Some Topological and Algebraic Properties of alpha-level Subsets' Topology of a Fuzzy Subset

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60162694%3AG43__%2F18%3A00536239" target="_blank" >RIV/60162694:G43__/18:00536239 - isvavai.cz</a>

Výsledek na webu

<a href="https://drive.google.com/drive/folders/1-1mM9UuI3RRE5aAi3PyuF1J4Llw_aveG?usp=sharing" target="_blank" >https://drive.google.com/drive/folders/1-1mM9UuI3RRE5aAi3PyuF1J4Llw_aveG?usp=sharing</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.2478/auom-2018-0042" target="_blank" >10.2478/auom-2018-0042</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Some Topological and Algebraic Properties of alpha-level Subsets' Topology of a Fuzzy Subset

Popis výsledku v původním jazyce

The theory of fuzzy sets, since its foundation, has advanced in a wide range of means and in many fields. One of the areas to which fuzzy set theory has been applied extensively is mathematical programming. Nevertheless, the applications of fuzzy theory can be found in e.g. logic, decision theory, artificial intelligence, computer science, control engineering, expert systems, management science, operations research, robotics, and others. Theoretical improvements have been made in many directions. Nowadays it has a lot of applications also on possibility theory, actuarial credibility theory, fuzzy logic and approximate reasoning, fuzzy control, fuzzy data analysis, fuzzy set models in operations research, etc. The aim of this paper is to investigate some topological properties of a set X when the topology defined on it is the collection of all the alpha-level subsets of a fuzzy subset A of X. We have been able to establish some results regarding fuzzy cluster level subsets, convergence of level subsets and quasicompactness among others.

Název v anglickém jazyce

Some Topological and Algebraic Properties of alpha-level Subsets' Topology of a Fuzzy Subset

Popis výsledku anglicky

The theory of fuzzy sets, since its foundation, has advanced in a wide range of means and in many fields. One of the areas to which fuzzy set theory has been applied extensively is mathematical programming. Nevertheless, the applications of fuzzy theory can be found in e.g. logic, decision theory, artificial intelligence, computer science, control engineering, expert systems, management science, operations research, robotics, and others. Theoretical improvements have been made in many directions. Nowadays it has a lot of applications also on possibility theory, actuarial credibility theory, fuzzy logic and approximate reasoning, fuzzy control, fuzzy data analysis, fuzzy set models in operations research, etc. The aim of this paper is to investigate some topological properties of a set X when the topology defined on it is the collection of all the alpha-level subsets of a fuzzy subset A of X. We have been able to establish some results regarding fuzzy cluster level subsets, convergence of level subsets and quasicompactness among others.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

An. St. Univ. Ovidius Constanta

ISSN

1224-1784

e-ISSN

1844-0835

Svazek periodika

26

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

RO - Rumunsko

Počet stran výsledku

15

Strana od-do

213-227

Kód UT WoS článku

000453259100014

EID výsledku v databázi Scopus

—