Towards Discrete Interval, Set, and Fuzzy Computations

Authors

Enrique Portillo, The University of Texas at El PasoFollow
Olga Kosheleva, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

7-2013

Comments

Technical Report: UTEP-CS-13-23a

To appear in Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics IEEE SMC'2013, Manchester, UK, October 13-16, 2013.

Abstract

In many applications, we know the function f(x1,...,xn), we know the intervals [xi] of possible values of each quantity xi, and we are interested in the range of possible values of y=f(x1,...,xn); this problem is known as the problem of interval computations. In other applications, we know the function f(x1,...,xn), we know the fuzzy sets Xi that describe what we know about each quantity xi, and we are interested in finding the fuzzy set Y corresponding to the quantity y=f(x1,...,xn); this problem is known as the problem of fuzzy computations. There are many efficient algorithms for solving these problems; however, most of these algorithms implicitly assume that each quantity xi can take any real value within its range. In practice, some quantities are discrete: e.g., xi can describe the number of people. In this paper, we provide feasible algorithms for interval, set, and fuzzy computations for such discrete inputs.