Generated necessities and possibilities

✍ Scribed by Loredana Biacino; Giangiacomo Gerla

• Publisher: John Wiley and Sons
• Year: 1992
• Tongue: English
• Weight: 502 KB
• Volume: 7
• Category: Article
• ISSN: 0884-8173
• DOI: 10.1002/int.4550070504

✦ Synopsis

A necessity measure is a function n from a Boolean algebra B to the real interval [0,1] such that n(x A y ) = min{n(x),n(y)} for every x , y E B and n(0) = 0, n( 1) = I. Necessities are strictly related to Shafer's consonant belief functions and are basic tools when dealing with imprecision and uncertainty. In this article we propose a technique to generate necessities given a collection of items of information quantified by an initial valuation. The method we employ enables us to define conditional necessities in a very natural way and the composition of two necessities by a rule analogous to Dempster's rule. This is obtained by skipping the condition n(0) = 0 and therefore considering necessities with a nonzero "degree of inconsistency."