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An Analysis of Generalised Approximate Equalities Based on Rough Fuzzy Sets

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Proceedings of the International Conference on Soft Computing for Problem Solving (SocProS 2011) December 20-22, 2011

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 130))

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Abstract

Three types of rough equalities were introduced by Novotny and Pawlak ([7, 8,9]), which take care of approximate equalities of sets. These sets may not be equal in the usual sense. These notions were generalized by Tripathy, Mitra and Ojha ([12]), who introduced the concepts of rough equivalences of sets. These approximate equalities of sets capture equality of the concerned sets at a higher level than their corresponding rough equalities. Some more properties were proved in [13]. Two more approximate equalities were introduced by Tripathy [11] and comparative analysis of their efficiency was provided. In this paper, we generalise these approximate equalities by considering rough fuzzy sets instead of only rough sets. A concept of leveled approximate equality is introduced and properties are studied. We also provide suitable examples to illustrate the applications of the new notions and provide an analysis of their relative efficiency.

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Authors and Affiliations

  1. SCSE, VIT University, Vellore, 632014, Tamilnadu, India

    B. K. Tripathy, Abhishek Jhawar & Ekta Vats

Authors
  1. B. K. Tripathy
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  2. Abhishek Jhawar
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  3. Ekta Vats
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Correspondence to B. K. Tripathy .

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Editors and Affiliations

  1. , Department of Mathematics, Indian Institute of Technology Roorkee, Uttarakhand, Roorkee, 247667, India

    Kusum Deep

  2. Department of Mathematics and, Computer Science, Liverpool Hope University, Hope Park, Liverpool, L16 9JD, United Kingdom

    Atulya Nagar

  3. , Department of Paper Technology, Indian Institute of Technology Roorkee, Uttarakhand, Roorkee, 247667, India

    Millie Pant

  4. Information Technology and Management, ABV-Indian Institute of, 109, E- Block, Gwalior, 474010, India

    Jagdish Chand Bansal

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Tripathy, B.K., Jhawar, A., Vats, E. (2012). An Analysis of Generalised Approximate Equalities Based on Rough Fuzzy Sets. In: Deep, K., Nagar, A., Pant, M., Bansal, J. (eds) Proceedings of the International Conference on Soft Computing for Problem Solving (SocProS 2011) December 20-22, 2011. Advances in Intelligent and Soft Computing, vol 130. Springer, India. https://doi.org/10.1007/978-81-322-0487-9_32

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  • DOI: https://doi.org/10.1007/978-81-322-0487-9_32

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  • Print ISBN: 978-81-322-0486-2

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