Multi-criteria decision making based on novel distance measure in intuitionistic fuzzy environment

In comparison to fuzzy sets, intuitionistic fuzzy sets are much more efficient at representing and processing uncertainty.  Distance measures quantify how much the information conveyed by intuitionistic fuzzy sets differs from one another.  Researchers have suggested many distance measures to assess the difference between intuitionistic fuzzy sets, but several of them produce contradictory results in practice and violate the fundamental axioms of distance measure. In this article, we introduce a novel distance measure for IFSs, visualize it, and discuss its boundedness and nonlinear characteristics using appropriate numerical examples.  In addition to establishing its validity, its effectiveness was investigated using real-life examples from multiple fields, such as medical diagnosis and pattern recognition.  We also present a technique to solve pattern recognition problems, and the superiority of the proposed approach over existing approaches is demonstrated by incorporating a performance index in terms of  "Degree of Confidence" (DOC).  Finally, we extend the applicability of the proposed approach to establish a new decision-making approach known as the IFIR (Intuitionistic Fuzzy Inferior Ratio) method, and its efficiency is analyzed with other established decision-making approaches.

  1. Zadeh L. A.  Fuzzy sets. Information and Control.  8 (3), 338–353 (1965).
  2. Atanassov K. T.  Intuitionistic fuzzy sets.  Fuzzy Sets And Systems.  20 (1), 87–96 (1986).
  3. Atanassov K. T.  New operations defined over the intuitionistic fuzzy sets. Fuzzy Sets and Systems.  61 (2), 137–142 (1994).
  4. Atanassov K. T.  Intuitionistic fuzzy sets.  In: Intuitionistic Fuzzy Sets. Studies in Fuzziness and Soft Computing, vol. 35. Physica, Heidelberg (1999).
  5. Hadi–Vencheh A., Mirjaberi M.  Fuzzy inferior ratio method for multiple attribute decision making problems.  Information Sciences.  277, 263–272 (2014).
  6. Joshi R., Kumar S.  $(R,S)$-norm information measure and a relation between coding and questionnaire theory.  Open Systems & Information Dynamics.  23 (03), 1650015 (2016).
  7. Joshi R., Kumar S.  A dissimilarity Jensen–Shannon divergence measure for intuitionistic fuzzy sets. International Journal of Intelligent Systems.  33 (11), 2216–2235 (2018).
  8. Joshi R.  A novel decision-making method using R-Norm concept and VIKOR approach under picture fuzzy environment.  Expert Systems with Applications.  147, 113228 (2020).
  9. Joshi R.  A new picture fuzzy information measure based on Tsallis–Havrda–Charvat concept with applications in presaging poll outcome.  Computational and Applied Mathematics.  39 (2), 71 (2020).
  10. Arya V., Kumar S.  A picture fuzzy multiple criteria decision-making approach based on the combined TODIM–VIKOR and entropy weighted method. Cognitive Computation.  13 (5), 1172–1184 (2021).
  11. Arya V., Kumar S.  Extended TODIM method based on VIKOR for q-rung orthopair fuzzy information measures and their application in MAGDM problem of medical consumption products.  International Journal of Intelligent Systems.  36 (11), 6837–6870 (2021).
  12. Garg H., Rani D.  Complex intuitionistic fuzzy power aggregation operators and their applications in multicriteria decision-making.  Expert Systems.  35 (6), e12325 (2018).
  13. Garg H., Kumar K.  Multiattribute decision making based on power operators for linguistic intuitionistic fuzzy set using set pair analysis.  Expert Systems.  36 (4), e12428 (2019).
  14. Garg H., Ali Z., Mahmood T.  Algorithms for complex interval-valued q-rung orthopair fuzzy sets in decision making based on aggregation operators, AHP, and TOPSIS.  Expert Systems.  38 (1), e12609 (2021).
  15. Garg H., Rani D.  An efficient intuitionistic fuzzy MULTIMOORA approach based on novel aggregation operators for the assessment of solid waste management techniques.  Applied Intelligence.  52 (4), 4330–4363 (2022).
  16. Garg H., Rani D.  Novel distance measures for intuitionistic fuzzy sets based on various triangle centers of isosceles triangular fuzzy numbers and their applications.  Expert Systems with Applications.  191, 116228 (2022).
  17. Vlachos I., Sergiadis G.  Intuitionistic fuzzy information – Applications to pattern recognition.  Pattern Recognition Letters.  28 (2), 197–206 (2007).
  18. Papakostas G. A., Hatzimichailidis A. G., Kaburlasos V. G.  Distance and similarity measures between intuitionistic fuzzy sets: A comparative analysis from a pattern recognition point of view.  Pattern Recognition Letters.  34 (14), 1609–1622 (2013).
  19. Nguyen H.  A novel similarity/dissimilarity measure for intuitionistic fuzzy sets and its application in pattern recognition.  Expert Systems with Applications.  45, 97–107 (2016).
  20. Jiang Q., Jin X., Lee S.-J., Yao S.  A new similarity/distance measure between intuitionistic fuzzy sets based on the transformed isosceles triangles and its applications to pattern recognition.  Expert Systems with Applications.  116, 439–453 (2019).
  21. De S. K., Biswas R., Roy A. R.  An application of intuitionistic fuzzy sets in medical diagnosis.  Fuzzy Sets and Systems.  117 (2), 209–213 (2001).
  22. Hung K.  Medical pattern recognition: applying an improved intuitionistic fuzzy cross-entropy approach.  Advances In Fuzzy Systems.  2012, 863549 (2012).
  23. Luo M., Zhao R.  A distance measure between intuitionistic fuzzy sets and its application in medical diagnosis.  Artificial Intelligence in Medicine.  89, 34–39 (2018).
  24. Gau W.-L., Buehrer D. J.  Vague sets.  IEEE Transactions On Systems, Man, and Cybernetics.  23 (2), 610–614 (1993).
  25. Bustince H., Burillo P.  Vague sets are intuitionistic fuzzy sets.  Fuzzy Sets and Systems.  79 (3), 403–405 (1996).
  26. Szmidt E., Kacprzyk J.  Intuitionistic fuzzy sets in some medical applications.  International Conference on Computational Intelligence.  148–151 (2001).
  27. Szmidt E., Kacprzyk J.  A similarity measure for intuitionistic fuzzy sets and its application in supporting medical diagnostic reasoning.  International Conference on Artificial Intelligence and Soft Computing.  388–393 (2004).
  28. Szmidt E., Kacprzyk J.  Distances between intuitionistic fuzzy sets.  Fuzzy Sets and Systems.  114 (3), 505–518 (2000).
  29. Wang W., Xin X.  Distance measure between intuitionistic fuzzy sets.  Pattern Recognition Letters.  26 (13), 2063–2069 (2005).
  30. Hung W.-L., Yang M.-S.  Similarity measures of intuitionistic fuzzy sets based on Hausdorff distance.  Pattern Recognition Letters.  25 (14), 1603–1611 (2004).
  31. Hung W.-L., Yang M.-S.  Similarity measures of intuitionistic fuzzy sets based on $L_p$ metric.  International Journal of Approximate Reasoning.  46 (1), 120–136 (2007).
  32. Hung W.-L., Yang M.-S.  On the $J$-divergence of intuitionistic fuzzy sets with its application to pattern recognition.  Information Sciences.  178 (6), 1641–1650 (2008).
  33. Grzegorzewski P.  Distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric.  Fuzzy Sets and Systems.  148 (2), 319–328 (2004).
  34. Chen T.-Y.  A note on distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric.  Fuzzy Sets and Systems.  158 (22), 2523–2525 (2007).
  35. Yang Y., Chiclana F.  Consistency of 2D and 3D distances of intuitionistic fuzzy sets.  Expert Systems with Applications.  39 (10), 8665–8670 (2012).
  36. Liang Z., Shi P.  Similarity measures on intuitionistic fuzzy sets.  Pattern Recognition Letters.  24 (15), 2687–2693 (2003).
  37. Deza M., Deza E.  Encyclopedia of distances.  In: Encyclopedia of Distances. Springer, Berlin, Heidelberg (2009).
  38. Luo X., Li W., Zhao W.  Intuitive distance for intuitionistic fuzzy sets with applications in pattern recognition.  Applied Intelligence.  48 (9), 2792–2808 (2018).
  39. Dengfeng L., Chuntian C.  New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions.  Pattern Recognition Letters.  23 (1–3), 221–225 (2002).
  40. Mitchell H. B.  On the Dengfeng–Chuntian similarity measure and its application to pattern recognition.  Pattern Recognition Letters.  24 (16), 3101–3104 (2003).
  41. Xu Z., Yager R. R.  Some geometric aggregation operators based on intuitionistic fuzzy sets.  International Journal of General Systems.  35 (4), 417–433 (2006).
  42. Chen S.-M., Tan J.-M.  Handling multicriteria fuzzy decision–making problems based on vague set theory.  Fuzzy Sets and Systems.  67 (2), 163–172 (1994).
  43. Xiao F.  A distance measure for intuitionistic fuzzy sets and its application to pattern classification problems.  IEEE Transactions On Systems, Man, And Cybernetics: Systems.  51 (6), 3980–3992 (2019).
  44. Song Y., Wang X., Quan W., Huang W.  A new approach to construct similarity measure for intuitionistic fuzzy sets.  Soft Computing.  23 (6), 1985–1998 (2019).
  45. Chen C., Deng X.  Several new results based on the study of distance measures of intuitionistic fuzzy sets.  Iranian Journal of Fuzzy Systems.  17 (2), 147–163 (2020).
  46. Hong D. H., Choi C.-H.  Multicriteria fuzzy decision-making problems based on vague set theory.  Fuzzy Sets and Systems.  114 (1), 103–113 (2000).
  47. Baczyński M., Jayaram B.  Fuzzy Implications.  Springer Berlin, Heidelberg (2008).
  48. Du W. S., Hu B. Q.  Aggregation distance measure and its induced similarity measure between intuitionistic fuzzy sets.  Pattern Recognition Letters.  60, 65–71 (2015).
  49. Baležentis T., Zeng Sh., Baležentis A.  MULTIMOORA-IFN: A MCDM method based on intuitionistic fuzzy number for performance management.  Economic Computation & Economic Cybernetics Studies & Research.  48 (4), 85–102 (2014).
  50. Park J., Lim K., Kwun Y.  Distance measure between intuitionistic fuzzy sets and its application to pattern recognition.  Journal of the Korean Institute of Intelligent Systems.  19 (4), 556–561 (2009).
  51. Wei C.-P., Wang P., Zhang Y.-Z.  Entropy, similarity measure of interval-valued intuitionistic fuzzy sets and their applications.  Information Sciences.  181 (19), 4273–4286 (2011).
  52. Xu Z.  Some similarity measures of intuitionistic fuzzy sets and their applications to multiple attribute decision making.  Fuzzy Optimization and Decision Making.  6 (2), 109–121 (2007).
  53. Mishra A. R., Mardani A., Rani P., Kamyab H., Alrasheedi M.  A new intuitionistic fuzzy combinative distance-based assessment framework to assess low-carbon sustainable suppliers in the maritime sector.  Energy.  237, 121500 (2021).
  54. Gohain B., Dutta P., Gogoi S., Chutia R. Construction and generation of distance and similarity measures for intuitionistic fuzzy sets and various applications.  International Journal Of Intelligent Systems.  36 (12), 7805–7838 (2021).
  55. Gohain B., Chutia R., Dutta P., Gogoi S.  Two new similarity measures for intuitionistic fuzzy sets and its various applications. International Journal of Intelligent Systems.  37 (9), 5557–5596 (2022).
  56. Kumar R., Kumar S.  A novel intuitionistic fuzzy similarity measure with applications in decision-making, pattern recognition, and clustering problems.  Granular Computing.  1–24 (2023).