Counting of finite fuzzy subsets with applications to fuzzy recognition and selection strategies
- Authors: Talwanga, Matiki
- Date: 2015
- Subjects: Möbius transformations , Fuzzy sets , Functions, Zeta , Partitions (Mathematics)
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:5431 , http://hdl.handle.net/10962/d1018186
- Description: The counting of fuzzy subsets of a finite set is of great interest in both practical and theoretical contexts in Mathematics. We have used some counting techniques such as the principle of Inclusion-Exclusion and the Mõbius Inversion to enumerate the fuzzy subsets of a finite set satisfying different conditions. These two techniques are interdependent with the M¨obius inversion generalizing the principle of Inclusion-Exclusion. The enumeration is carried out each time we redefine new conditions on the set. In this study one of our aims is the recognition and identification of fuzzy subsets with same features, characteristics or conditions. To facilitate such a study, we use some ideas such as the Hamming distance, mid-point between two fuzzy subsets and cardinality of fuzzy subsets. Finally we introduce the fuzzy scanner of elements of a finite set. This is used to identify elements and fuzzy subsets of a set. The scanning process of identification and recognition facilitates the choice of entities with specified properties. We develop a procedure of selection under the fuzzy environment. This allows us a framework to resolve conflicting issues in the market place.
- Full Text:
- Date Issued: 2015
The principle of inclusion-exclusion and möbius function as counting techniques in finite fuzzy subsets
- Authors: Talwanga, Matiki
- Date: 2009
- Subjects: Fuzzy logic , Fuzzy sets , Fuzzy systems , Möbius function
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5413 , http://hdl.handle.net/10962/d1005227 , Fuzzy logic , Fuzzy sets , Fuzzy systems , Möbius function
- Description: The broad goal in this thesis is to enumerate elements and fuzzy subsets of a finite set enjoying some useful properties through the well-known counting technique of the principle of inclusion-exclusion. We consider the set of membership values to be finite and uniformly spaced in the real unit interval. Further we define an equivalence relation with regards to the cardinalities of fuzzy subsets providing the Möbius function and Möbius inversion in that context.
- Full Text:
- Date Issued: 2009