## Abstract and Applied Analysis

- Abstr. Appl. Anal.
- Volume 2013 (2013), Article ID 736872, 8 pages.

### Some Types of Generalized Fuzzy $n$-Fold Filters in Residuated Lattices

#### Abstract

Fuzzy filters and their generalized types have been extensively studied in the literature. In this paper, a one-to-one correspondence between the set of all generalized fuzzy filters and the set of all generalized fuzzy congruences is established, a quotient residuated lattice with respect to generalized fuzzy filter is induced, and several types of generalized fuzzy $n$-fold filters such as generalized fuzzy $n$-fold positive implicative (fantastic and Boolean) filters are introduced; examples and results are provided to demonstrate the relations among these filters.

#### Article information

**Source**

Abstr. Appl. Anal., Volume 2013 (2013), Article ID 736872, 8 pages.

**Dates**

First available in Project Euclid: 27 February 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.aaa/1393512241

**Digital Object Identifier**

doi:10.1155/2013/736872

**Mathematical Reviews number (MathSciNet)**

MR3147858

#### Citation

Ma, Zhen Ming. Some Types of Generalized Fuzzy $n$ -Fold Filters in Residuated Lattices. Abstr. Appl. Anal. 2013 (2013), Article ID 736872, 8 pages. doi:10.1155/2013/736872. https://projecteuclid.org/euclid.aaa/1393512241