Paper Info
Title
Extended Fuzzy Logic: Sets and Systems
Abstract
The concepts of sets and approximate reasoning within extended fuzzy logic (FLe) provide a systematic procedure for transforming unprecisiated knowledge into a nonlinear mapping over what we define here as f-sets. An f-set differs from a fuzzy set in that it is associated with the restriction of validity in addition to that of possibility. Therefore, by f-set, we can simultaneously deal with two different types of uncertainties: one that is related to ill-known objects represented by incomplete information—information with its one or more aspects being imprecise/vague/partial/nonspecific/undetermined—and another that is related to truth values considering gradualness. Here, we define new concepts of ????????????-cuts and ????????????????????????-cuts, introduce the fextension principle, and consider arithmetic computations within FLe. We then address other aspects of the proposed FLe system such as fuzzification and validification operations in input processing stage, set-conversion and defuzzification in output processing stage, and inferencing. In fact, in this paper, we intend to develop FLe theoretically and practically from the stands of sets and systems to extend the concept of approximate reasoning. As a consequence of this development, we assert that considering the validity degree of methods and information can lead to more reasonable and trustworthy results through capturing more uncertainty.
Year
DOI
Venue
2016
10.1109/TFUZZ.2015.2453994
IEEE Trans. Fuzzy Systems
Keywords
Field
DocType
Approximate Reasoning,Extension Principle,Validity
Defuzzification,Fuzzy set operations,Fuzzy logic,Fuzzy set,Artificial intelligence,Fuzzy number,Fuzzy associative matrix,Type-2 fuzzy sets and systems,Membership function,Machine learning,Mathematics
Journal
Volume
Issue
ISSN
PP
99
1063-6706
Citations 
PageRank 
References 
7
0.46
15
Authors
2
Name
Order
Citations
PageRank
Farnaz Sabahi1211.08
Mohammad R. Akbarzadeh-Totonchi212518.26