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

Mendel, Jerry M.; Wu, Hongwei

doi:10.1109/tfuzz.2006.881441

Cited by 198 publications

(103 citation statements)

References 9 publications

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“…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.…”

Section: Midpoint-radius Formatmentioning

confidence: 99%

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

Marín

Defour

Milano

2016

ACM Trans. Math. Softw.

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This paper addresses the execution cost of arithmetic operations with a focus on fuzzy arithmetic. Thanks to an appropriate representation format for fuzzy intervals, we show that it is possible to halve the number of operations and divide by 2 to 8 the memory requirements compared to conventional solutions. In addition, we demonstrate the benefit of some hardware features encountered in today's accelerators (GPU) such as static rounding, memory usage, instruction level parallelism (ILP) and thread-level parallelism (TLP). We then describe a library of fuzzy arithmetic operations written in CUDA and C++. The library is evaluated against traditional approaches using compute-bound and memory-bound benchmarks on Nvidia GPUs, with an observed performance gain of 2 to 20.

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Section: Midpoint-radius Formatmentioning

confidence: 99%

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

Marín

Defour

Milano

2016

ACM Trans. Math. Softw.

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“…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…”

Section: Relation To Other Extensionsmentioning

confidence: 99%

A Survey of Interval‐Valued Fuzzy Sets

Bustince

Montero

Pagola

et al. 2008

Handbook of Granular Computing

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“…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…”

Section: N) Denote the Endpoints Of The Intervals Of X I And Wmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

The Linguistic Weighted Average

Mendel

2006

2006 IEEE International Conference on Fuzzy Systems

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Abstract-The focus of this paper is the linguistic weighted average (LWA), which is a generalization of the fuzzy weighted average (FWA) that is obtained by replacing the type-1 fuzzy inputs in the FWA by interval type-2 fuzzy sets (IT2 FSs). Consequently, the output of the LWA is an IT2 FS. In this paper, the relations between the LWA and the FWA are studied. It is shown that finding the LWA can be decomposed into finding two FWAs, where α-cuts and KM algorithms are used. Hence, the computational cost of a LWA is about twice that of a FWA. A flowchart for computing the LWA is also provided.

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

Cited by 198 publications

References 9 publications

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

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

A Survey of Interval‐Valued Fuzzy Sets

The Linguistic Weighted Average

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