From Interval Arithmetic to Interval Constraints

Arithmetic Aggregation Operators for Interval-valued Intuitionistic Linguistic Variables and Application to Multi-attribute Group Decision Making

The intuitionistic linguistic set (ILS) is an extension of linguisitc variable. To overcome the drawback of using single real number to represent membership degree and non-membership degree for ILS, the concept of interval-valued intuitionistic linguistic set (IVILS) is introduced through representing the membership degree and non-membership degree with intervals for ILS in this paper. The oper...

A Unified Framework for Interval Constraints and Interval Arithmetic

We are concerned with interval constraints: solving constraints among real unknowns in such a way that soundness is not aaected by rounding errors. The contraction operator for the constraint x + y = z can simply be expressed in terms of interval arithmetic. An attempt to use the analogous deenition for x y = z fails if the usual deenitions of interval arithmetic are used. We propose an alterna...

Exact soultion of full interval linear equation AX=B based on Kaucher arithmetic

Author's personal copy Resolution of nonlinear interval problems using symbolic interval arithmetic

An interval problem is a problemwhere the unknown variables take interval values. Such a problem can be defined by interval constraints, such as ‘‘the interval 1⁄2a; bŠ 1⁄2a; bŠ ’’. Interval problems often appear when we want to analyze the behavior of an interval solver. To solve interval problems, we propose to transform the constraints on intervals into constraints on their bounds. For insta...

Resolution of nonlinear interval problems using symbolic interval arithmetic

An interval problem is a problem where the unknown variables take interval values. Such a problem can be defined by interval constraints, such as "the interval [a, b] ⊂ [a, b]2". Interval problems often appear when we want to analyze the behavior of an interval solver. To solve interval problems, we propose to transform the constraints on intervals into constraints on their bounds. For instance...

Providing a Method for Solving Interval Linear Multi-Objective Problems Based on the Goal Programming Approach

Most research has focused on multi-objective issues in its definitive form, with decision-making coefficients and variables assumed to be objective and constraint functions. In fact, due to inaccurate and ambiguous information, it is difficult to accurately identify the values of the coefficients and variables. Interval arithmetic is appropriate for describing and solving uncertainty and inaccu...