The Discrete Basis Problem and Asso Algorithm for Fuzzy Attributes

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F19%3A73595300" target="_blank" >RIV/61989592:15310/19:73595300 - isvavai.cz</a>

Výsledek na webu

<a href="https://ieeexplore.ieee.org/abstract/document/8528862" target="_blank" >https://ieeexplore.ieee.org/abstract/document/8528862</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1109/TFUZZ.2018.2880418" target="_blank" >10.1109/TFUZZ.2018.2880418</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The Discrete Basis Problem and Asso Algorithm for Fuzzy Attributes

Popis výsledku v původním jazyce

We present an extension of the discrete basis problem, recently a profoundly studied problem, from the Boolean setting to the setting of fuzzy attributes, i.e., a setting of ordinal data. Our problem consists in finding for a given object-attribute matrix I containing truth degrees and a prescribed number k of factors the best approximate decomposition of I into an object-factor matrix A and a factor-attribute matrix B. Since such matrices represent fuzzy relations, the problem is related to but very different from that of decomposition of fuzzy relations as studied in fuzzy relational equations because neither A nor B are supposed to be known in our problem. We observe that our problem is NP-hard as an optimization problem. Consequently, we provide an approximation algorithm for solving this problem and provide its time complexity in the worst case. The algorithm is inspired by the Asso algorithm, which is known for Boolean attributes and is based on new considerations regarding associations among fuzzy attributes. We provide an experimental evaluation on various datasets and demonstrate that our algorithm is capable of extracting informative factors in data. We conclude with a discussion regarding future research issues.

Název v anglickém jazyce

The Discrete Basis Problem and Asso Algorithm for Fuzzy Attributes

Popis výsledku anglicky

We present an extension of the discrete basis problem, recently a profoundly studied problem, from the Boolean setting to the setting of fuzzy attributes, i.e., a setting of ordinal data. Our problem consists in finding for a given object-attribute matrix I containing truth degrees and a prescribed number k of factors the best approximate decomposition of I into an object-factor matrix A and a factor-attribute matrix B. Since such matrices represent fuzzy relations, the problem is related to but very different from that of decomposition of fuzzy relations as studied in fuzzy relational equations because neither A nor B are supposed to be known in our problem. We observe that our problem is NP-hard as an optimization problem. Consequently, we provide an approximation algorithm for solving this problem and provide its time complexity in the worst case. The algorithm is inspired by the Asso algorithm, which is known for Boolean attributes and is based on new considerations regarding associations among fuzzy attributes. We provide an experimental evaluation on various datasets and demonstrate that our algorithm is capable of extracting informative factors in data. We conclude with a discussion regarding future research issues.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/GA15-17899S" target="_blank" >GA15-17899S: Rozklady matic s booleovskými a ordinálními daty: teorie a algoritmy</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

IEEE TRANSACTIONS ON FUZZY SYSTEMS

ISSN

1063-6706

e-ISSN

—

Svazek periodika

27

Číslo periodika v rámci svazku

7

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

11

Strana od-do

1417-1427

Kód UT WoS článku

000473644200008

EID výsledku v databázi Scopus

2-s2.0-85056324587