A Note on the KM Algorithm for Computing the Variance of an Interval Type-2 Fuzzy Set

Juan Carlos Figueroa-García; Carlos Franco; Jhoan Sebastian Tenjo-García

doi:10.1007/978-3-030-82099-2_12

A Note on the KM Algorithm for Computing the Variance of an Interval Type-2 Fuzzy Set

Juan Carlos Figueroa-García
, Carlos Franco
, Jhoan Sebastian Tenjo-García

School of Business Administration

Research output: Chapter in Book/Inform › Chapter › Research

Abstract

This work presents some considerations about the computation of the relative variance for Interval Type-2 Fuzzy Sets. Based on experimental evidence, the computation of the relative variance of an interval Type-2 fuzzy set using the KM algorithm needs more computations than using the original KM algorithm in order to obtain their boundaries since the variance combined with the KM algorithm results in a nonlinear behavior. A modified KM algorithm for computing the relative variance of an interval type-2 fuzzy set is proposed and a comprehensive analysis of its behavior is provided through two examples.

Original language	English (US)
Title of host publication	Explainable AI and Other Applications of Fuzzy Techniques - Proceedings of the 2021 Annual Conference of the North American Fuzzy Information Processing Society, NAFIPS 2021
Editors	Julia Rayz, Victor Raskin, Scott Dick, Vladik Kreinovich
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	130-140
Number of pages	11
ISBN (Electronic)	978-3-030-82099-2
ISBN (Print)	9783030820985
DOIs	https://doi.org/10.1007/978-3-030-82099-2_12
State	Published - 2022
Event	Annual Conference of the North American Fuzzy Information Processing Society, NAFIPS 2021 - West Lafayette, United States Duration: Jun 7 2021 → Jun 9 2021

Publication series

Name	Lecture Notes in Networks and Systems
Volume	258
ISSN (Print)	2367-3370
ISSN (Electronic)	2367-3389

Conference

Conference	Annual Conference of the North American Fuzzy Information Processing Society, NAFIPS 2021
Country/Territory	United States
City	West Lafayette
Period	6/7/21 → 6/9/21

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 12 Responsible Consumption and Production

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Signal Processing
Computer Networks and Communications

Access to Document

10.1007/978-3-030-82099-2_12

Cite this

Figueroa-García, J. C., Franco, C., & Tenjo-García, J. S. (2022). A Note on the KM Algorithm for Computing the Variance of an Interval Type-2 Fuzzy Set. In J. Rayz, V. Raskin, S. Dick, & V. Kreinovich (Eds.), Explainable AI and Other Applications of Fuzzy Techniques - Proceedings of the 2021 Annual Conference of the North American Fuzzy Information Processing Society, NAFIPS 2021 (pp. 130-140). (Lecture Notes in Networks and Systems; Vol. 258). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-82099-2_12

Figueroa-García, Juan Carlos ; Franco, Carlos ; Tenjo-García, Jhoan Sebastian. / A Note on the KM Algorithm for Computing the Variance of an Interval Type-2 Fuzzy Set. Explainable AI and Other Applications of Fuzzy Techniques - Proceedings of the 2021 Annual Conference of the North American Fuzzy Information Processing Society, NAFIPS 2021. editor / Julia Rayz ; Victor Raskin ; Scott Dick ; Vladik Kreinovich. Springer Science and Business Media Deutschland GmbH, 2022. pp. 130-140 (Lecture Notes in Networks and Systems).

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abstract = "This work presents some considerations about the computation of the relative variance for Interval Type-2 Fuzzy Sets. Based on experimental evidence, the computation of the relative variance of an interval Type-2 fuzzy set using the KM algorithm needs more computations than using the original KM algorithm in order to obtain their boundaries since the variance combined with the KM algorithm results in a nonlinear behavior. A modified KM algorithm for computing the relative variance of an interval type-2 fuzzy set is proposed and a comprehensive analysis of its behavior is provided through two examples.",

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Figueroa-García, JC, Franco, C & Tenjo-García, JS 2022, A Note on the KM Algorithm for Computing the Variance of an Interval Type-2 Fuzzy Set. in J Rayz, V Raskin, S Dick & V Kreinovich (eds), Explainable AI and Other Applications of Fuzzy Techniques - Proceedings of the 2021 Annual Conference of the North American Fuzzy Information Processing Society, NAFIPS 2021. Lecture Notes in Networks and Systems, vol. 258, Springer Science and Business Media Deutschland GmbH, pp. 130-140, Annual Conference of the North American Fuzzy Information Processing Society, NAFIPS 2021, West Lafayette, United States, 6/7/21. https://doi.org/10.1007/978-3-030-82099-2_12

A Note on the KM Algorithm for Computing the Variance of an Interval Type-2 Fuzzy Set. / Figueroa-García, Juan Carlos; Franco, Carlos; Tenjo-García, Jhoan Sebastian.
Explainable AI and Other Applications of Fuzzy Techniques - Proceedings of the 2021 Annual Conference of the North American Fuzzy Information Processing Society, NAFIPS 2021. ed. / Julia Rayz; Victor Raskin; Scott Dick; Vladik Kreinovich. Springer Science and Business Media Deutschland GmbH, 2022. p. 130-140 (Lecture Notes in Networks and Systems; Vol. 258).

Research output: Chapter in Book/Inform › Chapter › Research

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Figueroa-García JC, Franco C, Tenjo-García JS. A Note on the KM Algorithm for Computing the Variance of an Interval Type-2 Fuzzy Set. In Rayz J, Raskin V, Dick S, Kreinovich V, editors, Explainable AI and Other Applications of Fuzzy Techniques - Proceedings of the 2021 Annual Conference of the North American Fuzzy Information Processing Society, NAFIPS 2021. Springer Science and Business Media Deutschland GmbH. 2022. p. 130-140. (Lecture Notes in Networks and Systems). doi: 10.1007/978-3-030-82099-2_12