Dr. Arun Kumar Srivastava

Professor
Ph.D (Indian Institute of Technology,Delhi)
Contact Information:
(+91)542 6702588 (Office), 91 542 2575938 (Home)
Email Id:: aks@bhu.ac.in, arunksrivastava@gmail.com

 
 
Academic Qualifications:
 
S. No.DegreeInstitutionYear
1.B.Sc.University of Allahabad,Allahabad1968
2.M.Sc.University of Allahabad,Allahabad1970
3.Ph. D.Indian Institute of Technology,Delhi1974
 
Area of specialization/awards/achievements:
 


Category Theory, Categorical Topology & Fuzzy Topology, Automata Theory Early work in category theory included a study of some weaker adjointness notions in category theory, e.g. local, stable and near adjunctions and their associated `reflections/coreflections’. One of the earliest uses of topological methods in automata theory was demonstrated. Introduced ‘new’ notions of Sierpinski spaces and the T0-separation in fuzzy topology, using motivations from category theory. Subsequent works have continued to show the significance of using categorical methods, particularly the notion of adjointness,(co) reflectivity, and monads, in studying fuzzy topology. Topological and, at times, categorical, methods have also been used to study fuzzy automata (including their intuitionistic fuzzy and rough sets anologues).

 
Current Research Projects:
Two (One UGC- and one DST-sponsored)
 
 

Additional information/Achievements:

(a)Visits (for research related activities) to:

  • University of Antwerp, Belgium (01 academic year)
  • Rhodes University, South Africa (about 02 months)
  • University of Bremen, Germany (lecture-visit)
  • University of Pretoria, South Africa (lecture-visit)
  • University of Linz, Austria (for Seminar)
  • Council Member, Indian Mathematical Society
  • Additional Coordinator, DST-Centre for Interdisciplinary Mathematical Sciences, B.H.U. and formerly:
  • Head, Department of Computer Science, B.H.U.
  • Lecturer, University of Roorkee (now I.I.T. Roorkee)
  • General Secretary, Indian Society for Fuzzy Mathematics & Information Processing
 
 
 

List of 10 major Publications:

  1. Fuzzy Sierpinski space, J. Math. Anal. Appl., 103, 1984, 103-105
  2. A topology for automata: A note (with W. Shukla), Information & Control., 32, 1976, 163- 168
  3. FTS0: The epireflective hull of the Sierpinski object in FTS (with R. Lowen), Fuzzy Sets and Systems, 29, 1988, 171-178
  4. On two epireflctive subcategories of the category of 2T0 – fuzzy bitopological spaces (with A. S. Khastgir), Quest. Math., 23, 2000, 163-177
  5. On relationshing among fuzzy approximation operators, fuzzy topology and fuzzy automata (with S. P. Tiwari) , Fuzzy Sets & Systems, 138, 2003, 197 – 204.
  6. Local reflectivity + stable reflectivity = reflectivity (with W. Shukla), Gen. Top. & its Appl., 5, 1975, 61-68
  7. Fuzzy Hausdorff topological spaces (with R. Srivastava and S.N. Lal) J. Math. Anal. Appl., 81, 1981, 497-506
  8. Non-Archemedian metric induced fuzzy uniform spaces (with R. Lowen and P. Wuytes), Intern. J. Math. & Math. Sc., 12, 1988, 47-60
  9. On fuzzy sobriety (with A. Khastgir), Information Sciences, 110, 1998, 195-205.
  10. On Preuss’ connectedness concept in fuzzy topology (with R. Lowen), Fuzzy Sets and Systems, 47, 1991, 99-104
Full List of Publications:
  1. Local reflectivity + stable reflectivity = reflectivity (with W. Shukla), Gen. Top. & its Appl., 5, 1975, 61-68
  2. A topology for automata: A note (with W. Shukla), Information & Control., 32, 1976, 163- 168
  3. Near reflections, Czech. Math. Jour., 27, 1977, 619-625
  4. Fuzzy Hausdorff topological spaces (with R. Srivastava and S.N. Lal) J. Math. Anal. Appl., 81, 1981, 497-506
  5. A note on local adjointness, in: Algebra & its Appls, Lecture Notes in Pure & Applied Mathematics, 91, 1984, 45-48, Marcel Dekker, New York
  6. Fuzzy T1-topological spaces (with R. Srivastava and S.N. Lal), J. Math. Anal. Appl., 102, 1984, 442-448
  7. Fuzzy Sierpinski space, J. Math. Anal. Appl., 103, 1984, 103-105
  8. Connected fuzzy topological spaces (with R. Srivastava and S.N. Lal), in : Proc. Int. Symp. OnModern Anal. & Appls, Prentice-Hall of India, 1985, 27-35
  9. On monads, monadicity, and top categories, Proc. Math. Soc. BHU, 1, 1985, 37-44
  10. On fuzzy Hausdorffness concepts (with R. Srivastava), Fuzzy Sets and Systems, 17, 1985, 67-71
  11. Fuzzy Sierpinski space: Another note, (with R. Srivastava), Fuzzy Maths., 3, 1985, 99- 103
  12. A topology for automata II (with W. Shukla), Intern. J. Math. & Math. Sc., 9, 1986, 425- 428
  13. A comparison of FT2-concepts (with D.M. Ali), Fuzzy Sets and Systems, 23, 1987, 289- 284
  14. Sierpinski objects in FTS, FNS and ?(TOP) (with R. Lowen), Comm. IFSA Maths. Chapter, 1, 1987, 24-27
  15. R1-fuzzy topological spaces, J. Math. Anal. Appl., 127, 1987, 151-154
  16. On Fuzzy T1-topological spaces (with R. Srivastava and S.N. Lal), J. Math. Anal. Appl., 136, 1988, 124-130
  17. On Fuzzy T0- and R0 -topological spaces (with R. Srivastava and S.N. Lal), J. Math. Anal. Appl.,136, 1988, 66-73
  18. On fuzzy connectedness (with D.M. Ali), Fuzzy Sets and Systems, 28, 1988, 203-208
  19. FTS0: The epireflective hull of the Sierpinski object in FTS (with R. Lowen), Fuzzy Sets and Systems, 29, 1988, 171-178
  20. Sierpinski objects in subcategories of FTS (with R. Lowen), Quest. Math., 11, 1988, 181- 193
  21. Non-Archemedian metric induced fuzzy uniform spaces (with R. Lowen and P. Wuytes), Intern. J. Math. & Math. Sc., 12, 1988, 47-60
  22. Fuzzy sets for linear logic (with S. Rai and W. Shukla), Comm. IFSA Maths. Chapter, 3, 1989, 55-58
  23. Note on fuzzy uniformities induced by non-Archemedean metrics, Prog. of Maths. 23, 1989, 49-54.
  24. On the R0 –property in fuzzy topological spaces (with D.M. Ali and P. Wuyts), Fuzzy and Systems, 38, 1990, 97-114
  25. Ultametrics and fuzzy uniform spaces, in: Proc. 2nd Biennial Conf. of Allhabad Math. Soc, 15-21, April 7-9, 1990.
  26. A note on K.K. Azad’s fuzzy Hausdorffness concept (with D.M. Ali), Fuzzy Sets and Systems, 42, 1991, 363-367
  27. On Preuss’ connectedness concept in fuzzy topology (with R. Lowen), Fuzzy Sets and Systems,47, 1991, 99-104
  28. On a–compact fuzzy compact topological spaces (with A. Choubey), Jour. Fuzzy Math., 1, 1993, 321-326
  29. Epis and injectives in fuzzy topology (with S.P. Mishra), Jour. Fuzzy Math., 1, 1993, 389-393
  30. On some fuzzy connectedness concepts in fuzzy topology (with A. Singh), Fuzzy Sets and Systems, 62, 1994, 227-229
  31. On an epireflective hull in fuzzy topology (with A. Choubey), Jour. Fuzzy Math., 2, 1994, 43-46
  32. Fuzzy closure spaces (with R. Srivastava and A. Choubey), Jour. of Fuzzy Math., 2, 1994, 525-534
  33. On disconnectedness in fuzzy topology (with A. Singh), Jour. of Fuzzy Math., 4, 1996, 85-91
  34. On certain initial completions in fuzzy topology (with A. Choubey), Quest. Math 1999
  35. On fuzzy sobriety (with A. Khastgir), Information Sciences, 110, 1998, 195-205
  36. On two epireflctive subcategories of the category of 2T0 – fuzzy bitopological spaces (with A. S. Khastgir), Quest. Math., 23, 2000, 163-177
  37. On T0 –objects in FTS and BFTS (with A. S. Khastgir), Fuzzy Sets & System, 109, 2000, 301 – 304.
  38. The role of Sierpinski object in fuzzy topology, in: Proc. Intern Conf. on Geom. Anal. & Appls., World Scientific Publ. (2001 ) 367 – 382.
  39. A topology for fuzzy automata (with S.P. Tiwari ) in: Proc. 2002 AFSS Intern. Conf. on Fuzzy Systems, (Springer) Lecture Notes in Artificial Intelligence vol. 2275 (2002) 485 – 490.
  40. On some injective congenerators in fuzzy topology, ibid, Lecture Notes in Artificial Intelligence, Vol. 2275, Springer (2002), 491 – 497.
  41. On some concepts related to fuzzy sobriety (with A. Singh ), Jl. of Fuzzy Math., 11, 2003, 17 – 25.
  42. On relationshing among fuzzy approximation operators, fuzzy topology and fuzzy automata (with S. P. Tiwari) , Fuzzy Sets & Systems, 138, 2003, 197 – 204.
  43. Fuzzy Chu spaces & fuzzy topologies (with S.P. Tiwari) Intern. J. Uncertainty, Fuzziness & Knowledge Based Systems, 12, 2004, 245 – 254.
  44. On decomposition of fuzzy automata (with S.P. Tiwari) Fuzzy Sets & Systems, 151, 2005, 503-511.
  45. Intuitionistic fuzzy automata and associated fuzzy topologies (with S.P. Tiwari), IEEE Comp. Soc. Conf. Proc.: ICCTA 07 (IEEE Intern. Conf. on Computation: Theory & Appls, Kolkata.), IEEE Press, 2007, 267-272.
  46. Injectives and essential extensions in fuzzy topology (with A. Singh and R. Srivastava), Aligarh Mathematical Bulletin, 26, 2007,15-19.
  47. IF-automata and IF-topologies (with S.P. Tiwari), Soft Computing (Springer) 14, 2010 571-578.
  48. On two topologies associated with a topology (with Sheo Kumar Singh) Quaestiones Math. 34(2011) 93-99.
  49. On some coreflective hulls in BFTS (with Veena Singh), Quaestiones Math., 2010, 33, 391-398.
  50. The coreflective hull of LD in L-TOP (with Veena Singh), Intern. Jour. of Fuzzy Mathematics, 19(2), 2011
  51. On categories of fuzzy Petri nets (with S.P. Tiwari), Advances in Fuzzy Systems2011, Article ID 812040, 5 Pages doi: 10.1155/2011/812040,
  52. On another decomposition of fuzzy automata, (with S. P. Tiwari), Jour. of Uncertain Systems Vol.5, No.1, pp.33-37, 2011
  53. On coreflective hulls in [0, 1]-TOP and s[0, 1]-TOP (with Veena Singh), Quaestiones Math. (accepted 2011)
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