochastic programming, etc.). The classical DEA methods are developed to handle the information in the form of cri...

This paper examines type-2 fuzzy arithmetic using interval analysis. It relies heavily on alpha-cuts and alpha-planes. Furthermore, we discuss the use of quasi type-2 fuzzy sets proposed by Mendel and Liu and define quasi type-2 fuzzy numbers. Arithmetic operations of such numbers are defined and a worked example is presented. Keywords— Fuzzy Arithmetic, Type-2 Fuzzy Arithmetic, Type-2 Fuzzy Nu...