We establish relationships between the set of trapezoidal intuitionistic fuzzy numbers and the set of interval-valued trapezoidal fuzzy numbers and, on the other hand, between the set of triangular intuitionistic fuzzy numbers and the set of triangular fuzzy numbers. Based on these main results of the paper, the methods or procedures elaborated for interval-valued trapezoidal or triangular fuzz...

In this paper I will introduce the trapezoidal intuitionistic fuzzy numbers (IF numbers) and will prove some operations for them. Also I am going to propose a new ordering method for IF numbers in which I will consider two characteristic values of membership and non-membership functions for an IF number. These values are defined by the integral of the inverse fuzzy membership and non-membership...

Ranking fuzzy numbers is one of very important research topics in fuzzy set theory because it is a base of decision-making in all application areas. However, fuzzy numbers cannot be easily arranged in the order of magnitude because they represent uncertain and vague values. When two fuzzy numbers overlap with each other, a fuzzy number may not be considered absolutely larger than the other. Tha...

This paper proposes to study the lattice properties of two closed binary operations in the set of discrete fuzzy numbers. Using these operations to represent the meet and the join, we prove that the set of discrete fuzzy numbers whose support is a set of consecutive natural numbers is a distributive lattice. Finally, we demonstrate that the subsets of discrete fuzzy numbers, which have the same...

there are two interesting methods, in the literature, for solving fuzzy linear programming problems in which the elements of coefficient matrix of the constraints are represented by real numbers and rest of the parameters are represented by symmetric trapezoidal fuzzy numbers. the first method, named as fuzzy primal simplex method, assumes an initial primal basic feasible solution is at hand. t...

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...

In this paper, we present a new method for ranking generalized fuzzy numbers for dealing with fuzzy risk analysis problems. The proposed method considers the defuzzified values, the heights and the spreads of generalized fuzzy numbers, simultaneously, for ranking generalized fuzzy numbers. It gets better ranking results to rank generalized fuzzy numbers than the existing methods. We also apply ...

Nanda 1 studied sequence of fuzzy numbers and showed that the set of all convergent sequences of fuzzy numbers form a complete metric space. Nuray 2 proved the inclusion relations between the set of statistically convergent and lacunary statistically convergent sequences of fuzzy numbers. Kwon and Shim 3 studied statistical convergence and lacunary statistical convergence of sequences of fuzzy ...