Topics are
- Belief Functions
- Choquet Integrals
- Competence Sets
- Data Envelopment Analysis
- Solving Nonlinear Equations
- Imprecise Probability
- Networks Problems
- Nonstandard Analysis
- Simulation
- Fuzzy Quantum Field Theory
- Quantum Probability
\begin{equation}{\label{a}}\tag{A}\mbox{}\end{equation}
Belief Functions.
\item Petit-Renaud, S. and Denoeux, T.:
Nonparametric Regression Analysis of Uncertain and Imprecise Data Using Belief Functions,
{\em International Journal of Approximate Reasoning} 35 (2004) 1-28.
\item Chateauneuf, A. and Jaffray, J.-Y.:
Some Characterizations of Lower Probabilities and Other Monotone Capacities through the Use of M\”{o}bius Inversion,
{\em Mathematical Social Sciences} 17 (1989) 263-283.
\item Cobb, B.R. and Shenoy, P.:
On the Plausibility Transformation Method for Translating Belief Function Models to Probability Models,
{\em International Journal of Approximate Reasoning} (2006)??
\item Cooke, R. and Smets, P.:
Self-Conditional Probabilities and Probabilistic Interpretations of Belief Functions,
{\em Annals of Mathematics and Artificial Intelligence} 32 (2001) 269-285.
\item da Silva, W.T. and Milidi\'{u}, R.L.:
Algorithms for Combining Belief Functions,
{\em International Journal of Approximate Reasoning} 7 (1992) 73-94.
\item Dubois, D. and Prade H. :
Consonant Approximations of Belief Functions,
{\me International Journal of Approximate Reasoning} 4 (1990) 419-449.
\item Hendon, E., Jacobsen, H.J., Sloth, B. and Tranes, T.:
The Product of Capacities and Belief Functions,
{\em Mathematical Social Sciences} 32 (1996) 95-108.
\item Hern\'{a}ndez, E., Recasens, J.:
Indistinguishability Relations in Dempster-Shafer Theory of Evidence,
{\em International Journal of Approximate Reasoning} 37 (2004) 145-187.
\item Hern\'{a}ndez, E., Recasens, J.:
On Possibilistic and Probabilistic Approximations of Unresricted
Belief Functions Based on the Concept of Fuzzy $t$-Preorder,
{\em International Journal of Uncertainty, Fuzziness and Knowledge-Based
Systems} 10 (2002) 185-200.
\item Jaffray, J.-Y.:
Bayesian Updating and Belief Functions,
{\em IEEE Trans. on Systems, Man, and Cybernetics} 22 (1992) 1144-1152.
\item Kramosil, I.:
Belief Functions Generated by Signed Measures,
{\em Fuzzy Sets and Systems} 92 (1997) 157-166.
\item Kramosil, I.:
Measure-Theoretic Approach to the Inversion Problem for Belief Functions,
{\em Fuzzy Sets and Systems} 102 (1999) 363-369..
\item Kramosil, I.: (Belief Functions)
Boolean-Valued Belief Functions,
{\em International Journal of General Systems} 31 (2002) 153-181.
\item Kramosil, I.:
Belief Functions Generated by Fuzzy and Randomized Compatibility Relations,
{\em Fuzzy Sets and Systems} 135 (2003) 341-366.
\item Lo, K.C.:
Agreement and Stochastic Independence of Belief Functions,
{\em Mathematical Social Sciences} 51 (2006) 1-22.
\item Narens, L.:
A Theory of Belief,
{\em Journal of Mathematical Psychology} 47 (2003) 1-31.
\item R\”{o}mer, C. and Kandel, A.:
Constraints on Belief Functions Imposed by Fuzzy Random Variable,
{\em IEEE Trans. on Systems, Man, and Cybernerics} 25 (1995) 86-99.
\item Shafer, G.:
Allocations of Probability,
{\em The Annals of Probability} 7 (1979) 827-839.
\item Shafer, G.:
Belief Functions and Parametric Models,
{\em Journal of the Royal Statistical Society}, Series B, 44 (1982) 322-352.
\item Smet, P:
The Application of the Matrix Calculus to Belief Functions,
{\em International Journal of Approximate Reasoning} 31 (2002) 1-30.
\item Smet, P:
Decision Making in the TBM: The Necessity of the Pignistic Transformation,
{\em International Journal of Approximate Reasoning} 38 (2005) 133-147.
\item Smet, P:
Belief Functions on Real Numbers,
{\em International Journal of Approximate Reasoning} 40 (2005) 181-223.
\item Wakker, P.P.:
Dempster Belief Functions Are Based on the Principle of Complete Ignorance,
{\em International Journal of Uncertainy, Fuzziness and Knowledge-Based
Systems} 8 (2000) 271-284.
\item Walley, P.:
Belief Function Representations of Statistical Evidence,
{\em The Annals of Probability} 15 (1987) 1439-1465.
\item Weiler, T.:
Approximation of Belief Functions,
{\em International Journal of Uncertainty, Fuzziness and Knowledge-Based
Systems} 11 (2003) 749-777.
\item Yager, R.R.:
On the Normalization of Fuzzy Belief Structures,
{\em International Journal of Approximate Reasoning} 14 (1996) 127-153.
\item Yager, R.R.:
Decision Making Using Minimization of Regret,
{\em International Journal of Approximate Reasoning} 36 (2004) 109-128.
\item Yaghlane, B.B., Smets, P. and Mellouli, K.:
Belief Function Independence: I. The Marginal Case,
{\em International Journal of Approximate Reasoning} 29 (2002) 47-70.
\item Yaghlane, B.B., Smets, P. and Mellouli, K.:
Belief Function Independence: II. The Conditional Case,
{\em International Journal of Approximate Reasoning} 31 (2002) 31-75.
\item Yu, C. and Arasta, F.:
On Conditional Belief Functions,
{\em International Journal of Approximate Reasoning} 10 (1994) 155-172.
\begin{equation}{\label{b}}\tag{B}\mbox{}\end{equation}
Choquet Integrals.
\item Berrah, L., Mauris, G. and Montmain, J.:
Monitoring the Improvement of an Overall Industrial Peformance Based
on Choquet Integral Aggregation,
{\em Omega} 36 (2008) 340-351.
\item Cao-Van, K. and de Baets, B.:
A Decomposition of $k$-Additive Choquet and $k$-Maxitive Sugeno Integrals,
{\em International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems} 9 (2001) 127-143.
\item Chiang, J.-H.:
Aggregating Membership Values by a Choquet-Fuzzy-Integral Based Operator,
{\em Fuzzy Sets and Systems} 114 (2000) 367-375.
\item de Campos and Bolanos, M.J.:
Characterization and Comparison of Sugeno and Choquet Integrals,
{\em Fuzzy Sets and Systems} 52 (1992) 61-67.
\item Denneberg, D.:
Representation of the Choquet Integral with the $\sigma$-Additive M\”{o}bius Transform,
{\em Fuzzy Sets and Systems} 92 (1997) 139-156.
\item Grabisch, M.:
A Graphical Interpretation of the Choquet Integral,
{\em IEEE Trans. on Fuzzy Systems} 8 (2000) 627-631.
\item Grabisch, M. and Labreuche, C.:
Bi-Capacities — I: Definition, M\”{o}bius Transform and Interaction,
{\em Fuzzy Sets and Systems} 151 (2005) 211-236.
\item Grabisch, M. and Labreuche, C.:
Bi-Capacities — II: The Choquet Integral,
{\em Fuzzy Sets and Systems} 151 (2005) 237-259.
\item Jang, L.C., Kil, B.M., Kim, Y.K. and Kwon, J.S. :
Some Properties of Choquet Integrals of Set-Valued Functions,
{\em Fuzzy Sets and Systems} 91 (1997) 95-98.
\item Jang, L.C. and Kwon, J.S.:
On the Representation of Choquet Integrals of Set-Valued Functions and
Null Sets,
{\em Fuzzy Sets and Systems} 112 (2000) 233-239.
\item Kawabe, J.:
The Choquet Integral in Riesz Space,
{\em Fuzzy Sets and Systems} 159 (2008) 629-645.
\item Kr\”{a}tschmer, V.:
Coherent Lower Previsions and Choquet Integrals,
{\em Fuzzy Sets and Systems} 138 (2003) 469-484.
\item Lehrer, E. and Teper, R.:
The Concave Integral over Large Spaces,
{\em Fuzzy Sets and Systems} 159 (2008) 2130-2144.
\item Murofushi, T. and Sugeno, M. :
An Interpretation of Fuzzy Measures and the Choquet Integral asan Integral with Respect to a Fuzzy Measure,
{\em Fuzzy Sets and Systems} 29 (1989) 201-227.
\item Murofushi, T. and Sugeno, M. :
Fuzzy t-Conorm Integral with Respect to Fuzzy Measures : Gereralization
of Sugeno Integral and Choquet Integral,
{\em Fuzzy Sets and Systems} 42 (1991) 57-71.
\item Murofushi, T. and Sugeno, M. :
A Theory of Fuzzy Measures : Representations, the Choqueyt Integral, and Null Sets,
{\em Journal of Mathematical Analysis and Applications} 159 (1991) 532-549.
\item Murofushi, T., Sugeno, M. and Machida, M.:
Non-monotonic Fuzzy Measures and the Choquet Integral,
{\em Fuzzy Sets and Systems} 64 (1994) 73-86.
\item Narukawa, Y. and Murofushi, T.:
Conditions for Choquet Integral Representation of the Comonotonically Additive and Monotone Functional,
{\em Journal of Mathematical Analysis and Applications} 282 (2003) 201-211.
\item Ogura, Y., Li, S. and Ralescu, D.A.:
Set Defuzzification and Choquet Integral,
{\em International Journal of Uncertaint, Fuzziness and Knowledge-Based Systems} 9 (2001) 1-12.
\item Rebille, Y.:
Sequentially Continuous Non-Monotonic Choquet Integrals,
{\em Fuzzy Sets and Systems} 153 (2005) 79-94.
\item Skala, H.J.:
Generalized Comonotonically Additive Operators: Representations by Choquet Integrals,
{\em International Journal of Uncertainty, Fuziness and Knowledge-Based Systems} 10 (2002) 329-346.
\item Teper, R.:
On the Continuity of the Concave Integral,
{\em Fuzzy Sets and Systems} 160 (2009) 1318-1326.
\item Torra, V. and Narukawa, Y.:
The Interpretation of Fuzzy Integrals and Their Application to Fuzzy Systems,
{\em International Journal of Approximate Reasoning} 41 (2006) 43-58.
\item Wang, Z. and Klir, G.J.:
Choquet Integrals and Natural Extensions of Lower Probabilities,
{\em International Journal of Approximate Reasoning} 16 (1997) 137-147.
\item Wang, Z., Klir, G.J. and Wang, W.:
Monotone Set Function Defined by Choquet Integral,
{\em Fuzzy Sets and Systems} 81 (1996) 241-250.
\item Wang, Z., Leung, K.-S., Wong, M.-L., Fang, J. and Xu, K.:
Nonlinear Nonnegative Multiregressions Based on Choquet Integrals,
{\em International Journal of Approximate Reasoning} 25 (2000) 71-87.
\item Wang, Z., Yang, R., Heng, P.-A. and Leung, K.-S.:
Real-Valued Choquet Integrals with Fuzzy-Valued Integrand,
{\em Fuzzy Sets and Systems} 157 (2006) 256-269.
\item Yang, R., Wang, Z., Heng, P.-A. and Leung, K.-S.:
Fuzzy Numbers anf Fuzzification of the Choquet Integral.
{\em Fuzzy Sets and Systems} 153 (2005) 95-113.
\item Zhang, D., Guo, C. and Liu, D.:
Set-Valued Choquet Integrals Revisited,
{\em Fuzzy Sets and Systems} 147 (2004) 475-485.
\begin{equation}{\label{c}}\tag{C}\mbox{}\end{equation}
Competence Sets.
\item Chan, S.J. and Yu, P.L.:
Stable Habitual Domains: Existence and Implications,
{\em Journal of Mathematical Analysis and Applications} 110 (1985) 469-482.
\item Chen, T.-Y.:
Using Competence Sets to Analyze the Consumer Decision Problem,
{\em European Journal of Operational Research} 128 (2001) 98-118.
\item Chen, T.-Y.:
Expanding Competence Sets for the Consumer Decision Problem,
{\em European Journal of Operational Research} 138 (2002) 622-648.
\item Feng, J.W. and Yu, P.L.:
Minimum Spanning Table and Optimal Expansion of Competence Set,
{\em Journal of Optimization Theory and Applications} 99 (1998) 655-679.
\item Hu, Y.-C., Chen, R.-S. and Tzeng, G.-H.:
Generating Learning Sequences for Decision Makers Through Data Mining and Competence Set Expansion,
{\em IEEE Trans. on Systems, Man, and Cybernetics, part B (2002) 679-686.
\item Hu, Y.-C., Chen, R.-S., Tzeng, G.-H. and Chiu, Y.-J.:
Acquisition of Compound Skills and Learning Costs for Expanding Competence Sets,
{\em Computers and Mathematics with Applications} 46 (2003) 831-848.
\item Li, H.L. and Yu, P.L.:
Optimal Competence Set Expansion Using Deduction Graphs,
{\em Journal of Optimization Theory and Applications} 80 (1994) 75-91.
\item Li, J.-M., Chiang, C,-I. and Yu, P.-L.:
Optimal Multiple Stage Expansion of Competence Set,
{\em European Journal of Operational Research} 120 (2000) 511-524.
\item Lin, C.-C.:
Competence Set Expansion Using an Efficient 0-1 Programming Model,
{\em European Journal of Operational Research} 170 (2006) 950-956.
\item Shi, D.S. and Yu, P.L.:
Optimal Expansion and Design of Competence Sets with Asymmetric Acquiring Costs,
{\em Journal of Optimization Theory and Applications} 88 (1996) 643-658.
\item Shi, D.S. and Yu, P.L.:
Optimal Expansion of Competence Sets with Intermediate Skills and Compound Nodes,
{\em Journal of Optimization Theory and Applications} 102 (1999) 643-657.
\item Tzeng, G.-H., Chen, T.-Y. and Wang, J.-C.:
A Weight-Assessing Method with Habitual Domains,
{\em European Journal of Operational Research} 110 (1998) 342-367.
\item Wang, H.-F. and Wang, C.H.:
Modelling of Optimal Expansion of a Fuzzy Competence Set,
{\em International Transactions in Operational Research} 5 (1998) 413-424.
\item Yu, P.L. and Zhang, D.:
Comperence Set Analysis for Effective Decision Making,
{\em Control Theory and Advanced Technology} 5 (1989) 523-547.
\item Yu, P.L. and Zhang, D.:
A Foundation for Competence Set Analysis,
{\em Mathematical Social Sciences} 20 (1990) 251-299.
\item Yu, P.L. and Zhang, D.:
Competence Set Analysis for Fuzzy Problems,
{\em IEEE Int. Conference on Fuzzy Systems, 1992, pp.323-330.
\begin{equation}{\label{d}}\tag{D}\mbox{}\end{equation}
Data Envelopment Analysis.
\item Appa, G. and Williams, H.P.:
A New Framework for the Solutions of DEA Models,
{\em European Journal of Operational Research} 172 (2006) 604-615.
\item Banker, R.D., Charnes, A. and Cooper, W.W.:
Some Models for Estimating Technical and Scale Inefficiencies in Data
Envelopment Analysis,
{\em Management Sciences} 30 (1984) 1078-1092.
\item Charnes, A., Cooper, W.W. and Huang, Z.M.:
Polyhedral Cone-Ratio DEA Models with an Illustrative Application to Large
Commercial Banks,
{\em Journal of Ecomonetrics} 46 (1990) 73-91.
\item Charnes, A., Cooper, W.W., Wei, Q.L. and Huang, Z.M.:
Cone Ratio Data Envelopment Analysis and Multi-Objective Programming,
{\em Int. J. Systems Sci.} 20 (1989) 1099-1118.
\item F\”{a}re, R. and Li, S.K.:
Inner and Outer Approximations of Technology: A Data Envelopment Analysis Approach,
{\em European Journal of Operational Research} 105 (1998) 622-625.
\item Hao, G., Wei, Q. and Yan, H.:
The Generalized DEA Model and the Convex Cone Constrained Game,
{\em European Journal of Operational Research} 126 (2000) 515-525.
\item Kao, C.:
Interval Efficiency Measures in Data Envelopment Analysis with Imprecise Data,
{\em European Journal of Operational Research} 174 (2006) 1087-1099.
\item Liu, F.-H. F., Huang, C.-C. and Yen, Y.-L.:
Using DEA to Obtain Efficient Solutions for Multi-Objective 0-1 Linear Programs,
{\em European Journal of Operational Research} 126 (2000) 51-68.
\item Pitaktong, U., Brockett, P.L., Mote, J.R. and Rousseau, J.J.:
Identification of Pareto-Efficient Facets in Data Envelopment Analysis,
{\em European Journal of Operational Research} 109 (1998) 559-570.
\item Seiford, L.M. and Thrall, R.M.:
Recent Development in DEA: The Mathematical Programming Approach to Frontier Analysis,
{\em Journal of Ecomonetrics} 46 (1990) 7-38.
\item Wei, Q. and Yu, G.:
Analyzing Properties of $K$-Cones in the Generalized Data Envelopment Analysis Model,
{\em Journal of Ecomonetrics} 80 (1997) 63-84.
\begin{equation}{\label{e}}\tag{E}\mbox{}\end{equation}
Solving Nonlinear Equations.
\item Basto, M., Semiao, V. and Calheiros, F.L.:
A New Iterative Method to Compute Nonlinear Equations,
{\em Applied Mathematics and Computation} 173 (2006) 468-483.
\item Chun, C.:
A New Iterative Method for Solving Nonlinear Equations,
{\em Applied Mathematics and Computation} 2005 ???
\item Jafari, H. and Daftardar-Gejji, V.:
Revised Adomian Decomposition Method for Solving a System of Nonlinear
Equations,
{\em Applied Mathematics and Computation} 175 (2006) 1-7.
\item Kou, J., Li, Y. and Wang, X.:
Efficient Continuation Newton-Like Method for Solving Systems of
Nonlinear Equations,
{\em Applied Mathematics and Computation} 174 (2006) 846-853.
\item Noor, M.A. and Ahmad, F.:
Numerical Comparison of Iterative Methods for Solving Nonlinear Equations,
{\em Applied Mathematics and Computation} (2006) ???
\item Ujevi\'{c}, N.:
A Method for Solving Nonlinear Equations,
{\em Applied Mathematics and Computation} 175 (2006) 1416-1426.
\begin{equation}{\label{f}}\tag{F}\mbox{}\end{equation}
Imprecise Probability.
\item Baroni, P. and Vicig, P:
An Uncertainty Interchange Format with Imprecise Probabilities,
{\em International Journal of Approximate Reasoning} 40 (2005) 147-180.
\item Hansen, P., Jaumard, B., de Aragao, M.P., Chauny, F. and Perron, S.:
Probabilistic Satisfiability with Imprecise Probabilities,
{\em International Journal of Approximate Reasoning} 24 (2000) 171-189.
\item Vicig, P.:
Epistemic Independence for Imprecise Probabilisties,
{\em International Journal of Approximate Reasoning} 24 (2000) 235-250.
\item Walley, P.:
Measures of Uncertainty in Expert Systems,
{\em Artificial Intelligence} 83 (1996) 1-58.
\item Walley, P.:
Towards a Unified Theory of Imprecise Probability,
{\em International Journal of Approximate Reasoning} 24 (2000) 125-148.
\begin{equation}{\label{g}}\tag{G}\mbox{}\end{equation}
Networks Problems.
\item Ali, A.I., Padman, R. and Thiagarajan, H. :
Dual Algorithms for Pure Network Problems.
{\em Operations Research} 37 (1989) 159-171.
\item Aneja, Y.P. and Nair, K.P.K. :
Bicriteria Transportation Problem.
{\em Management Science} 25 (1979) 73-78.
\item Carstensen, P.J. :
Complexity of Some Parametric Integer and Network Programming Problems.
{\em Mathematical Programming} 26 (1983) 64-75.
\item Current, J. and Min, H. :
Multiobjective Design of Transportation Networks : Taxonomy and Annotation.
{\em European J. Operational Research} 26 (1986) 187-201.
\item Fruhwirth, B., Burkard, R.E. and Rote, G. :
Approximation of Convex Curves with Application to the Bicriteria Minimum Cost Flow Problem.
{\em European J. Operational Research} 42 (1989) 326-338.
\item Gallo, G., Grigoriadis, M.D. and Tarjan, R.E. :
A Fast Parametric Maximum Flow Algorithm and Applications.
{\em SIAM J. on Computing} 18 (1989) 30-55.
\item Hamacher, H.W. and Foulds, L.R. :
Algorithms for Flows with Parametric Capacties.
{\em ZOR} 33 (1988) 21-37.
\item Kennington, J. and Shalaby, M. :
An Effective Subgradient Procedure for Minimal Cost Multicommodity Flow Problems.
{\em Management Science} 23 (1977) 994-1004.
\item Ringuest, J.L. and Rinks, D.B. :
Interactive Solutions for the Linear Multiobjectivw Transportation Problem.
{\em European J. Operational Research} 32 (1987) 96-106.
\item Ruhe, G. :
Characterization of All Optimal Solutions and Parametric Maximal Flows in Networks.
{\em Optimization} 16 (1985) 51-61.
\item Ruhe, G. :
Complexity Results for Multicriteria and Parametric Network Flows Using
a Pathological Graph of Zadeh.
{\em ZOR (Zeitshrift fur Operations Research)} (1987) 9-27.
\item Ruhe, G. :
Parametric Maximal Flows in Generalized Networks – Complexity and Alorithms.
{\em Optimization} 19 (1988) 235-251.
\item Zadeh, N. :
More Pathological Examples for Networks Flow Problems.
{\em Mathematical Programming} 5 (1973) 217-224.
\item Zadeh, N. :
A Bad Network Problem for the Simplex Method and Other Minimum Cost Flow Algorithms.
{\em Mathematical Programming} 5 (1973) 255-266.
\item Bit, A.K., Biswal, M.P. and Alam, S.S. :
Fuzzy Programming Approach to Multicriteria Decision Making Transportation Problem.
{\ Fuzzy Sets and Systems} 50 (1992) 135-141.
\item Buckley, J.J. and Hayashi, Y. :
Fuzzy Neural Networks : A Survey.
{\em Fuzzy Sets and Systems} 66 (1994) 1-13.
\item Ignizio, J.P. and Daniels, S.C. :
Fuzzy Multicriteria Integer Programming via Fuzzy Generalized Networks.
{\em Fuzzy Sets and Systems} 10 (1983) 261-270.
\item Alexopoulos, C. and Fishman, G.S. :
Characterizing Stochastic Flow Networks Using the Monte Carlo Method.
{\em Networks} 21 (1991) 775-798.
\item Connors, M.M. and Zangwill, W.I. :
Cost Minimization in Networks with Discrete Stochastic REquirements.
{\em Operations Research} 19 (1971) 794-821.
\item Leondes, C.T. and Nandi, R.K. :
Capacity Expansion in Convex Cost Networks with Uncertain Demand.
{\em Operations Research} 23 (1975) 1172-1178.
\item Mulvey, J.M. and Vladimirou, H. :
Solving Multistage Stochastic Networks : An Application of Scenario Recourse.
{\em Networks} 21 (1991) 619-643.
\item Nagamochi, H. and Ibaraki, T. :
Maximum Flows in Probabilistic Networks.
{\em Networks} 21 (1991) 645-666.
\item Wallace, S.W. :
Solving Stochastic Programs with Network Recourse.
{\em Networks} 16 (1986) 295-317.
\item Williams, A.C. :
A Stochastic Transportation Problem.
{\em Operations Research} 11 (1963) 759-770.
\item Baskett, F., Chandy, K.M., Muntz, R.R. and Palacios, F.G. :
Open, Closed, and Mixed Networks of Queues with Different Classes of Customers.
{\em J. the Association for Computing Machinery} 22 (1975) 248-260.
\item Kelly, F.P. :
Networks of Queues.
{\em Advances in Applied Probability} 8 (1976) 416-432.
\item Kelly, F.P. :
Networks of Queues with Customers of Different Types.
{\em J. Applied Probability} 12 (1975) 542-554.
\begin{equation}{\label{h}}\tag{H}\mbox{}\end{equation}
Nonstandard Analysis.
\item Anderson, R.M.:
A Nonstandard Representation for Brownian Motion and Ito Integration,
{\em Israel Journal of Mathematics} 25 (1976) 15-46.
\item Anderson, R.M. and Rashid, S.:
A Nonstandard Characterization of Weak Convergence,
{\em Proceedings of the American Mathematical Society} 69 (1978) 327-332.
\item Ballard, D. and Hrbacek, K.:
Standard Foundations for Nonstandard Analysis,
{\em The Journal of Symbolic Logic} 57 (1992) 741-748.
\item Farrukh, M.O.:
Applications of Nonstandard Analysis to Quantum Mechanics,
{\em Journal of Mathematical Physics} 16 (1975) 177-200.
\item Henle, J.M.:
Nonstandard Analysis: Real Infinitesimals,
{\em The Mathematical Intelligencer} 21 (1999) 67-73.
\item Henle, J.M.:
Second-Order Nonstandard Analysis,
{\em Studia Logica} 74 (2003) 399-426.
\item Henson, C.W.:
The Isomorphism Property in Nonstandard Analysis and Its USe in the Theory of Banach Spaces,
{\em The Journal of Symbolic Logic} 39 (1974) 717-731.
\item Henson, C.W. and Keisler, H.J.: (Nonstandard Analysis)
On the Strength of Nonstandard Analysis,
{\em The Journal of Symbolic Logic} 51 (1986) 377-386.
\item Henson, C.W. and Moore, L.C.: (Nonstandard Analysis)
The Nonstandard Theory of Topological Vector Spaces,
{\em Transactions of the American Mathematical Society} 172 (1972) 405-435.
\item Hurd, A.E.:
Nonstandard Analysis and Lattice Statistical Mechanics: A Variational Principle,
{\em Transactions of the American Mathematical Society} 263 (1981) 89-110.
\item Loeb, P.A.:
A Combinatorial Analog of Lyapunov’s Theorem for Infinitesimally Generated Atomic Vector Measures,
{\em Proceedings of the American Mathematical Society} 39 (1973) 585-586.
\item Loeb, P.A.:
Conversion from Nonstandard to Standard Measure Spaces and Applications in Probability Theory,
{\em Transactions of the American Mathematical Society} 211 (1975) 113-122.
\item Loeb, P.A.:
Applications of Nonstandard Analysis to Ideal Boundaries in Potential Theory,
{\em Israel Journal of Mathematics} 25 (1976) 154-187.
\item Nelson, E.:
Interval Set Theory: A New Approach to Nonstandard Analysis,
{\em Bulletin of the American Mathematical Society} 83 (1977) 1165-1198.
\item Osswald, H. and Sun, Y.:
On the Extensions of Vector-Valued Loeb Measures,
{\em Proceedings of the American Mathematical Society} 111 (1991) 663-675.
\item Palmgren, E.:
A Constructive Approach to Nonstandard Analysis,
{\em Annals of Pure and Applied Logic} 73 (1995) 297-325.
\item Phillips, N.C.K.:
The Set Theoretical Foundations of Nonstandard Analysis,
{\em The Journal of Symbolic Logic} 38 (1973) 189-192.
\item Salbany, S. and Todorov, T.:
Nonstandard Analysis in Topology: Nonstandard and Standard Compactifications,
{\em The Journal of Symbolic Logic} 65 (2000) 1836-1840.
\item Sun, Y.:
Integration of Correspondences on Leob Spaces,
{\em Transactions of the American Mathematical Society} 349 (1997) 129-153.
\item Voros, A.:
Introduction to Nonstandard Analysis,
{\em Journal of Mathematical Physics} 14 (1973) 292-296.
\begin{equation}{\label{i}}\tag{I}\mbox{}\end{equation}
Simulation.
\item Andraa\'{o}ttir, S., Heyman, D.P. and Ott, T.J.:
Variance Reduction Through Smoothing and Control Variates for Markov
Chain Simulations,
{\em ACM Trans. on Modelling and Computer Simulation} 3 (1993) 167-189.
\item Barros, F.J.:
Modeling Formalisms for Dynamic Structure Systems,
{\em ACM Trans. on Modelling and Computer Simulation} 7 (1997) 501-515.
\item Buchholz, P.:
A New Approach Combining Simulation and Randomization for the Analysis
of Large Continuous Time Markov Chains,
{\em ACM Trans. on Modelling and Computer Simulation} 8 (1998) 194-222.
\item Calvin, J.M. and Nakayama, M.K.:
Using Permutations in Regenerative Simulations to Reduce Variance,
{\em ACM Trans. on Modelling and Computer Simulation} 8 (1998) 153-193.
\item Coates, R.F.W., Janacek, G.J. and Lever, K.V.:
Monte Carlo Simulation and Random Number Generation,
{\em IEEE Journal on Selected Areas in Communications} 6 (1988) 58-66.
\item Damerdji, H. and Nakayama, M.K.:
Two-Stage Multiple-Comparison Procedures for Steady-State Simulations,
{\em ACM Trans. on Modelling and Computer Simulation} 9 (1999) 1-30.
\item Devroye, L.:
Random Variate Generation for Multivariate Unimodal Densities,
{\em ACM Trans. on Modelling and Computer Simulation} 7 (1997) 447-477.
\item Eichenauer-Nerrmann, J. and Grothe, H.:
A New Inversive Congruential Pseudorandom Number Generator with
Power of Two Modulus,
{\em ACM Trans. on Modelling and Computer Simulation} 2 (1992) 1-11.
\item Eichenauer-Herrmann, J. and Niederreiter, H.:
On the Statistical Independence of Nonlinear Congruential
Pseudorandom Numbers,
{\em ACM Trans. on Modelling and Computer Simulation} 4 (1994) 89-95.
\item Eichenauer-Herrmann, J. and Niederreiter, H.:
Digital Inversive Pseudorandom Numbers,
{\em ACM Trans. on Modelling and Computer Simulation} 4 (1994) 339-349.
\item Emmerich, F.:
Statistical Independence Properties of Inversive Pseudorandom Vectors
over Parts of the Period,
{\em ACM Trans. on Modelling and Computer Simulation} 8 (1998) 140-152.
\item Entacher, K.:
Bad Subsequences of Well-Known Linear Congruential Pseudorandom
Number Generators,
{\em ACM Trans. on Modelling and Computer Simulation} 8 (1998) 61-70.
\item Entacher, K.:
Parallel Streams of Linear Random Numbers in the Spectral Test,
{\em ACM Trans. on Modelling and Computer Simulation} 9 (1999) 31-44.
\item Epstein, P. and Sack, J.-R.:
Gnerating Triangulations at Random,
{\em ACM Trans. on Modelling and Computer Simulation} 4 (1994) 267-278.
\item Falkner, M., Devetsikiotis, M. and Lambadaris, I.:
Fast Simulation of Networks of Queues with Effective and Decoupling
Bandwiths,
{\em ACM Trans. on Modelling and Computer Simulation} 9 (1999) 45-58.
\item Fishwick, P.A. and Zeigler, B.P.:
A Multimodel Methodology for Qualitative Model Engineering,
{\em ACM Trans. on Modelling and Computer Simulation} 2 (1992) 52-81.
\item Glasserman, P. and Kou, S.-G.:
Analysis of an Importance Sampling Estimator for Tandem Queues,
{\em ACM Trans. on Modelling and Computer Simulation} 5 (1995) 22-42.
\item Heidelberger, P.:
Fast Simulation of Rare Events in Queueing and Reliability Models,
{\em ACM Trans. on Modelling and Computer Simulation} 5 (1995) 43-85.
\item Hellekalek, P. and Niederreiter, H.:
The Weighted Spectral Test: Diaphony,
{\em ACM Trans. on Modelling and Computer Simulation} 8 (1998) 43-60.
\item H\”{o}rmann, W.:
A Note on the Quality of Random Variates Generated by the Ratio of
Uniforms Method,
{\em ACM Trans. on Modelling and Computer Simulation} 4 (1994) 96-106.
\item Keane, M.S. and Obrien, G.L.:
A Bernoulli Factory,
{\em ACM Trans. on Modelling and Computer Simulation} 4 (1994) 213-219.
\item Kiviat, P.J.:
Simulation, Technology, and the Decision Process,
{\em ACM Trans. on Modelling and Computer Simulation} 1 (1991) 89-98.
\item L’ecuyer, P., Blouin, F. and Couture, R.:
A Search for Good Multiple Recursive Random Number Generators,
{\em ACM Trans. on Modelling and Computer Simulation} 3 (1993) 87-98.
\item Lee, L.-P. and Wong, K.-W.:
A Random Number Generator Based on Elliptic Curve Operations,
{\em Computers and Mathematics with Applications} 47 (2004) 217-226.
\item Matsumoto, M.:
Simple Cellular Automata as Pseudorandom $m$-Sequence Generators for
Built-in Self-test,
{\em ACM Trans. on Modelling and Computer Simulation} 8 (1998) 31-42.
\item Matsumoto, M. and Nishimura, T.:
Mersenne Twister: A 623-Dimensionally Equidistributed Uniform
Pseudorandom Number Generator,
{\em ACM Trans. on Modelling and Computer Simulation} 8 (1998) 3-30.
\item Miller, D.P., Firby, R.J., Fishwick, P.A., Franke, D.W. and
Rothenberg, J.:
AI: What Simulations Really Need to Know,
{\em ACM Trans. on Modelling and Computer Simulation} 2 (1992) 269-284.
\item Nakayama, M.K.:
A Characterization of the Simple Failure-Biasing Method for Simulations
of Highly Reliable Markovian Systems,
{\em ACM Trans. on Modelling and Computer Simulation} 4 (1994) 52-88.
\item Nelson, B.:
Robust Multiple Comparisons under Common Random Numbers,
{\em ACM Trans. on Modelling and Computer Simulation} 3 (1993) 225-243.
\item Nicol, D.M. and Heidelberger, P.:
A Comparative Study of Parallel Algorithms for Simulating Continuous
Time Markov Chains,
{\em ACM Trans. on Modelling and Computer Simulation} 5 (1995) 326-354.
\item Niederreiter, H.:
Pseudorandom Vector Generation by the Inversive Method,
{\em ACM Trans. on Modelling and Computer Simulation} 4 (1994) 191-212.
\item Owen, A.B.:
Latin Supercube Sampling for Very High-Dimensional Simulations,
{\em ACM Trans. on Modelling and Computer Simulation} 8 (1998) 71-102.
\item Percus, O.E. and Whitlock, P.A.:
Theory and Application of Marsagila’s Monkey Test for Pseudorandom
Number Generators,
{\em ACM Trans. on Modelling and Computer Simulation} 5 (1995) 87-100.
\item Radiya, A. and Sargent, R.G.:
A Logic-Based Foundation of Discrete Event Modeling and Simulation,
{\em ACM Trans. on Modelling and Computer Simulation} 4 (1994) 3-51.
\item Rajasenkaran, S. and Ross, K.W.:
Fast Algorithms for Generating Discrete Random Variates with Changing
Distributions,
{\em ACM Trans. on Modelling and Computer Simulation} 3 (1993) 1-19.
\item Ross, K.W. and Wang, J.:
Asymptotically Optimal Importance Sampling for Product-Form
Queueing Networks,
{\em ACM Trans. on Modelling and Computer Simulation} 3 (1993) 244-268.
\item Srinivasan, S. and Reynolds, P.F.:
Elastic Time,
{\em ACM Trans. on Modelling and Computer Simulation} 8 (1998) 103-139.
\item Stadlober, E. and Zechner, H.:
The Patchwork Rejection Technique for Sampling from Unimodal Distributions,
{\em ACM Trans. on Modelling and Computer Simulation} 9 (1999) 59-80.
\item Tezuka, S. and Lecuyer, P.:
Efficient and Portable Combined Tausworthe Random Number Generators,
{\em ACM Trans. on Modelling and Computer Simulation} 1 (1991) 99-112.
\item Tezuka, S., Lecuyer, P. and Couyure, R.:
On the Lattice Structure of the Add-With-Carry and Subtract-With-
Borrow Random Number Generators,
{\em ACM Trans. on Modelling and Computer Simulation} 3 (1993) 315-331.
\item Tuffin, B.:
Variance Reduction Applied to Product-Form Multiclass Queueing Networks,
{\em ACM Trans. on Modelling and Computer Simulation} 7 (1997) 478-500.
\item Yuan, M. and Nelson, B.L.:
Multiple Comparisons with the Best for Steady-State Simulation,
{\em ACM Trans. on Modelling and Computer Simulation} 3 (1993) 66-79.
\item Y\”{u}cesan, E. and Schruben, L.:
Structural and Behavioral Equivalence of Simulation Models,
{\em ACM Trans. on Modelling and Computer Simulation} 2 (1992) 82-103.
\begin{equation}{\label{J}}\tag{J}\mbox{}\end{equation}
Fuzzy Quantum Field Theory.
\item Castro, C.:
Beyond Strings, Multiple Times and Gauge Theories of Area-Scalings
Relativistic Trenaformations,
{\em Chaos, Solitions and Fractals} 10 (1999) 295-309.
\item El Naschie, M.S.: (Fuzzy Quantum Field Theory)
On the Cohomology and Instantons Number in E-Infinity Cantorian Spacetime,
{\em Chaos, Solitions and Fractals} 26 (2005) 13-17.
\item El Naschie, M.S.: (Fuzzy Quantum Field Theory)
From the Two-Slit Experiments to the Expected Number of Higgs
Partic;es in the Standard Model,
{\em Chaos, Solitions and Fractals} 26 (2005) 67-70.
\item El Naschie, M.S.: (Fuzzy Quantum Field Theory)
On a Class of Fuzzy K\”{a}hler-like Manifolds,
{\em Chaos, Solitions and Fractals} 26 (2005) 257-261.
\item El Naschie, M.S.: (Fuzzy Quantum Field Theory)
Stability Analysis of the Two-Slit Experiment with
Quantum Particles,
{\em Chaos, Solitions and Fractals} 26 (2005) 291-294.
\item El Naschie, M.S.: (Fuzzy Quantum Field Theory)
Spinorial Content of the Standard Model, A Different Look
at Super-Symmetry and Fuzzy E-Infinity Hyper K\”{a}hler,
{\em Chaos, Solitions and Fractals} 26 (2005) 303-311.
\item El Naschie, M.S.: (Fuzzy Quantum Field Theory)
From Experimental Quantum Optics to Quantum Gravity via a
Fuzzy K\”{a}hler Manifold,
{\em Chaos, Solitions and Fractals} 25 (2005) 969-977.
\item El Naschie, M.S.: (Fuzzy Quantum Field Theory)
K\”{a}hler-like Manifolds, Weyl Spinor Particles and
E-Infinity High Energy Physics,
{\em Chaos, Solitions and Fractals} 26 (2005) 665-670.
\item El Naschie, M.S.:
Hilbert Space, the Number of Higgs Particles and the
Quantum Two-Slit Experiment,
{\em Chaos, Solitions and Fractals} 27 (2006) 9-13.
\item El Naschie, M.S.: (Fuzzy Quantum Field Theory)
The Idealized Quantum Two-Slit Gedanken Experiment Revisited —
Critism and Reinterpretation,
{\em Chaos, Solitions and Fractals} 27 (2006) 843-849.
\item El Naschie, M.S.: (Fuzzy Quantum Field Theory)
Holographic Dimensional Reduction: Center Manifold Theorem
and $E$-Infinity,
{\em Chaos, Solitions and Fractals} 29 (2006) 816-822.
\item El Naschie, M.S.:
On Two New Fuzzy K\”{a}hler Manifold, Klein Modular Space
and ‘t Hooft Holographic Principles,
{\em Chaos, Solitions and Fractals} 29 (2006) 876-881.
\item El Naschie, M.S.:
Fuzzy Dodecahedron Topology and $E$-Infinity Spacetime as a
Model for Quantum Physics,
{\em Chaos, Solitions and Fractals} 30 (2006) 1025-1033.
\item El Naschie, M.S.:
The Elementary Particles Content of Quantum Spacetime via Feynman
Graphs and Higher Dimensional Polytops,
{\em Chaos, Solitions and Fractals} 31 (2007) 1-4.
\item El Naschie, M.S.:
SO(10) Grand Unification in a Fuzzy Setting,
{\em Chaos, Solitions and Fractals} 32 (2007) 958-961.
\item El Naschie, M.S.:
String Theory, Exceptional Lie Groups Hierarchy and the
Structural Constant of the Universe,
{\em Chaos, Solitions and Fractals} 35 (2008) 7-12.
\item El Naschie, M.S.:
Quantum Gravity Unification via Trasnfinite Arithmetic and
Geometrical Averaging,
{\em Chaos, Solitions and Fractals} 35 (2008) 252-256.
\item El Naschie, M.S.:
Fuzzy Knot Theory Interpretation of Yang-Mills Instantons and
Witten’s 5-Brane Model,
{\em Chaos, Solitions and Fractals} (2008).
\item Marek-Crhjac, L.:
On the Unification of All Fundamental Forces in a Fundamentally
Fuzzy Cantorian $\varepsilon^{(\infty )}$-Manifold and
High Energy Particle Physics,
{\em Chaos, Solitions and Fractals} 20 (2004) 669-682.
\item Marek-Crhjac, L.:
Higher Dimensional Dodecahedra as Models of the Macro and
Micro Universe in $E$-Infinity Cantorian Spacetime,
{\em Chaos, Solitions and Fractals} 32 (2007) 944-950.
\item Marek-Crhjac, L.:
Fuzzy K\”{a}hler Manifolds,
{\em Chaos, Solitions and Fractals} 34 (2007) 677-681.
\item Nozari, K. and Fazlpour, B.:
Some Consequences of Spacetime Fuzziness,
{\em Chaos, Solitions and Fractals} 34 (2007) 224-234.
\item Sidharth, B.G.:
The Mystery of the Kerr-Newman Metric,
{\em Chaos, Solitions and Fractals} 22 (2004) 537-540.
\item Sidharth, B.G.:
Strings and Plank Ocillators,
{\em Chaos, Solitions and Fractals} 30 (2006) 300-311.
\item Sidharth, B.G.:
Self-Similar Super Universes,
{\em Chaos, Solitions and Fractals} 30 (2006) 463-469.
\begin{equation}{\label{k}}\tag{K}\mbox{}\end{equation}
Quantum Probability.
\item Anastopoulos, C.:
Classical Versus Quantum Probability in Sequential Measurements,
{\em Foundations of Physics} 36 (2006) 1601-1661.
\item Barchielli, A., Paganoni, A.M. and Zucca, F.:
On Stochastic Differential Equations and Semigroups of Probability Operators in Quantum Probability,
{\em Stochastic Processes and Their Applications} 73 (1998) 69-86.
\item Barnum, H., Caves, C.M., Finkelstein, J., Fuchs, C.A. and Schack, R.:
Quantum Probability from Decision Theory?
{\em Proc. R. Soc. Lond.} A, 456 (2000) 1175-1182.
\item Belavkin, V.P.:
Quantum Probabilities ad Paradoxes of the Quantum Century,
{\em Infinite Dimensional Analysis, Quantum Probability and Related Topics} 3 (2000) 577-610.
\item Caves, C.M., Fuchs, C.A. and Schack, R.:
Quantum Probabilities as Bayesian Probabilities,
{\em Physical Review} A, Vol. 65, 022305, 2000.
\item Hofer-Szab\'{o}, G., R'{e}dei, M. and Szab\'{o}, L.E.:
Common Cause Completability of Classical and Quantum Probability Spaces,
{\em International Journal of Theoretical Physics} 39 (2000) 913-919.
\item Pitowsky, I.:
Betting on the Outcomes of Measurements: A Bayesian Theory of Quantum Probability,
{\em Studies in History and Philosophy of Modern Physics} 34 (2003) 395-414.
\item Pykacz, J.:
Fuzzy Quantum Logics as a Basis for Quantum Probability Theory,
{\em International Journal of Theoretical Physics} 37 (1998) 281-290.
\item Streater, R.F.:
Classical and Quantum Probability,
{\em Journal of Mathematical Physics} 41 (2000) 3556-3603.
