....

• B. A., Sam Houston State College, 1950 (Mathematics)
• M. A., Sam Houston State College, 1952 (Mathematics)
• Ph.D., University of Kansas, 1955 (Mathematics)
• M. S., Colorado State University, 1978 (Statistics)

• Date of Birth - March 11, 1930
• Place of Birth - Huntsville, Texas
• Citizenship - USA

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.

• Fellowship in College Teaching, University of Kansas, 1952-1953;

• University Fellowship, University of Kansas, 1953-1955;

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

• National Science Foundation Senior Postdoctoral Fellow, 1963-1964;

• Westhafer Award for Research, 1965 (New Mexico State University award to its outstanding faculty researcher of that year);

• National Science Faculty Professional Development Fellowship, 1977-1978.

1. Cancellation in direct sums of groups, Proc. Amer. Math. Soc., 7(1956), 898-902.
   

2. Subdirect sums and infinite Abelian groups, Pac. Jour. of Math., 9(1959), 287-291.
 
3. Almost locally pure Abelian groups, Pac. Jour. of Math., 9(1959), 409-413 (with D. L. Boyer).
 
4. Non-linear recursive sequences, Can. Jour. of Math., 11(1959), 370-378.
 
5. Direct summands of direct products of Abelian groups, Arkiv der Mathematik, 4(1960), 241-243.
 
6. On the orders of the automorphism groups of infinite torsion Abelian groups, Journal London Math. Soc., 35(1960), 385-388.
 
7. Quotient groups of reduced Abelian groups, Proc. Amer. Math. Soc., 12(1961), 91-92.
 
8. Torsion endomorphic images of mixed Abelian groups, Pac. Jour. of Math., 11(1961), 375-377.
   

9. On N-high subgroups of Abelian groups, Pac. Jour. of Math., vol. 11, No. 4 (1961), 1363-1374 (with J. M. Irwin).


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


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


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


13. On p^ß-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).
   

14. The number of basic subgroups of primary groups, Acta Math. Acad. Sci. Hung., 15(1964), 153-155 (with S. Khabbaz).
   

15. Quotient categories and quasi-isomorphisms of Abelian groups, Proceedings of the Colloquium on Abelian Groups, 147-162, Hungarian Academy of Sciences, Budapest, 1964.


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


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


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


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


24. Projective classes of Abelian groups, Studies on Abelian Groups, Dunod, Paris, (1968) 335-343 (with C. Walker and F. Richman).
   

25. Extending Ulm's theorem without group theory, Proc. Amer. Math. Soc., 21(1969), 194-196 (with F. Richman).


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


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


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


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


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


31. The groups P_ß, Symposia Mathematica, XIII(1974), 245-255.
   

32. An algebraic treatment of algebraically compact groups, Rocky Mountain Jour. of Math., 5(1975), 291-299 (with M. Legg).
 
33. Homological dimension of Abelian groups over their endomorphism rings, Proc. Amer. Math. Soc., 54(1976), 65-68 (with F. Richman).
 
34. Warfield modules, Lecture Notes in Mathematics, 616(1976), 87-123 (with R. Hunter and F. Richman).


35. Ext in preabelian categories, Pac. Jour. of Math., 71(1977), 521-535 (with F. Richman).
   

36. Simply presented valuated p-groups, J. Algebra, 49 (1977), 125-133 (with R. Hunter and F. Richman).


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


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


39. Valuated groups, Journal of Algebra, 56(1979), 145-167 (with F. Richman).
    
    
40. Direct sums of cyclic valuated groups, Symposia Mathematica, 23(1979), 77-84 (with D. Arnold and R. Hunter).
 
41. Cyclic Ext, Rocky Mountain Jour. of Math., 11(1981), 611-615 (with F. Richman).
   

42. S-groups revisited, Proc. Amer. Math. Soc., 82(1981) 13-18 (with R. Hunter).
   

43. Valuated p-groups, Lecture Notes in Mathematics, 874(1981), 350-373 (with R. Hunter).


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


48. 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).
   

49. Delayed exponential models in survival analysis, Publ. Inst. Statist. Univ. Paris, XXX, fasc. 3(1985), 59-85 (with H. Nguyen and G. Rogers).


50. 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).


51. 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).


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


53. 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.


54. 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).


55. Stone Algebras, Conditional Events, and Three Valued Logic, IEEE Transactions of Man, Systems, and Cybernetics 24(12) (1994), 1699-1707.
   

56.  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).


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


59. 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).
   

60. 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).


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


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


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


64. 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).
    
    
65. Filtered Modules over Discrete Valuations Domains,  Journal of Algebra,  199 (1998) 618-645 (with F. Richman).
    
 

66. Some Group Theoretic Aspects of t-Norms, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems,  8(2000), 1-6 (with F. Richman).
   

67. A Note On Negations and Nilpotent t-Norms, International Journal of Approximate Reasoning, 21(1999) 137-155 (with M. Gehrke and C. Walker).


68. 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).
    
    
69. Subgroups of p⁵ -bounded groups, Trends in Mathematics, (1999), Birkhauser Verlag, Basel, 55-73 (with F. Richman).
    


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


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


73. 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).
   

74. 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).


75. 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).
   

76. Generalizing leximin to t-norms and t-conorms: the lexit and lexis orderings,  Fuzzy Sets and System,  151 (2005) 327-340  (with R. Yager and C. Walker).


77. The algebra of fuzzy truth values, Fuzzy Sets and Systems, 149(2), Jan. 2005, 309-347  (with C. Walker).
    
    
78. Varieties of algebras in fuzzy set theory,  Logical, 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).
    
    
79. Estimability and Optimality in Sample Survey Models I, Journal of Taiwan Intelligent Technologies and Applied Statistics, Vol. 3,. No. 2 (2005), 1-25.
    
   
80. Estimability and Optimality in Sample Survey Models II, Journal of Taiwan Intelligent Technologies and Applied Statistics, Vol. 4, No. 1, (2006), 1-18.
    
    
81. 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).
    
    
82. Automorphisms of the Algebra of Fuzzy Truth Values, International Journal of Uncertainty, Fuzziness and Knowledge-based Systems, 14(6) (2006), 711-732.
    
    
83. Automorphisms of the Algebra of Fuzzy Truth Values II, International Journal of Uncertainty, Fuzziness and Knowledge-based Systems, submitted (with C. Walker).
    
    
84. Lattices of Convex Normal Functions, Fuzzy Sets and Systems, 159 (2008), 1061-1071  (with J. Harding and C. Walker).
    
    
85. Some General Comments on Fuzzy Sets of  Type-2,  International Journal of Intelligent Systems, to appear (with C. Walker).
    
    
86. Sets With Type-2 Operations,  International Journal of Approximate Reasoning, paper for special issue,  to appear (with C. Walker).

 
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 Sets,  Proceedings 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 Models,  Soft 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, (2004), 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 Sets,  Algebraic 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 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).
    
    
34. Sets with type-2 operations,  2006 Proceedings of the 21-st NAFIPS International Conference, Montreal, Canada, June 3-6, 5pp. abstract, (with C. Walker).
    
    
35. 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).
    
    
36. A  Survey of  Some Mathematical Aspects of Fuzzy Sets of Type-2,  Proceedings 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).
    
    
37. Subalgebras of the Algebra of Truth Values of type-2 Sets and their Automorphisms,  Fuzzy Sets, Probability, and Statistics, 28-th Linz Seminar on Fuzzy Set Theory, February 6-10, 2007, Linz, Austria (with C. Walker).
    
    
38. Points With Type-2 Operations, 2007 IFSA World Congress, June 18-21, 2007, Cancun (with C. Walker).
    
    
39. Type-2 Intervals of Constant Height,  2007 Proceedings of the NAFIPS International Conference,, June 24-27, 2007, San Diego (with C. Walker).
    
    
40. 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).
    
    
41. 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).
    
    
42. On Some Topological Properties of the Subalgebra of Normal Convex Functions of the Algebra of Truth Values of Type-2 Fuzzy Sets,  Foundations 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).
    
    
43. Automorphisms of Subalgebras of Truth Values of Type-2 Fuzzy Sets,  Foundations 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).
    
    
44. The Algebra of  Truth Values of Type-2 Fuzzy Sets: A Survey,  International 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).
    
    
45. Generating a Maximum Entropy Probability Density from an Interval-Valued Fuzzy Set, 2008 Proceedings of the NAFIPS International Conference, May 19-2224-27, 2008, New York,  (with C. Walker and R. Yager ).
     
46. Some Comments on Level Sets of  Fuzzy Sets,  2008 Proceedings of the World Congress on Computational Intelligence, Hong Kong,  June 1-61, (with C. Walker and R. Yager).
    
    
    

• An Introduction to Modern Algebra and Analysis, Holt, Rinehart and Winston, New York, 1962 (with R. Crouch).
• College Trigonometry, Scott Foresman and Co., Chicago, 1970 (with F. Richman and C. Walker).
• Introduction to Abstract Algebra, Random House/Birkhauser, New York, 1987. (PDF files available below)
• Conditional Inference and Logic for Intelligent Systems, North-Holland, Amsterdam, 1991 (with I. R. Goodman and H. T. Nguyen).
• Fundamentals of Uncertainty Calculi with Applications to Fuzzy Inference, Kluwer Academic Publishers, Dordrecht, 1995 (with H. T. Nguyen and M. Grabisch).
• A First Course in Fuzzy Logic, CRC Press, Boca Raton, Florida (1997); Second Edition (1999), Third Edition (2006), (with H. T. Nguyen).
• A First Course in Fuzzy and Neural Control, Chapman & Hall/CRC, Boca Raton, Florida (2003) (with H. Nguyen, R. Prasad, and C. Walker).
   


PDF FILES OF INTRODUCTION TO ABSTRACT ALGEBRA

Table of Contents
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Appendix
Bibliography And Index
Whole Book
 

BOOKS EDITED

• Topics in Abelian Groups, Proceedings of the First New Mexico State University Abelian Group Theory Conference, Scott Foresman and Co., Chicago, 1963 (with J. M. Irwin).
• Abelian Group Theory, Proceedings of the Second New Mexico State University Abelian Group Theory Conference, Lecture Notes in Mathematics, 616, Springer-Verlag, Berlin, 1976 (with D. Arnold and R. Hunter).
• Abelian Group Theory, Proceedings of the Oberwolfach Abelian Group Theory Conference, January 12-17, 1981, Lecture Notes in Mathematics, 874, Springer-Verlag, Berlin, 1981 (with R. Goebel).
• Abelian Group Theory, Proceedings of the Third Conference on Abelian Group Theory at Oberwolfach, August 11-17, 1985, Gordon and Breach, New York, 1987 (with R. Goebel).
      

SLIDES

RESEARCH GRANTS

• National Science Foundation G17978, Principal Investigator, June 1961 - June 1963
• National Science Foundation GP377, Principal Investigator, June 1963 - June 1965
• National Science Foundation GP3581, Principal Investigator, June 1965 - June 1967
• National Science Foundation GP6564, Principal Investigator, June 1967 - June 1969
• National Science Foundation DP13286, Principal Investigator, June 1969 - June 1970
• National Science Foundation GP21558, Principal Investigator, June 1970 - June 1971
• National Science Foundation GP283379, Principal Investigator, June 1971 - June 1975
• National Science Foundation MPS75-01734, Principal Investigator, June 1975 - June 1976
• National Science Foundation MPS-11378, Principal Investigator, June 1976 - June 1977
• National Science Foundation MPS-03458, Principal Investigator, June 1977 - June 1980
• National Science Foundation DMS-8003060, Principal Investigator, June 1980 - June 1983
• Southwest Resource Center for Science and Engineering, Principal Investigator (For Graduate Student Support), July 1982 - June 1983
• National Science Foundation DMS-8305049, Principal Investigator (Research Equipment Grant), August 83 -January 85
• National Science Foundation DMS-8301606, Principal Investigator, June 1983 - June 1986
• National Science Foundation DMS-8505018, Principal Investigator (Research Equipment Grant), June 1985 - June 1986

PH.D. STUDENTS

• Thirteen Ph.D. students - most of the dissertations involved applications of homological algebra and category theory to Abelian Group Theory. Two dissertations were in ring theory.

• Abelian Group Theory
• Statistics
• Applications of Computing to Mathematical Research
• Lattice Theory
• The mathematics of fuzzy sets and fuzzy logic.

• American Mathematical Society
• Mathematics Association of America
• American Statistical Association
• Biometric Society
• Phi Kappa Phi
• IEEE
• NAFIPS