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Foundational theories of hesitant fuzzy sets and families of hesitant fuzzy sets (2311.04256v4)

Published 7 Nov 2023 in cs.AI, cs.IT, cs.LG, and math.IT

Abstract: Hesitant fuzzy sets find extensive application in specific scenarios involving uncertainty and hesitation. In the context of set theory, the concept of inclusion relationship holds significant importance as a fundamental definition. Consequently, as a type of sets, hesitant fuzzy sets necessitate a clear and explicit definition of the inclusion relationship. Based on the discrete form of hesitant fuzzy membership degrees, this study proposes multiple types of inclusion relationships for hesitant fuzzy sets. Subsequently, this paper introduces foundational propositions related to hesitant fuzzy sets, as well as propositions concerning families of hesitant fuzzy sets.

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References (36)
  1. Perceptual maps to aggregate assessments from different rating profiles: A hesitant fuzzy linguistic approach. Applied Soft Computing, 147:110803, 2023.
  2. K. T. Atanassov. Intuitionistic fuzzy sets. Fuzzy Sets And Systems, 32:87–96, 1986.
  3. Hesitant fuzzy soft sets. Journal of New Results in Science, 3:98–107, 2013.
  4. E. J. Barbeau. University of Toronto Mathematics Competition (2001-2015), Problem Books in Mathematics book series. Springer Press, 2016.
  5. Measures of embedding for interval-valued fuzzy sets. Fuzzy Sets and Systems, 467:108505, 2023.
  6. Decomposition theorems and extension principles for hesitant fuzzy sets. Information Fusion, 41:48–56, 2018.
  7. Interval-valued fuzzy discernibility pair approach for attribute reduction in incomplete interval-valued information systems. Information Sciences, 642:119215, 2023.
  8. Balanced scorecard-based analysis about european energy investment policies: A hybrid hesitant fuzzy decision-making approach with quality function deployment. Expert Systems With Applications, 115:152–171, 2019.
  9. A hybrid decision-making method using robust programming and interval-valued fuzzy sets for sustainable-resilient supply chain network design considering circular economy and technology levels. Journal of Industrial Information Integration, 33:100440, 2023.
  10. Group Theory Application to the Physics of Condensed Matter. Springer Press, 2008.
  11. J. L. García-Lapresta and D. Pérez-Román. Consensus-based clustering under hesitant qualitative assessments. Fuzzy Sets and Systems, 292:261–273, 2016.
  12. Graph Theory Favorite Conjectures and Open Problems-2, Problem Books in Mathematics. Springer Press, 2018.
  13. M. B. Gorzalczany. A method of inference in approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets and Systems, 21:1–17, 1987.
  14. Probabilistic dual hesitant fuzzy set and its application in risk evaluation. Knowledge-Based Systems, 127:16–28, 2017.
  15. Dominance-based rough set model in intuitionistic fuzzy information systems. Knowledge-Based Systems, 28:115–123, 2012.
  16. H. Jiang and B. Q. Hu. A decision-theoretic fuzzy rough set in hesitant fuzzy information systems and its application in multi-attribute decision-making. Information Sciences, 579:103–127, 2021.
  17. An improved entropy function for the intuitionistic fuzzy sets with application to cloud vendor selection. Decision Analytics Journal, 7:100262, 2023.
  18. Two-sided matching model for complex product manufacturing tasks based on dual hesitant fuzzy preference information. Knowledge-Based Systems, 186:104989, 2019.
  19. Air quality deterministic and probabilistic forecasting system based on hesitant fuzzy sets and nonlinear robust outlier correction. Knowledge-Based Systems, 237:107789, 2022.
  20. L. Li and Y. Xu. An extended hesitant fuzzy set for modeling multi-source uncertainty and its applications in multiple-attribute decision-making. Expert Systems With Applications, 238:121834, 2024.
  21. Three-way multi-attribute decision-making under the double hierarchy hesitant fuzzy linguistic information system. Applied Soft Computing, 154:111315, 2024.
  22. A new type of dyad fuzzy β𝛽\betaitalic_β-covering rough set models base on fuzzy information system and its practical application. International Journal of Approximate Reasoning, 142:13–30, 2022.
  23. L. Pan and Y. Deng. A novel similarity measure in intuitionistic fuzzy sets and its applications. Engineering Applications of Artificial Intelligence, 107:104512, 2023.
  24. M. Pant and N. Mehra. Strong (α,k)𝛼𝑘(\alpha,k)( italic_α , italic_k )-cut and computational-based segmentation based novel hesitant fuzzy time series forecasting model. Applied Soft Computing, 153:111251, 2024.
  25. F. Patras. The Essence of Numbers, Lecture Notes in Mathematics book series. Springer Press, 2020.
  26. Z. Pawlak. Rough sets: Theoretical aspects of reasoning about data. Dordrecht: Kluwer Academic Publishers, 1991.
  27. Z. Pawlak and A. Skowron. Rough sets: Some extensions. Information Sciences, 177:28–40, 2007.
  28. D. Shi and X. Zhang. Probabilistic decision making based on rough sets in interval-valued fuzzy information systems. Granular Computing, 4:391–405, 2019.
  29. T. Tao and T. Zhao. A data-driven fuzzy system for the automatic determination of fuzzy set type based on fuzziness. Information Sciences, 642:119173, 2023.
  30. V. Torra. Hesitant fuzzy sets. International Journal of Intelligent Systems, 25:529–539, 2010.
  31. S. Waldmann. Topology An Introduction. Dordrecht: Kluwer Academic Publishers, 2014.
  32. A regret-theory-based three-way decision method with a priori probability tolerance dominance relation in fuzzy incomplete information systems. Information Fusion, 89:382–396, 2023.
  33. M. Xia and Z. Xu. Hesitant fuzzy information aggregation in decision making. International Journal of Approximate Reasoning, 52:395–407, 2011.
  34. G. Xin and L. Ying. Multi-attribute decision-making based on comprehensive hesitant fuzzy entropy. Expert Systems With Applications, 237:121459, 2024.
  35. A new multi-objective decision-making method with diversified weights and pythagorean fuzzy rough sets. Computers &\&& Industrial Engineering, 182:109406, 2023.
  36. L. A. Zadeh. Fuzzy sets. Information and control, 8:338–353, 1965.
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