Computing with Words: Towards a New Tuple-Based Formalization

Authors

Olga Kosheleva, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow
Ariel Garcia, The University of Texas at El PasoFollow
Felipe Jovel, The University of Texas at El PasoFollow
Luis A. Torres Escobedo, The University of Texas at El PasoFollow
Thavatchai Ngamsantivong, King Mongkut's University of Technology North BangkokFollow

Publication Date

7-2013

Comments

Technical Report: UTEP-CS-13-31a

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

Abstract

An expert opinion describes his or her opinion about a quantity by using imprecise ("fuzzy") words from a natural language, such as "small", "medium", "large", etc. Each of these words provides a rather crude description of the corresponding quantity. A natural way to refine this description is to assign degrees to which the observed quantity fits each of the selected words. For example, an expert can say that the value is reasonable small, but to some extent it is medium. In this refined description, we represent each quantity by a tuple of the corresponding degrees.

Once we have such a tuple-based information about several quantities x₁, ..., x_m, and we know that another quantity y is related to x_i by a known relation y=f(x₁, ..., x_m), it is desirable to come up with a resulting tuple-based description of y. In this paper, we describe why a seemingly natural idea for computing such a tuple does not work, and we show how to modify this idea so that it can be used.