Type-2 Fuzzistics for Symmetric Interval Type-2 Fuzzy Sets: Part 1, Forward Problems

An Efficient Representation Format for Fuzzy Intervals Based on Symmetric Membership Functions

“…This section considers a membership function symmetric with respect to a vertical axis, which is of particular relevance in several fuzzy arithmetic applications [Chang and Wu 1995;Mendel and Wu 2006]. For symmetric membership functions, all α-cuts are centered on the kernel, which leads to relevant properties that are exploited by the proposed implementation.…”

A Survey of Interval‐Valued Fuzzy Sets

“…In [17,[31][32][33], it turns out that an interval type 2 fuzzy set is the same as an IVFS if we take a = 1. Handbook of Granular Computing…”

The Linguistic Weighted Average

“…Using KM algorithms [5], [9] presented in [15], f L (α j ) and f R (α j ) can be efficiently computed as (11) and (12) (given at the top of this page), where k L and k R are switch points satisfying…”

“…Dongrui Wu and Jerry M. Mendel are with the Department of Electrical Engineering-Systems, University of Southern California, Los Angeles, CA 90089-2564, USA (phone: 213-740-4445; fax: 213-740-4651; email: dongruiw@usc.edu, mendel@sipi.usc.edu). 1 How to obtain IT2 FS models for words is an on-going research area, and one method for doing this can be found in [11] and [12]. In this paper, we assume that such models have already been established.…”