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The knowledge of determining equalities in sets is not equal in mathematical sense for all the users. Based on this concept Novotony and Pawlak (Bull Polish Acad Sci Math, 33:99–104, 1985; Bull Polish Acad Sci Math, 33:91–97, 1985; Bull Polish Acad Sci Math, 33, 99–104, 1985), introduce three kinds of approximate rough equalities. Later on, Tripathy et al. (On Rough Equalities and Rough Equivalence, LNAI, 5306:92–102, 2008) generalized theses notions to approximate rough equivalences sets. In contrast to rough equalities, rough equivalences capture a heightened level of equality between sets. The properties of these equivalence were extensively investigated by Tripathy et al. (Int J Artif Intell Soft Comput (Switzerland), 1, 271–289, 2009). Initially using rough set theory to analyse approximate equalities (Tripathy, Int J Adv Sci Technol, 31:23–36, 2011), Tripathy later transitioned to rough fuzzy sets, proposing four types of approximate equalities. Tripathy and Panda (Int J Comput Sci, 9, 2012) further extended this exploration by introducing approximate equalities grounded in rough intuitionistic fuzzy sets, providing a comprehensive analysis. This paper presents the introduction of approximate equalities and their analysis within the framework of rough neutrosophic set theory. Specifically, we introduce approximate equalities of rough neutrosophic sets and investigate their properties.

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Approximate Equalities Based on Rough Neutrosophic Set with Their Analysis

  • 会议论文

  • 发表日期：

    2026年

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  • Seema Singh,
  • Kuldeep Kumar Tiwari,
  • Navjot Kaur

摘要

The knowledge of determining equalities in sets is not equal in mathematical sense for all the users. Based on this concept Novotony and Pawlak (Bull Polish Acad Sci Math, 33:99–104, 1985; Bull Polish Acad Sci Math, 33:91–97, 1985; Bull Polish Acad Sci Math, 33, 99–104, 1985), introduce three kinds of approximate rough equalities. Later on, Tripathy et al. (On Rough Equalities and Rough Equivalence, LNAI, 5306:92–102, 2008) generalized theses notions to approximate rough equivalences sets. In contrast to rough equalities, rough equivalences capture a heightened level of equality between sets. The properties of these equivalence were extensively investigated by Tripathy et al. (Int J Artif Intell Soft Comput (Switzerland), 1, 271–289, 2009). Initially using rough set theory to analyse approximate equalities (Tripathy, Int J Adv Sci Technol, 31:23–36, 2011), Tripathy later transitioned to rough fuzzy sets, proposing four types of approximate equalities. Tripathy and Panda (Int J Comput Sci, 9, 2012) further extended this exploration by introducing approximate equalities grounded in rough intuitionistic fuzzy sets, providing a comprehensive analysis. This paper presents the introduction of approximate equalities and their analysis within the framework of rough neutrosophic set theory. Specifically, we introduce approximate equalities of rough neutrosophic sets and investigate their properties.