Updating non-additive measures with fuzzy information

✍ Scribed by Virginia R. Young; Shaun S. Wang

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 589 KB
• Volume: 94
• Category: Article
• ISSN: 0165-0114
• DOI: 10.1016/s0165-0114(96)00238-2

✦ Synopsis

We present several rules for updating non-additive set functions, defined and conditioned on fuzzy sets. Among these formulas are the Dempster-Shafer rule for belief functions and the Bayes' conditioning rule. We develop the update formulas in the framework of non-additive measure and integration theory; thus, we generalize the work of Denneberg (1994). We explore the properties of the update rules and relate them to measures of (weak) fuzzy subsethood and to fuzzy inference operators. Specifically, we connect the Bayes' update rule with Kosko's measure of fuzzy subsethood and with Mamdani's implication operator. Also, we connect the Dempster-Shafer update rule with the weak inclusion measure of fuzzy subsethood and with a well-known implication operator.