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Four Operations over Extended Intuitionistic Fuzzy Index Matrices and Some of Their Applications

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Advances in High Performance Computing (HPC 2019)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 902))

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Abstract

In this paper, four new operations are introduced over extended intuitionistic fuzzy index matrices and over their simpler cases, such as intuitionistic fuzzy index matrices, extended index matrices and index matrices. Some of the properties of the four new operators are discussed and their applications in intercriteria analysis are shown. A theorem for stratification of an index matrix is formulated and proved.

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References

  1. Andreev, N., Sotirova, E., Ribagin, S.: Intercriteria analysis of data from data from the centers for transfusion haematology in Bulgaria. Comptes Rendus de l’Academie Bulgare des Science 72(7), 982–990 (2019)

    Google Scholar 

  2. Angelova, M., Pencheva, T.: InterCriteria analysis approach for comparison of simple and multi-population genetic algorithms performance. In: Fidanova, S. (ed.) Recent Advances in Computational Optimization. Studies in Computational Intelligence, vol. 795, pp. 117–130 (2019)

    Google Scholar 

  3. Atanassov, K.: Generalized index matrices. Comptes rendus de l’Academie Bulgare des Sciences 40(11), 15–18 (1987)

    Google Scholar 

  4. Atanassov, K.: Intuitionistic Fuzzy Sets. Springer, Heidelberg (1999)

    Book  Google Scholar 

  5. Atanassov, K.: On index matrices. Part 1: Standard cases. Adv. Stud. Contemp. Math. 20(2), 291–302 (2010)

    Google Scholar 

  6. Atanassov, K.: On index matrices. Part 2: Intuitionistic fuzzy case. Proc. Jangjeon Math. Soc. 13(2), 121–126 (2010)

    Google Scholar 

  7. Atanassov, K.: On Intuitionistic Fuzzy Sets Theory. Springer, Berlin (2012)

    Book  Google Scholar 

  8. Atanassov, K.: On extended intuitionistic fuzzy index matrices. Notes Intuitionistic Fuzzy Sets 19(4), 27–41 (2013)

    Google Scholar 

  9. Atanassov, K.: Index Matrices: Towards an Augmented Matrix Calculus. Springer, Cham (2014)

    MATH  Google Scholar 

  10. Atanassov, K.: \(n\)-Dimensional extended index matrices. Adv. Stud. Contemp. Math. 28(2), 245–259 (2018)

    MATH  Google Scholar 

  11. Atanassov, K., Szmidt, E., Kacprzyk, J.: On intuitionistic fuzzy pairs. Notes Intuitionistic Fuzzy Sets 19(3), 1–13 (2013)

    Google Scholar 

  12. Atanassov, K., Szmidt, E., Kacprzyk, J., Bureva, V.: Two examples for the use of 3-dimensional intuitionistic fuzzy index matrices. Notes Intuitionistic Fuzzy Sets, 20(2), 52–59 (2014)

    Google Scholar 

  13. Atanassova, V.: Interpretation in the intuitionistic fuzzy triangle of the results, obtained by the InterCriteria analysis. In: 16th World Congress of the International Fuzzy Systems Association (IFSA), 9th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), Gijon, Spain, 30 June–03 July 2015, pp. 1369–1374 (2015). https://doi.org/10.2991/ifsa-eusflat-15.2015.193

  14. Atanassova, V.: New modified level operator N over intuitionistic fuzzy sets. In: Christiansen, H., Jaudoin, H., Chountas, P., Andreasen, T., Larsen, H.L. (eds.) Proceedings of 12th International Conference on Flexible Query Answering Systems (FQAS 2017), London, UK, 21–22 June 2017. LNAI, vol. 10333, pp. 209–214. Springer (2017). https://doi.org/10.1007/978-3-319-59692-1_18. ISBN 978-3-319-59691-4. ISSN 0302-9743

  15. Atanassova, V., Doukovska, L., Michalikova, A., Radeva, I.: Intercriteria analysis: from pairs to triples. Notes Intuitionistic Fuzzy Sets 22(5), 98–110 (2016). Print ISSN 1310-4926. Online ISSN 2367-8283

    Google Scholar 

  16. Atanassova, V., Vardeva, I.: Sum- and average-based approach to criteria shortlisting in the InterCriteria Analysis. Int. J. Notes Intuitionistic Fuzzy Sets 20(4), 41–46 (2014)

    Google Scholar 

  17. Bureva, V.: Application of the index matrix operations over relational databases. Adv. Stud. Contemp. Math. 26(4), 669–679 (2016)

    MATH  Google Scholar 

  18. Bureva, V., Sotirova, E., Moskova, M., Szmidt, S.: Solving the problem of appointments using index matrices. In: 13th International Workshop on Generalized Nets London, 29 October 2012, pp. 43–48 (2012)

    Google Scholar 

  19. Fidanova, S., Roeva, O.: InterCriteria analysis of different metaheuristics applied to E. coli cultivation process. Numerical Methods for Scientific Computations and Advanced Applications, pp. 21–25 (2016)

    Google Scholar 

  20. Fidanova, S., Roeva, O.: Comparison of different metaheuristic algorithms based on InterCriteria analysis. J. Comput. Appl. Math. 7 (2017). https://doi.org/10.1016/j.cam.2017.07.028

  21. Fidanova, S., Roeva, O., Mucherino, A., Kapanova, K.: InterCriteria analysis of ant algorithm with environment change for GPS surveying problem. Lecture Notes in Computer Science, vol. 9883, pp. 271–278. Springer (2016)

    Google Scholar 

  22. Fidanova, S., Roeva, O., Paprzycki, M.: InterCriteria analysis of ant colony optimization application to GPS surveying problems. Issues Intuitionistic Fuzzy Sets Generalized Nets 12, 20–38 (2015/2016)

    Google Scholar 

  23. Georgieva, V., Angelova, N., Roeva, O., Pencheva, T.: InterCriteria analysis of wastewater treatment quality. J. Int. Sci. Publ. Ecol. Saf. 10, 365–376 (2016)

    Google Scholar 

  24. Georgieva, V., Angelova, N., Roeva, O., Pencheva, T.: Simulation of parallel processes in wastewater treatment plant using generalized net integrated development environment. Comptes rendus de l’Académie bulgare des Sciences 69(11), 1493–1502 (2016). ISI IF:0.233

    Google Scholar 

  25. Ikonomov, N., Vassilev, P., Roeva, O.: ICrAData – software for InterCriteria analysis. Int. J. Bioautomation 22(1), 1–10 (2018)

    Google Scholar 

  26. Ilkova, T., Petrov, M.: Application of InterCriteria analysis to the Mesta river pollution modelling. Notes Intuitionistic Fuzzy Sets 21(2), 118–125 (2015)

    Google Scholar 

  27. Ilkova, T., Roeva, O., Vassilev, P., Petrov, M.: InterCriteria analysis in structural and parameter identification of L-lysine production model. Issues Intuitionistic Fuzzy Sets Generalized Nets 12, 39–52 (2015/2016)

    Google Scholar 

  28. Krawczak, M., Bureva, V., Sotirova, E., Szmidt, E.: Application of the InterCriteria decision making method to universities ranking. In: Atanassov, K., et al. (eds.) Novel Developments in Uncertainty Representation and Processing. Advances in Intelligent Systems and Computing, vol. 401, pp. 365–372. Springer, Cham (2016)

    Chapter  Google Scholar 

  29. Krumova, S., Todinova, D., Mavrov, P., Marinov, V., Atanassova, K., Atanassov, S., Taneva, S.: Intercriteria analysis of calorimetric data of blood serum proteome. Biochimica et Biophysica Acta - Gener. Subjects 2017(2), 409–417 (1861). https://doi.org/10.1016/j.bbagen.2016.10.012

    Article  Google Scholar 

  30. Marinov, P., Fidanova, S.: Intercriteria and correlation analyses: similarities, differences and simultaneous use. Ann. “Inf.” Sect. Union Sci. Bulgaria, 8, 45–53 (2015/2016)

    Google Scholar 

  31. Mucherino, A., Fidanova, S., Ganzha, M.: Ant colony optimization with environment changes: an application to GPS surveying. In: Proceedings of the Federated Conference on Computer Science and Information Systems, ACSIS, vol. 5, pp. 495–500. https://doi.org/10.15439/2015F33

  32. Pencheva, T., Angelova, M., Atanassova, V., Roeva, O.: InterCriteria analysis of genetic algorithm parameters in parameter identification. Notes Intuitionistic Fuzzy Sets 21(2), 99–110 (2015)

    Google Scholar 

  33. Pencheva, T., Roeva, O., Angelova, M.: Investigation of genetic algorithm performance based on different algorithms for InterCriteria relations calculation. In: Lirkov, I., Margenov, S. (eds.) Large-Scale Scientific Computing. Lecture Notes in Computer Science, vol. 10665, pp. 390–398 (2018)

    Google Scholar 

  34. Petrov, M., Ilkova, T.: Application of the intercriteria analysis for selection of growth rate models for cultivation of strain Kluyveromyces marxianus var. lactis MC 5. Notes Intuitionistic Fuzzy Sets 21(5), 49–60 (2015)

    Google Scholar 

  35. Petrov, M., Ilkova, T.: Intercriteria decision analysis for choice of growth rate models of batch cultivation by strain Kluyveromyces marxianus var. lactis MC 5. J. Int. Sci. Publ. Mater. Methods Technol. 10, 468–486 (2016)

    Google Scholar 

  36. Roeva, O., Fidanova, S., Paprzycki, M.: InterCriteria analysis of ACO and GA hybrid algorithms. Studies in Computational Intelligence, vol. 610, pp. 107–126. Springer (2016). https://doi.org/10.1007/978-3-319-21133-6_7

  37. Roeva, O., Vassilev, P.: InterCriteria analysis of generation gap influence on genetic algorithms performance. In: Atanassov, K.T., et al. (eds.) Novel Developments in Uncertainty Representation and Processing, Part V. Advances in Intelligent Systems and Computing, vol. 401, pp. 301–313 (2016)

    Google Scholar 

  38. Roeva, O., Vassilev, P., Angelova, M., Su, J., Pencheva, T.: Comparison of different algorithms for InterCriteria relations calculation. In: IEEE 8th International Conference on Intelligent Systems, pp. 567–572 (2016)

    Google Scholar 

  39. Roeva, O., Vassilev, P., Angelova, M., Pencheva, T.: InterCriteria analysis of parameters relations in fermentation processes models. Lecture Notes Computer Science, vol. 9330, pp. 171–181 (2015)

    Google Scholar 

  40. Roeva, O., Vassilev, P., Ikonomov, N., Angelova, M., Su, J., Pencheva, T.: On different algorithms for InterCriteria relations calculation. In: Hadjiski, M., Atanassov, K.T. (eds.) Intuitionistic Fuzziness and Other Intelligent Theories and Their Applications. Studies in Computational Intelligence, vol. 757, pp. 143–160 (2019)

    Google Scholar 

  41. Roeva, O., Zoteva, D.: Knowledge discovery from data: InterCriteria analysis of mutation rate influence. Notes Intuitionistic Fuzzy Sets 24(1), 120–130 (2018)

    Google Scholar 

  42. Shannon, A., Atanassova, V., Atanassov, K.: Operation, “concatenation” over intuitionistic fuzzy index matrices. Notes Intuitionistic Fuzzy Sets 22(3), 106–111 (2016)

    MATH  Google Scholar 

  43. Sotirov, S., Atanassova, V., Sotirova, E., Bureva, V., Mavrov, D.: Application of the intuitionistic fuzzy InterCriteria analysis method to a neural network preprocessing procedure. In: 9th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), Gijon, Spain, 30 June–03 July 2015, pp. 1559–1564 (2015). https://doi.org/10.2991/ifsa-eusflat-15.2015.222

  44. Sotirov, S., Atanassova, V., Sotirova, E., Doukovska, L., Bureva, V., Mavrov, D., Tomov, J.: Application of the intuitionistic fuzzy InterCriteria analysis method with triples to a neural network preprocessing procedure. In: Computational Intelligence and Neuroscience, Hindawi 2017, Article ID 2157852, p. 9 (2017). https://doi.org/10.1155/2017/2157852

  45. Stratiev, D., Sotirov, S., Shishkova, I., Nedelchev, A., Sharafutdinov, I., Vely, A., Mitkova, M., Yordanov, D., Sotirova, E., Atanassova, V., Atanassov, K., Stratiev, D.D., Rudnev, N., Ribagin, S.: Investigation of relationships between bulk properties and fraction properties of crude oils by application of the intercriteria analysis. Petrol. Sci. Technol. 34(13), 1113–1120 (2016)

    Google Scholar 

  46. Todorova, L., Vassilev, P., Surchev, J.: Using Phi coefficient to interpret results obtained by InterCriteria analysis. In: Novel Developments in Uncertainty Representation and Processing. Advances in Intelligent Systems and Computing, vol. 401, pp. 231–239. Springer (2106). https://doi.org/10.1007/978-3-319-26211-6_20

  47. Traneva, V.: Internal operations over 3-dimensional extended index matrices. In: Proceedings of the Jangjeon Mathematical Society, vol. 18, no. 4, pp. 547–569 (2015)

    Google Scholar 

  48. Traneva, V.: One application of the index matrices for a solution of a transportation problem. Adv. Stud. Contemp. Math. 26(4), 703–715 (2016)

    MATH  Google Scholar 

  49. Traneva, V., Atanassova, V., Tranev, S.: Index matrices as a decision-making tool for job appointment. In: Nikolov, G., et al. (eds.) NMA 2018, pp. 1–9. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10692-8_18

  50. Traneva, V., Marinov, P., Atanassov, K.: Index matrix interpretations of a new transportation-type problem. Comptes Rendus de L’Academie Bulgare des Sciences 69(10), 1275–1282 (2016)

    Google Scholar 

  51. Traneva, V., Marinov, P., Atanassov, K.: Transportation-type problems and their index matrix interpretations. Adv. Stud. Contemp. Math. 26(4), 587–594 (2016)

    MATH  Google Scholar 

  52. Traneva, V., Sotirova, E., Bureva, V., Atanassov, K.: Aggregation operations over 3-dimensional extended index matrices. Adv. Stud. Contemp. Math. 25(3), 407–416 (2015)

    MATH  Google Scholar 

  53. Traneva, V., Tranev, S.: Existence of solution of the problem of optimal control of mines for minerals. In: Proceedings of the Jangjeon Mathematical Society, vol. 21, no. 3, pp. 443–478 (2018)

    Google Scholar 

  54. Traneva, V., Tranev, S., Atanassova, V.: An intuitionistic fuzzy approach to the Hungarian algorithm. In: Nikolov, G., Kolkovska, N., Georgiev, K. (eds.) Numerical Methods and Applications. NMA 2018. Lecture Notes in Computer Science, vol. 11189, pp. 167–175. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10692-8_19

  55. Traneva, V., Tranev, S., Szmidt, E., Atanassov, K.: Three dimensional intercriteria analysis over intuitionistic fuzzy data. In: Kacprzyk, J., et al. (eds.) Advances in Fuzzy Logic and Technology 2017. Advances in Intelligent Systems and Computing, vol. 641, pp. 442–449. Springer International Publishing AG (2018). https://doi.org/10.1007/978-3-319-66827-7_40

  56. Vassilev, P., Ribagin, S.: Todorova, on an aggregation of expert value assignments using index matrices. Notes Intuitionistic Fuzzy Sets 23(4), 75–78 (2017)

    Google Scholar 

  57. Vankova, D., Sotirova, E., Bureva, V.: An application of the InterCriteria method approach to health-related quality of life. Notes Intuitionistic Fuzzy Sets 21(5), 40–48 (2015)

    Google Scholar 

  58. Vassilev, P., Todorova, L., Andonov, V.: An auxiliary technique for InterCriteria analysis via a three dimensional index matrix. Notes Intuitionistic Fuzzy Sets 21(2), 71–76 (2015)

    Google Scholar 

  59. Zoteva, D., Roeva, O.: InterCriteria analysis results based on different number of objects. Notes Intuitionistic Fuzzy Sets 24(1), 110–119 (2018)

    Google Scholar 

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Acknowledgements

The first author is grateful for the support under Grant Ref. No. DN 17/6 “A New Approach, Based on an Intercriteria Data Analysis, to Support Decision Making in in silico Studies of Complex Biomolecular Systems” of the Bulgarian National Science Fund.

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Authors and Affiliations

  1. Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, Acad. G. Bonchev Street, Bl. 105, 1113, Sofia, Bulgaria

    Krassimir Atanassov

  2. Intelligent Systems Laboratory, Prof. Asen Zlatarov University, 8000, Bourgas, Bulgaria

    Krassimir Atanassov & Veselina Bureva

Authors
  1. Krassimir Atanassov
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  2. Veselina Bureva
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Correspondence to Veselina Bureva .

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Editors and Affiliations

  1. Institute of Information and Communication Technology, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Dimov

  2. Institute of Information and Communication Technology, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Stefka Fidanova

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Atanassov, K., Bureva, V. (2021). Four Operations over Extended Intuitionistic Fuzzy Index Matrices and Some of Their Applications. In: Dimov, I., Fidanova, S. (eds) Advances in High Performance Computing. HPC 2019. Studies in Computational Intelligence, vol 902. Springer, Cham. https://doi.org/10.1007/978-3-030-55347-0_3

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