Fuzzification of crisp domains

Title:

Fuzzification of crisp domains

Creator:

Frič, Roman and Papčo, Martin

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:8bce134e-c301-4f07-b276-9d16ae5329e6
uuid:8bce134e-c301-4f07-b276-9d16ae5329e6

Subject:

domain of probability, fuzzy random variable, crisp random event, fuzzy observable, fuzzification, category of ID-poset, epireflection, and simplex-valued domains

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

The present paper is devoted to the transition from crisp domains of probability to fuzzy domains of probability. First, we start with a simple transportation problem and present its solution. The solution has a probabilistic interpretation and it illustrates the transition from classical random variables to fuzzy random variables in the sense of Gudder and Bugajski. Second, we analyse the process of fuzzification of classical crisp domains of probability within the category ID of D-posets of fuzzy sets and put into perspective our earlier results concerning categorical aspects of fuzzification. For example, we show that (within ID) all nontrivial probability measures have genuine fuzzy quality and we extend the corresponding fuzzification functor to an epireflector. Third, we extend the results to simplex-valued probability domains. In particular, we describe the transition from crisp simplex-valued domains to fuzzy simplex-valued domains via a "simplex'' modification of the fuzzification functor. Both, the fuzzy probability and the simplex-valued fuzzy probability is in a sense minimal extension of the corresponding crisp probability theory which covers some quantum phenomenon.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

[1009]-1024

Source:

Kybernetika | 2010 Volume:46 | Number:6

Harvested from:

CDK

Metadata only:

false