Elbert A. Walker

....


Dept. of Mathematical Sciences  Phone: (505) 646-2027
New Mexico State University Fax: (505) 646-1064
Las Cruces, NM 88003 elbert@nmsu.edu


Office Location: New Science Hall Room 245
Professional Experience Education Publications
 Research Interests
Professional Service


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EDUCATION


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PERSONAL DATA


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PROFESSIONAL EXPERIENCE

Mathematics and English Teacher, Tarkington Prairie Rural Independent School District, Cleveland, Texas, 1950-1951;

Mathematics Teacher and Tennis Coach, Kingsville Independent School District, Kingsville, Texas, 1951-1952;

Graduate Student, University of Kansas, 1952-1955;

Research Mathematician, National Security Agency, Washington, D. C., 1955-1956;

Assistant Professor of Mathematics, University of Kansas, 1956-1957;

Assistant Professor of Mathematics, New Mexico State University, 1957-1959;

Associate Professor of Mathematics, New Mexico State University, 1959-1963;

Distinguished Associate Professor of Mathematics, New Mexico State University, 1961-1963;

Professor of Mathematics, New Mexico State University, 1963-87;

Member, Institute of Advanced Study, Princeton, New Jersey, 1963-1964 (on sabbatical leave from New Mexico State University);

Visiting Professor of Mathematics, Rice University, 1970-1971 (on sabbatical leave from New Mexico State University);

Graduate Student, Colorado State University, 1977-1978 (on sabbatical leave from New Mexico State University);

Professor Emeritus, New Mexico State University, 1987-;

Program Director for Special Projects, Division of Mathematical Sciences, National Science Foundation, Washington, D.C., 1987-1989;

Consultant, TCI Software Research, Las Cruces, New Mexico, 1992-96.


FELLOWSHIPS AND HONORS


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RESEARCH PAPERS
  1. Cancellation in direct sums of groups, Proc. Amer. Math. Soc., 7(1956), 898-902.
  2.    
  3. Subdirect sums and infinite Abelian groups, Pac. Jour. of Math., 9(1959), 287-291.
  4.  
  5. Almost locally pure Abelian groups, Pac. Jour. of Math., 9(1959), 409-413 (with D. L. Boyer).
  6.  
  7. Non-linear recursive sequences, Can. Jour. of Math., 11(1959), 370-378.
  8.  
  9. Direct summands of direct products of Abelian groups, Arkiv der Mathematik, 4(1960), 241-243.
  10.  
  11. On the orders of the automorphism groups of infinite torsion Abelian groups, Journal London Math. Soc., 35(1960), 385-388.
  12.  
  13. Quotient groups of reduced Abelian groups, Proc. Amer. Math. Soc., 12(1961), 91-92.
  14.  
  15. Torsion endomorphic images of mixed Abelian groups, Pac. Jour. of Math., 11(1961), 375-377.
  16.    
  17. On N-high subgroups of Abelian groups, Pac. Jour. of Math., vol. 11, No. 4 (1961), 1363-1374 (with J. M. Irwin).

  18. On isotype subgroups of Abelian groups, Bull. Soc. Math. France, 89(1961), 451-460 (with J. M. Irwin and C. Peercy).

  19. Splitting properties of high subgroups, Bull. Soc. Math. France, 90(1962), 185-192 (with J. M. Irwin and C. Peercy).

  20. High extensions of Abelian groups, Acta. Math. Sci. Hung., 14(1962), 319-330 (with D. K. Harrison, J. M. Irwin, and C. L. Walker).

  21. On p-pure sequences of Abelian groups, Topics in Abelian Groups, Scott Foresman and Co., Chicago, (1963) 69-119 (with J. M. Irwin and C. L. Walker).
  22.    
  23. The number of basic subgroups of primary groups, Acta Math. Acad. Sci. Hung., 15(1964), 153-155 (with S. Khabbaz).
  24.    
  25. Quotient categories and quasi-isomorphisms of Abelian groups, Proceedings of the Colloquium on Abelian Groups, 147-162, Hungarian Academy of Sciences, Budapest, 1964.

  26. On n-extensions of Abelian groups, Ann. Univ. Sci. Budapest, 8(1965), 71-74.
  27.  
  28. Primary Abelian groups as modules over their endomorphism rings, Math. Zeit., 89(1965), 77-81 (with F. Richman).
  29.  
  30. Quotient categories of modules, Proceedings of the Conference on Categorical Algebra La Jolla 1965, Springer-Verlag, Berlin, (1966) 404-420 (with C. L. Walker).

  31. Countable direct sums of torsion complete groups, Proc. Amer. Math. Soc., 17(1966), 763-766 (with J. M. Irwin and F. Richman).
  32.  
  33. Direct sum representations of injective modules, Journal of Algebra, 5(1967), 203-221 (with C. C. Faith).

  34. A note on direct products of free modules, Math. Monthly, 74(1967), 1079-1080.

  35. Cotorsion free, an example of relative injectivity, Math. Zeit., 192(1967), 115-117 (with F. Richman).
  36.  
  37. An extension of the Ulm-Kolettis theorem, Studies on Abelian Groups, Dunod, Paris, (1968), 309-325 (with L. Parker).

  38. Projective classes of Abelian groups, Studies on Abelian Groups, Dunod, Paris, (1968) 335-343 (with C. Walker and F. Richman).
  39.    
  40. Extending Ulm's theorem without group theory, Proc. Amer. Math. Soc., 21(1969), 194-196 (with F. Richman).

  41. Divisible quotient groups of reduced Abelian groups, Rocky Mountain Math. Jour., 1(1971), 353-355.

  42. Modules over PID's that are injective over their endomorphism rings, Ring Theory, 363-372, Academic Press, New York, 1972 (with F. Richman).

  43. Decompositions of direct sums of cyclic p-groups, Rocky Mountain Jour. of Math., 2(1972), 275-282 (with D. Tarwater).

  44. Quotient categories and rings of quotients, Rocky Mountain Jour. of Math., 2(1972), 513-555 (with C. Walker).

  45. Ulm's theorem for totally projective groups, Proc. Amer. Math. Soc., 37(1973), 387-392.

  46. The groups P, Symposia Mathematica, XIII(1974), 245-255.
  47.    
  48. An algebraic treatment of algebraically compact groups, Rocky Mountain Jour. of Math., 5(1975), 291-299 (with M. Legg).
  49.  
  50. Homological dimension of Abelian groups over their endomorphism rings, Proc. Amer. Math. Soc., 54(1976), 65-68 (with F. Richman).
  51.  
  52. Warfield modules, Lecture Notes in Mathematics, 616(1976), 87-123 (with R. Hunter and F. Richman).

  53. Ext in preabelian categories, Pac. Jour. of Math., 71(1977), 521-535 (with F. Richman).
  54.    
  55. Simply presented valuated p-groups, J. Algebra, 49 (1977), 125-133 (with R. Hunter and F. Richman).

  56. Finite direct sums of cyclic valuated p-groups, Pac. Jour. of Math., 69(1977), 97-133 (with R. Hunter and F. Richman).

  57. Existence theorems for Warfield groups, Trans. Amer. Math. Soc., 235(1978), 345-362 (with R. Hunter and F. Richman).

  58. Valuated groups, Journal of Algebra, 56(1979), 145-167 (with F. Richman).

  59. Direct sums of cyclic valuated groups, Symposia Mathematica, 23(1979), 77-84 (with D. Arnold and R. Hunter).
  60.  
  61. Cyclic Ext, Rocky Mountain Jour. of Math., 11(1981), 611-615 (with F. Richman).
  62.    
  63. S-groups revisited, Proc. Amer. Math. Soc., 82(1981) 13-18 (with R. Hunter).
  64.    
  65. Valuated p-groups, Lecture Notes in Mathematics, 874(1981), 350-373 (with R. Hunter).

  66. Finite valuated p-groups, Lecture Notes in Mathematics, 1006(1982), 471-507 (with D. Beers and R. Hunter).
  67.  
  68. Group algebras of Abelian groups, Rend. Sem. Mat. Univ. Padova, 69(1983), 41-50 (with D. Beers and F. Richman).
  69.  
  70. Estimation in change-point hazard rate models, Biometrika, 71(1984), 299-304 (with H. Nguyen and G. Rogers).
  71.  
  72. Subgroups of bounded abelian groups, Abelian groups and modules, CISM Lectures 287, Udine, (1984), 17-36 (with R. Hunter and F. Richman).

  73. The thermodynamics of bovine and porcine insulin and proinsulin association determined by concentration difference spectroscopy, Archives of Biochemistry and Biophysics, 238(1985), 30-42 (with S. Strazza, R. Hunter and D. Darnall).
  74.    
  75. Delayed exponential models in survival analysis, Publ. Inst. Statist. Univ. Paris, XXX, fasc. 3(1985), 59-85 (with H. Nguyen and G. Rogers).

  76. Ulm's theorem for simply presented valuated p-groups, Abelian Group Theory, Proceedings of the third Conference on Abelian Group Theory at Oberwolfach, August 11-17, 1985, Gordon and Breach, New York, 1986, 33-64 (with R. Hunter and F. Richman).

  77. Computing valuated trees, Abelian Group Theory, Proceedings of the third Conference on Abelian Group Theory at Oberwolfach, August 11-17, 1985, Gordon and Breach, New York, 1986, 65-88 (with D. Beers, R. Hunter and F. Richman).

  78. A Mathematical Analysis of the Bjerrum Function for the Stepwise Equilibrium Model, Journal of Mathematical Chemistry 1(1987) 235-247 (with E. Birnbaum).

  79. A Simple Look at Conditional Events, Conditional Logic in Expert Systems, I. R. Goodman, M. M. Gupta, H. T. Nguyen, and G. S. Rogers, editors, North-Holland, Amsterdam, 1991, 101-114.

  80. On Decision Making Using Belief Functions, Advances in Dempster-Shafer Theory of Evidence, (R. Yager et al Eds.), J. Wiley, (1994) 311-330 (with H. Nguyen).

  81. Stone Algebras, Conditional Events, and Three Valued Logic, IEEE Transactions of Man, Systems, and Cybernetics 24(12) (1994), 1699-1707.
  82.    
  83.  A History and Introduction to the Algebra of Conditional Events and Probability Logic, IEEE Transactions of Man, Systems, and Cybernetics 24(2) 1671-1675 (with H. Nguyen).

  84. Iterated Conditionals and Symmetric Stone Algebras, Discrete Mathematics ,148(1996) 49-61(with Mai Gehrke).
  85.  
  86. On the Structure of Rough Sets, Bull.Polish Academy of Sci. Math., 40(1992) 235-245 (with Mai Gehrke).

  87. Calculating maximum-entropy probability densities for belief functions, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2(4) (1994) 377-389 (with A. Meyerwitz, and F. Richman).
  88.    
  89. Maximum Entropy Method in Expert Systems and Intelligent Control: New Possibilities and Limitations, Maximum Entropy and Bayesian Methods, (K. M. Hanson and R. N. Siver, Eds), Kluwer Academic (1996) 93-100 (with H. Nguyen and V. Kreinovich).

  90. Stone Algebra Extensions with Bounded Dense Sets, Algebra Universalis, 37(1997) 1-23 (with M. Gehrke and C. Walker).

  91. DeMorgan Systems on the Unit Interval, International Journal of Intelligent Systems 11(1996) 733-750 (with M. Gehrke and C. Walker).

  92. Some Comments on Interval Valued Fuzzy Sets, International Journal of Intelligent Systems 11(1996) 751-759 (with M. Gehrke and C. Walker).

  93. A Mathematical Setting for Fuzzy Logics, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 5(1997) 223-238 (with M. Gehrke and C. Walker).

  94. Filtered Modules over Discrete Valuations Domains,  Journal of Algebra,  199 (1998) 618-645 (with F. Richman).
  95.  
  96. Some Group Theoretic Aspects of t-Norms, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems,  8(2000), 1-6 (with F. Richman).
  97.    
  98. A Note On Negations and Nilpotent t-Norms, International Journal of Approximate Reasoning, 21(1999) 137-155 (with M. Gehrke and C. Walker).

  99. Averaging Operators On the Unit Interval, International Journal of Intelligent Systems, (Special Issue: The Mathematics of Fuzzy Sets) 14(9) (1999) 883-898 (with M. Gehrke and C. Walker).

  100. Subgroups of p5 -bounded groups, Trends in Mathematics, (1999), Birkhauser Verlag, Basel, 55-73 (with F. Richman).

  101. Powers of t-Norms, Fuzzy Sets and Systems, 129 (2002) 1-18, (with C. Walker).
  102.  
  103. Varieties generated by t-norms, Soft Computing, vol. 8, no. 4 (2004), 264-267 (with M. Gehrke and C. Walker).

  104. Abelian Groups at New Mexico State University, Rocky Mountain Journal of Mathematics, volume 32, Number 4, Winter 2002, 1257-1265.

  105. Fuzzy Logics Arising from Strict De Morgan Systems, Topological and Algebraic Structures in Fuzzy Sets, A Handbook of Recent Developments in the Mathematics of Fuzzy Sets, S. Rodabaugh and E. P. Klement, Eds., Kluwer, Dordrecht, (2003) Chapter 9, 257-276 (with M. Gehrke and C. Walker).
  106.    
  107. Groups, t-Norms, and Families of De Morgan Systems, Topological and Algebraic Structures in Fuzzy Sets, A Handbook of Recent Developments in the Mathematics of Fuzzy Sets, S. Rodabaugh and E. P. Klement, Eds., Kluwer, Dordrecht, (2003) Chapter 19, 455-  (with C. Walker).

  108. Normal forms and truth tables for fuzzy logics, Fuzzy Sets and Systems: Special Focus Issue,  volume 138, number 1 (2003), pp 25-51 (with M. Gehrke and C. Walker).
  109.    
  110. Generalizing leximin to t-norms and t-conorms: the lexit and lexis orderingsFuzzy Sets and System,  151 (2005) 327-340  (with R. Yager and C. Walker).

  111. The algebra of fuzzy truth values, Fuzzy Sets and Systems, 149(2), Jan. 2005, 309-347  (with C. Walker).

  112. Varieties of algebras in fuzzy set theoryLogical, Algebraic, Analytic, and Probabilistic Aspects of Triangular Norms, E. P. Klement and R. Mesier, eds., Elsevier, Amsterdam, 2005, pp. 321-344, (with G. Bezhanisvili, M. Gehrke, J. Harding, and C.Walker).

  113. Estimability and Optimality in Sample Survey Models I, Journal of Taiwan Intelligent Technologies and Applied Statistics, Vol. 3,. No. 2 (2005), 1-25.
  114.    
  115. Estimability and Optimality in Sample Survey Models II, Journal of Taiwan Intelligent Technologies and Applied Statistics, Vol. 4, No. 1, (2006), 1-18.

  116. Automorphisms of powers of linearly ordered sets, International Journal of Uncertainty, Fuzziness and Knowledge-based Systems, Vol. 14, No.1 (2006), 77-85, (with C. Walker).

  117. Automorphisms of the Algebra of Fuzzy Truth Values, International Journal of Uncertainty, Fuzziness and Knowledge-based Systems, 14(6) (2006), 711-732 (with C. Walker).

  118. Automorphisms of the Algebra of Fuzzy Truth Values II, International Journal of Uncertainty, Fuzziness and Knowledge-based Systems, 16(5) (2008) 627-643 (with C. Walker).

  119. Lattices of Convex Normal Functions, Fuzzy Sets and Systems, 159 (2008), 1061-1071  (with J. Harding and C. Walker).

  120. Some General Comments on Fuzzy Sets of  Type-2International Journal of Intelligent Systems, 24(1) (2009) 62-75 (with C. Walker).

  121. Sets With Type-2 OperationsInternational Journal of Approximate Reasoning, 50(2009) 63-71 (with C. Walker).

  122. Convex normal functions revisited, Fuzzy Sets and Systems, 161 (2010)  pp. 1343-1349  (with J. Harding and C. Walker). 

  123. The variety generated by the truth value algebra of type-2 fuzzy sets, Fuzzy Sets and Systems, 161 (2010) (5)  pp. 735-749 (with J. Harding and C. Walker).

  124. Projective Bichains, Algebra Universalis, 67 (2012) 347-374 (with J. Harding and C. Walker).

  125. A Family of Finite DeMorgan and Kleene Algebras, International Journal of Uncertainty, Fuzziness and Knowledge-based Systems, vol. 20-5, October 2012, pp.631-653  (with C. Walker).

  126. Type-2 Operations on Finite Chains, Fuzzy Sets and Systems, 236 (2014), 33-49  (with C. Walker).

  127. Categories with Fuzzy Sets and Relations, Fuzzy Sets and Systems, 256 (2014) 149-165  (J. Harding and C. Walker).

  128.  Type-2 Fuzzy Sets and BiChains, Advances in Type-2 Fuzzy Sets and Systems, Theory and Applications, A. Sadeghian, J. Mendel, and H. Tahayori, Eds., Springer, Berlin, 2013, pp. 97-112 (with J. Harding and C. Walker).  

  129. Partial Orders on Fuzzy Truth Value Algebras, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 23(2) (2015) 193-219 (with J. Harding and C. Walker).

95. The convolution algebra, arXiv 1702.02847, https://arxiv.org/abs/1702.02847 (with J. Harding and C. Walker).



SURVEYS, PROCEEDINGS, AND ABSTRACTS

     
  1. A mathematical setting for fuzzy propositional logic, Enriched Lattice Structures for Many-Valued and Fuzzy Logics, Linz '97, February 25-March 1, 1997  (with M. Gehrke and C. Walker).

  2. Nilpotent t-norms and negations, Enriched Lattice Structures for Many-Valued and Fuzzy Logics, Linz '97, February 25-March 1, 1997  (with M. Gehrke and C. Walker).

  3. De Morgan systems on the unit interval, Enriched Lattice Structures for Many-Valued and Fuzzy Logics, Linz '97, February 25-March 1, 1997  (with M. Gehrke and C. Walker).

  4. Averaging operators on the unit interval, Non-Classical Measures and their Applications to Decision Making, Linz '98, February 24-February 28, 1998 (with M. Gehrke and C. Walker).

  5. Algebraic aspects of fuzzy sets and fuzzy logic, (a survey of several papers up to 1998) Proceedings of the Workshop on Current Trends and Developments in Fuzzy Logic, Thessaloniki, Greece, October 16-20, 1998 (1999) 101-170 (with M. Gehrke and C. Walker).

  6. Some group theoretic aspects of t-norms, Proceedings of the Eighth International Fuzzy System Association World Congress, Vol I, Taipei, Taiwan ROC, August 17-20 (1999) 255-259 (with C. Walker).

  7. Algebraic aspects of fuzzy connectives (a survey of several papers) Proceedings of International symposium on Medical Informatics and fuzzy Technology: MIF'99,  Hanoi, Vietnam, August 26-29 (1999) 306-314 (with M. Gehrke, C. Walker).

  8. Groups and Families of Triple Systems, Topological and Algebraic Structures, Linz '99 Seminar on Fuzzy Set Theory, February 2-6, 1999 (with C. Walker).

  9. Powers of  T-Norms, Topological and Algebraic Structures, Linz '99 Seminar on Fuzzy Set Theory, February 2-6, 1999 (with C. Walker).

  10. Varieties generated by strict de Morgan systems on the unit interval, Topological and Algebraic Structures, Linz '99 Seminar on Fuzzy Set Theory, February 2-6, 1999 (with M. Gehrke and C. Walker).

  11. Some algebraic aspects of fuzzy sets and fuzzy logic (condensed version of invited address), Intech 2000, Assumption University, Bangkok, Thailand (with M Gehrke and C. Walker).

  12. Fuzzy normal forms and truth tables, Proceedings of  the JCIS 2000, 4 pp., Atlantic City, New Jersey, February 17-March 2, 2000 (with M. Gehrke and C. Walker).

  13. Some comments on fuzzy normal forms, Proceedings of the ninth IEEE international conference on fuzzy systems: FUZZ-IEEE 2000, San Antonio, TX, May 7-10, vol 2 (2000), pp. 593-596.

  14. Inequalities in De Morgan systems, Proceedings of the second International conference on Intelligent Technologies: InTech 2001, Bangkok, Thailand, November 27-29 (2001) 255-259 (with C. Walker).

  15. Categories of Fuzzy SetsProceedings of the second International conference on Intelligent Technologies: InTech 2001, Bangkok, Thailand, November 27-29 (2001)  ( C. Walker only).

  16. Normal Forms and Truth Tables for Interval-valued Fuzzy Logic, 2001 Transactions of the Joint IFSA World Congress and 20-th NAFIPS International Conference, July 25-28, Vancouver, British Columbia, 1327-1331 (with M. Gehrke and C. Walker).

  17. Some Basic Theory of Interval-valued Fuzzy Sets, Transactions of the Joint IFSA World Congress and 20-th NAFIPS International Conference, Vancouver, British Columbia,July 25-28 (2001) 1332-1336 (with M. Gehrke and C. Walker).

  18.  Inequalities in De Morgan Systems I, 2002 IEEE Proceedings of the International Conference on Fuzzy Systems, Honolulu, Hawaii, May 12-17 (2002) 607-609 (with C. Walker).

  19.  Inequalities in De Morgan Systems II, 2002 IEEE Proceedings of the International Conference on Fuzzy Systems, Honolulu, Hawaii, May 12-17 (2002) 610-615 (with C. Walker).

  20. Varieties generated by t-norms, Proceedings of the Third International Conference on Intelligent Technologies and Third Vietnam-Japan Symposium on Fuzzy Systems and Applications, Hanoi, Vietnam, December 3-5 (2002) 22-24 (with G. Bezhanisvili, M. Gehrke, J. Harding, and C. Walker).

  21. Algebraic Structures on fuzzy sets of type-2, Proceedings of International conference on Fuzzy Information Processing: Theories and Applications, Beijing, China, March 1-4 (2003) 97-100 (with C. Walker).

  22. T-Norms on Fuzzy Sets of  Type-2, Triangular Norms and Related Operators in Many-Valued Logics, 24-th Linz Seminar on Fuzzy Set Theory,  February 4-8,  2003, Linz, Austria (with C. Walker).

  23. Varieties Generated by t-Norms, Triangular Norms and Related Operators in Many-Valued Logics, 24-th Linz Seminar on Fuzzy Set Theory,  February 4-8,  2003, Linz, Austria (with G. Bezhanishvili, M. Gehrke, J. Harding, and C. Walker).

  24. Estimability and Admissibility in Sample Survey ModelsSoft Methodology and Random Information Systems,  May 2004, pp. 93-100  (extended abstract of paper presented at the 2nd International Conference on Soft methods in Probability and Statistics held in Oviedo at the Univeristy of Oviedo), M. Lopez, M. Gil, P. Grzegorzweski, O. Hyrniewicz, and J. Lawry, eds.,

  25. Ordinary, Interval-valued, and Type-2 Fuzzy Sets, (Invited address) Proceedings  of the International Conference on Intelligent Technologies 2003,  Chiang Mai, Thailand, December 17-19, (2003), xiii (with C. Walker).

  26. Generalizing  Leximin to t-norms and t-conorms, 2004 Proceedings of the 20-th NAFIPS International Conference, June 27-30, Banff, Alberta, Canada, 343-345 ( with C. Walker and R. Yager).

  27. Automorphisms of Algebras of  Fuzzy Truth Values, Proceedings of the International Conference on Intelligent Technologies 2004, Houston, Texas,  5 pp. (with C. Walker).

  28. Some Comments on Lexi-T Orderings for Strict t-Norms, IEEE International Conference on Fuzzy Systems, May 22-25, 2005, Reno, Nevada, abstract, 669-671, (with C. Walker and R. Yager).

  29. Automorphisms of Powers of Linearly Ordered SetsAlgebraic and Topological Methods in Non-Classical Logics II, June 15-18, 2005, Barcelona, Spain,  89-90, abstract, (with C. Walker).

  30. An Algebraic Setting for Belief Functions, 2005 Proceedings of the 21-st NAFIPS International Conference, June 22-25, Ann Arbor, Michigan, 5pp.

  31. Automorphisms of the Algebra of Fuzzy Truth Values I, Proceedings of the 8-th Joint Conference on Information Sciences, July 21-25, 2005, Salt Lake City, Utah, 3pp. abstract, (with C. Walker). 

  32. Automorphisms of the Algebra of Fuzzy Truth Values II, Proceedings of the 8-the Joint Conference on Information Sciences, July 21-25, 2005, Salt Lake City, Utah, 2 pp. abstract, (with C. Walker).

  33.  Some General Comments of Fuzzy Sets of Type-2, BISCSE05, Forging New Frontiers, November 2-5, 2005,  Berkeley, Cal., abstract, (with C. Walker).

  34. Some General Comments on Type-2 Fuzzy Sets, Proceedings of the 6-th International Conference on Intelligent Technologies  (InTech '05) , (Abstract of Plenary Address), Dec 14-16, 2005,  Phuket, Thailand, (with C. Walker).

  35. Sets with type-2 operations2006 Proceedings of the 21-st NAFIPS International Conference, Montreal, Canada, June 3-6, 5pp. abstract, (with C. Walker).

  36. T-norms for type-2 fuzzy sets, 2006 Proceedings of the World Congress on Computational Intelligence, Vancouver, Canada, July 16-21, 4 pp. abstract, (with C. Walker).

  37. A  Survey of  Some Mathematical Aspects of Fuzzy Sets of Type-2Proceedings of the 7-th International Conference on Intelligent Technologies  (InTech '06) , (Abstract of one hour Invited Address), Dec 13-15, 2006, Taipei, Taiwan, (with C. Walker).

  38. Subalgebras of the Algebra of Truth Values of type-2 Sets and their AutomorphismsFuzzy Sets, Probability, and Statistics, 28-th Linz Seminar on Fuzzy Set Theory, February 6-10, 2007, Linz, Austria (with C. Walker).

  39. Points With Type-2 Operations, 2007 IFSA World Congress, June 18-21, 2007, Cancun (with C. Walker).

  40. Type-2 Intervals of Constant Height2007 Proceedings of the NAFIPS International Conference,, June 24-27, 2007, San Diego (with C. Walker).

  41. On Complete Sublattices of the Algebra of Truth Values of Type-2 Fuzzy Sets, 2007 IEEE Conference on Fuzzy Systems, Imperial College, London, 23-26 July 2007 (with J. Harding and C. Walker).

  42. A Family of Finite De Morgan Algebras, Algebraic and Topological Methods in Non-Classical Logics III (TANCL '07), August 5-9, 2007, St. Anne's College, University of Oxford, Oxford, England (with C. Walker).

  43. On Some Topological Properties of the Subalgebra of Normal Convex Functions of the Algebra of Truth Values of Type-2 Fuzzy SetsFoundations of Lattice-Valued Mathematics with Applications to Algebra and Topology,  29-th Linz Seminar on Fuzzy Set Theory,  February 12-16,  2008, Linz, Austria (with J. Harding and C. Walker).

  44. Automorphisms of Subalgebras of Truth Values of Type-2 Fuzzy SetsFoundations of Lattice-Valued Mathematics with Applications to Algebra and Topology,  29-th Linz Seminar on Fuzzy Set Theory,  February 12-16,  2008, Linz, Austria (with C. Walker).

  45. The Algebra of  Truth Values of Type-2 Fuzzy Sets: A SurveyInternational Workshop of  Interval/Probabilistic Uncertainty and Non-Clasical Logics (UncLog '08), Japan Advanced Institute of Science and Technology, Ishikawa, Japan, March 25-28, 2008 (with C. Walker).

  46. Generating a Maximum Entropy Probability Density from an Interval-Valued Fuzzy Set, 2008 Proceedings of the NAFIPS International Conference, May 19-22, 24-27, 2008, New York,  (with C. Walker and R. Yager ).
     
  47. Some Comments on Level Sets of  Fuzzy Sets2008 Proceedings of the World Congress on Computational Intelligence, Hong Kong,  June 1-61, (with C. Walker and R. Yager).

  48. Fuzzy Sets of Type-2: A Survey, Proceedings of the 9-th International Conference on Intellignet Technologies (InTech 08), (Abstract of one hour Invited Talk), Oct. 7-9, Samui, Thailand,(with C. Walker).

  49. Varieties Generated by Truth Value Algebras of Type-2 Fuzzy Sets, Topology, Algebra and Categories in Logic, Amsterdam, July 7-11, 2009 (with J. Harding and C. Walker).
  50. Generating Minimum Dispersion Densities from an Interval-Valued Fuzzy Set, Proceedings IFSA/EUSFLAT 2009, Lisbon, Portugal, July 20-24, 219-224 (with C. Walker and R. Yager).

  51. A Family of Finite De Morgan Algebras, 2009 Proceedings of the NAFIPS International Conference, June 14-17, 6pp., Cincinnati, Ohio  (with C. Walker ).

  52. Varieties Generated by Truth Value Algebras of Type-2 Fuzzy Sets, BLAST, New Mexico State University, Aug. 10-14, 2009, Las Cruces, N.M. (with J. Harding and C. Walker).

  53. Type-2 Fuzzy Sets and Bichains, 2010 Proceedings of the NAFIPS International Conference, July 12-14, 6pp., Toronto, Canada  (with J. Harding and C. Walker ).

  54. Bichains, Decision Theory: Qualitative and Quantative Approaches, 32nd Linz Seminar on Fuzzy Set Theory, February 1-5, 2011, Linz, Austria (with J. Harding and C. Walker).

  55. A Prioritized Measure for Multi-Criteria Aggregation and its Shapely Index, Proceedings of the NAFIPS International Conference,March 18-20, 2011, El Paso (with C. Walker, and R. Yager)

  56. Bichains, Proceedings of the NAFIPS International Conference, March 18-20, 2011, El Paso (with J. Harding and C. Walker)

  57. Bichains, Colloquium, Faculty of Science, Chiang Mai University, April, 2011, Chiang Mai, Thailand (with C. Walker).

  58. Equational Bases for Type-2 Fuzzy Sets, World Conference on Soft Computing, May 23-26, 2011, San Francisco (with J. Harding and C. Walker)

  59. Bichains, Second International Conference on Order, Algebra, and Logics, June 6-10, 2011, Krakow (with J. Harding and C. Walker)

  60. Type-2 Operations on Finite Chains, Fall Symposium on Fuzzy Mathematics, Kent State and Youngstown State Universities, Oct 13-16, 2011,  (with C. Walker)

  61. Type-2 Operations on Finite Chains, Enriched Category Theory and Related Topics, 33rd Linz Seminar on Fuzzy Set Theory, February 14-`18, 2012, Linz, Austria (with C. Walker)

  62. Categories of Fuzzy Sets and Relations, Enriched Category Theory and Related Topics, 33rd Linz Seminar on Fuzzy Set Theory, February 14-`18, 2012, Linz, Austria (with J. Harding and C. Walker) 

  63. Categories of Interval-Valued Fuzzy Sets2012 Proceedings of the NAFIPS International Conference, August 6-8, Berkeley,  (with J. Harding and C. Walker ).

  64. Type-2 Operations on Finite Chains, Colloquium, Mathematics Department, Sam Houston State University, Nov 2, 2011.

  65. Partial Orders on the Truth Value Algebra of Type-2 Fuzzy Sets, Non-Classical Measures and Integrals, 34th Linz Seminar on Fuzzy Set Theory, February 26-March 2, 2013, Linz, Austria (with J. Harding and C. Walker) 


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Last modified: March 21, 2003