Title:

Developments in fuzzy sets, intuitionistic fuzzy sets, generalized nets and related topics. Volume I: Foundations * On fuzzy implications with ordered fuzzy numbers

Subtitle:

Książka = Book ; KS/5/2010/T1P13

Creator:

Kosiński, Witold ; Wilczyńska-Sztyma, Dorota

Publisher:

Instytut Badań Systemowych. Polska Akademia Nauk ; Systems Research Institute. Polish Academy of Sciences

Place of publishing:

Warszawa

Date issued/created:

2010

Description:

[5], 121-130 pages ; 21 cm ; Bibliography p. 128-130

Type of object:

Book/Chapter

Abstract:

Ordered fuzzy numbers (OFN) invented by the first author and his two coworkers in 2002 make possible to utilize the fuzzy arithmetic and to construct the Abelian group of fuzzy numbers and then an ordered ring. This new model of fuzzy numbers overcomes known drawbacks of classical convex fuzzy numbers and at the same time has the algebra of crisp (non-fuzzy) numbers inside. The definition of OFN uses the extension of the parametric representation of convex fuzzy numbers. Operation of addition and multiplication by a positive scalar defined on OFNs give the same result as addition and scalar multiplication of their corresponding convex fuzzy numbers, if the numbers have the same orientation. However, subtraction, multiplication and division give quit different results for interval arithmetic and presented new algebra of OFNs. Fuzzy implications are discussed. With the help of a perceptron that realizes the classical binary implication a new fuzzy implication with ordered fuzzy numbers is proposed.

Relation:

Książka = Book

Resource type:

Text

Detailed Resource Type:

Book

Source:

KS-2010-05-T1P13

Language:

eng

Language of abstract:

eng

Rights:

Creative Commons Attribution BY 4.0 license

Terms of use:

Copyright-protected material. [CC BY 4.0] May be used within the scope specified in Creative Commons Attribution BY 4.0 license, full text available at: ; -

Digitizing institution:

Systems Research Institute of the Polish Academy of Sciences

Original in:

Library of Systems Research Institute PAS

Projects co-financed by:

Operational Program Digital Poland, 2014-2020, Measure 2.3: Digital accessibility and usefulness of public sector information; funds from the European Regional Development Fund and national co-financing from the state budget.

Access:

Open