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Fuzzy Locating Code and Dominating Sets for Optimized Sensor Deployment in Uncertain Environments.

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Title: Fuzzy Locating Code and Dominating Sets for Optimized Sensor Deployment in Uncertain Environments.
Authors: Shanmugapriya, R.1 spriyasathish11@gmail.com, Amuthini, D.2 damuthini@gmail.com
Source: IAENG International Journal of Applied Mathematics. Mar2026, Vol. 56 Issue 3, p1117-1122. 6p.
Subjects: Fuzzy graphs, Dominating set, Sensor networks, Mathematical optimization, Fuzzy sets, Graph theory
Abstract: In this work, we use fuzzy graph theory to introduce the concept of a fuzzy locating dominating set. Let fG(V, σ, μ) be simple, connected fuzzy graphs. Consider a nonempty fuzzy subset D ⊆ V (fG) of vertices. For each vertex v ∈ V\D, its relationship with the vertices of D is described by a strength vector formed using the maximum strength of connectedness to the vertices in D. The set D is called a fuzzy locating dominating set (FLDS) if it satisfies two conditions: first, every vertex in the graph is strongly dominated by at least one vertex in D second, any two vertices outside D can be distinguished by their strength vectors with respect to D. The minimum possible size of such a set is defined as the fuzzy locating domination number, denoted by γL(fG). [ABSTRACT FROM AUTHOR]
Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Fuzzy Locating Code and Dominating Sets for Optimized Sensor Deployment in Uncertain Environments.
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  Data: <searchLink fieldCode="AR" term="%22Shanmugapriya%2C+R%2E%22">Shanmugapriya, R.</searchLink><relatesTo>1</relatesTo><i> spriyasathish11@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Amuthini%2C+D%2E%22">Amuthini, D.</searchLink><relatesTo>2</relatesTo><i> damuthini@gmail.com</i>
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  Data: <searchLink fieldCode="JN" term="%22IAENG+International+Journal+of+Applied+Mathematics%22">IAENG International Journal of Applied Mathematics</searchLink>. Mar2026, Vol. 56 Issue 3, p1117-1122. 6p.
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  Data: <searchLink fieldCode="DE" term="%22Fuzzy+graphs%22">Fuzzy graphs</searchLink><br /><searchLink fieldCode="DE" term="%22Dominating+set%22">Dominating set</searchLink><br /><searchLink fieldCode="DE" term="%22Sensor+networks%22">Sensor networks</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+optimization%22">Mathematical optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Fuzzy+sets%22">Fuzzy sets</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink>
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  Data: In this work, we use fuzzy graph theory to introduce the concept of a fuzzy locating dominating set. Let fG(V, σ, μ) be simple, connected fuzzy graphs. Consider a nonempty fuzzy subset D ⊆ V (fG) of vertices. For each vertex v ∈ V\D, its relationship with the vertices of D is described by a strength vector formed using the maximum strength of connectedness to the vertices in D. The set D is called a fuzzy locating dominating set (FLDS) if it satisfies two conditions: first, every vertex in the graph is strongly dominated by at least one vertex in D second, any two vertices outside D can be distinguished by their strength vectors with respect to D. The minimum possible size of such a set is defined as the fuzzy locating domination number, denoted by γL(fG). [ABSTRACT FROM AUTHOR]
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  Label:
  Group: Ab
  Data: <i>Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Text: English
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        PageCount: 6
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      – SubjectFull: Fuzzy graphs
        Type: general
      – SubjectFull: Dominating set
        Type: general
      – SubjectFull: Sensor networks
        Type: general
      – SubjectFull: Mathematical optimization
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      – SubjectFull: Fuzzy sets
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      – SubjectFull: Graph theory
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      – TitleFull: Fuzzy Locating Code and Dominating Sets for Optimized Sensor Deployment in Uncertain Environments.
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              Text: Mar2026
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