In the paper, we consider interval linear algebraic systems of equations Ax = b, with an interval matrix A and interval right-hand side vector b, as a model of imprecise systems of linear algebraic equations of the same form. We propose a new regularization procedure that reduces the solution of the imprecise linear system to computing a point from the tolerable solution set for the interval li...

Abstract – In this paper, we introduce a Satisfaction Function (SF) to compare interval values on the basis of Tseng and Klein’s idea. The SF estimates the degree to which arithmetic comparisons between two interval values are satisfied. Then, we define two other functions called Lower and Upper SF based on the SF. We apply these functions in order to present a new interpretation of inequality ...

In this paper, a preference aggregation method is developed for ranking alternative courses of actions by combining preference rankings of alternatives given on individual criteria or by individual decision makers. In the method, preference rankings are viewed as constraints on alternative utilities, which are normalized, and linear programming models are constructed to estimate utility interva...

Upper and lower regression models (dual possibilistic models) are proposed for data analysis with crisp inputs and interval or fuzzy outputs. Based on the given data, the dual possibilistic models can be derived from upper and lower directions, respectively, where the inclusion relationship between these two models holds. Thus, the inherent uncertainty existing in the given phenomenon can be ap...

In this paper, we study the classical sensitivity analysis when the right - hand – side vector, and the coefficients of the objective function are allowed to vary. 

Optimization methods have been widely applied in statistics. Among them, capability measuring techniques are widely applied in industries. Process Capability Indices (PCIs) have been proposed for measuring process production capability. This paper concentrates, the lower and upper confidence limits for the PCIs are obtained from generalized pivotal quantity of random model and also, use this co...

The Netlib library of linear programming problems is a well known suite containing many real world applications. Recently it was shown by Ordóñez and Freund that 71% of these problems are ill-conditioned. Hence, numerical difficulties may occur. Here, we present rigorous results for this library that are computed by a verification method using interval arithmetic. In addition to the original in...