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Soft Computing: Theories and Applications pp 85–95Cite as

The Min-transitive Fuzzy Left-Relation \(\lambda _d(A, B)\) on Intervals: A Generalization of \(\lambda (A, B)\)

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1053))

Abstract

We present a powerful generalization \(\lambda _d(A, B)\) of the min-transitive fuzzy left-relation \(\lambda (A, B)\) on finite intervals, where the parameter d is a weight-distribution function for the points of A and B. For many applications, \(\lambda _d(A, B)\) and \(\lambda (A, B)\) are better models of “left” (“<”) for intervals than the min-transitive fuzzy relation \({\textit{Left}}(A, B)\) and they are also more well-behaved in several ways than \({\textit{Left}}(A, B)\).

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Notes

  1. 1.

    We used the notation \(\mu ^s_N(A, B)\) in [7] for \(\lambda (A, B)\). It was derived from the non-min-transitive left-relation \(\mu _N(A, B)\), which was in turn derived from ideas in [8].

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Authors and Affiliations

  1. Computer Science and Engineering, Louisiana State University, Baton Rouge, LA, 70803, USA

    Sukhamay Kundu

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  1. Sukhamay Kundu
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Correspondence to Sukhamay Kundu .

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Editors and Affiliations

  1. Department of Paper Technology, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    Millie Pant

  2. Department of Computer Science and Engineering, Amity School of Engineering and Technology, Amity University Rajasthan, Jaipur, Rajasthan, India

    Tarun K. Sharma

  3. Department of Instrumentation and Control Engineering, Dr. B. R. Ambedkar National Institute of Technology, Jalandhar, Punjab, India

    Om Prakash Verma

  4. Dr. B. R. Ambedkar National Institute of Technology, Jalandhar, Punjab, India

    Rajesh Singla

  5. Dr. B. R. Ambedkar National Institute of Technology, Jalandhar, Punjab, India

    Afzal Sikander

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Kundu, S. (2020). The Min-transitive Fuzzy Left-Relation \(\lambda _d(A, B)\) on Intervals: A Generalization of \(\lambda (A, B)\). In: Pant, M., Sharma, T., Verma, O., Singla, R., Sikander, A. (eds) Soft Computing: Theories and Applications. Advances in Intelligent Systems and Computing, vol 1053. Springer, Singapore. https://doi.org/10.1007/978-981-15-0751-9_8

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