Title:

New developments in fuzzy sets, intuitionistic fuzzy sets, generalized nets and related topics. Volume I: Foundations * Fuzzy logical connectives in approximate reasoning. dual operations

Subtitle:

Książka = Book ; KS/3/2012/T1P[3]

Creator:

Drewniak, Józef

Publisher:

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

Place of publishing:

Warszawa

Date issued/created:

2012

Description:

[6], 41-59 pages ; 21 cm ; Bibliography p. 58-59

Type of object:

Book/Chapter

Abstract:

This paper concerns applications of Duality Principle in fuzzy algebra, fuzzy logics and approximate reasoning. Usually dual definitions, theorems, proofs and examples are neglected, omitted or left as a simple exercise. They are treated as an image in mirror. However, such opinion can be quite false, because duality is an equivalence relation. Thus both dual objects are equally important or non important. It can be easy seen in the case of linear programming: one handbook describesmainly maximization of linear functionals, while another concentrates on minimization. We tray to fill up this gap in treating of dual objects by presentation of examples of important dual notions and properties from lattice theory to relation theory and from fuzzy logic to fuzzy relational equations. In particular we describe properties of dual connectives of multivalued logic and summarize properties of dual relation compositions. Finally, a similarity between fuzzy coimplication and poset difference is analyzed.

Relation:

Książka = Book

Resource type:

Text

Detailed Resource Type:

Book

Source:

KS-2012-03-T1P[3]

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