Center for Mathematics of Uncertainty

Center for Mathematics of Uncertainty

Mission and Current Research

The mission of the Center for Mathematics of Uncertainty (Fuzzy Math) is to support the paradigm shift in the sciences involving uncertainty and to support colleagues in third world countries. The Center has supported visiting professors from the People's Republic of China, India, Saudi Arabia, Korea and Japan.

Members of the Center do basic research in fuzzy abstract algebra, fuzzy graph theory, fuzzy integration theory and integral equations, fuzzy automata theory, and fuzzy social networks.

he current focus of the Center is to support the fight against human trafficking and modern slavery. The Center plans to extend its focus to further the use of mathematics for uncertainty in the social sciences.

In fuzzy abstract algebra, it has demonstrated that the theory of primary representations for fuzzy ideals can be applied to the solution of fuzzy intersection equations via a corresponding theory of algebraic varieties.

The members of the Center have also developed a Galois theory of fuzzy subgroups and fuzzy subfields.  Creation of a Galois theory of correspondence like this is frequently useful for classification of fields and in solving equations.

Significant work is being done on the structural results for fuzzy graphs and fuzzy automata, both of which have applications in many disciplines.

Fifteen books, approximately 200 journal articles and 50 conference papers have been published by various research members. Current research concerns vague algebraic structures. To download a more complete list of publications, click here.

Director:  Dr. Davender Malik, Department of Mathematics

Research Applications and Research Projects

Research Applications and Research Projects

Research members have successfully carried out research programs with the Creighton University Osteoporosis Research Center and the Departments of Neurology and Psychiatry at the College of Medicine at the University of Illinois at Chicago.

Center members are collaborating with members of other countries. Their focus is on the application of fuzzy mathematics to human trafficking and modern slavery.


Children with Special Needs

The Center for Mathematics of Uncertainty (CMU) supports research that benefits children with special needs. Through the Center for Mathematics of Uncertainty at Creighton University, CMU provides research staffs at no cost for Omaha local area schools such as Omaha Hearing School and Madonna School. CMU also provides software and hardware needs for these schools. OHS works with deaf and hard of hearing young children while Madonna School works with autistic children and children with down syndrome. CMU plans to extend its services for special needs children nationally.


Medical Mathematics Specialization

Mathematics 347, 513, 529, 545, 547, 583, and 591.

MTH347 Calculus
This course covers vector algebra and calculus in two- and three-dimensional space.

MTH513 Probability and Statics in the Health Sciences
This course covers topics in probability and statistics considered useful to those students planning on a career in the health sciences.  The topics covered include probability principles and distributions in health sciences, types of epidemoiiologic study designs, estimation of medical parameters in defined patient populations, test of hypothesis, measures and analysis of treatment of the sick, analysis of variance, methods of medical outcome prediction, and prospective, retrospective and cross-sectional studies of disease occurrence.

MTH529 Linear Algebra
Vector spaces, subspaces, linear transformations, matrices, eigenvalues and eigenvectors.

MTH545 Differential Equations
This course examines qualitative, analytical, and numerical techniques for studying differential equations.  Course begins with single differential equations, then covers systems of equations, n-th order linear differential equations, forcing, nonlinear differential equations, difference equations, and Laplace transforms.

Mathematics in Medicine and the Life Sciences

  • Fuzzy Cube, Strokes
  • Fuzzy Logic
  • Bone Mineral Density
  • Belief Functions
  • Osteoporosis
  • Methods of Medical Outcome Prediction
  • Gas Exchange in the Lungs
  • Probability and Statistics
  • Epidemiologic Study Designs
  • Heart Circulation
  • Electrical Properties of Cell Membranes

MTH547 Mathematics in Medicine and the Life Sciences
This course is intended to be an overview of a variety of mathematical topics considered useful to those students intending to pursue a career in medicine or the life sciences.  The topics covered include mathematics of populations, growth of bacterial cultures, inheritance, bacterial genetics, plasmids, theory of epidemics, biography, the growth of bacteria on plates; heart and circulations, gas exchange in the lungs, electrical properties of cell membranes, and muscle mechanics.

MTH583 Fuzzy Mathematics: Applications in Health Sciences
This course focuses on crisp sets; fuzzy sets; classical logic; fuzzy logic; fuzzy complement; fuzzy union; fuzzy intersection; crisp and fuzzy relations; similarly relations; compatibility relations; orderings; morphism; fuzzy relational equations application to health sciences.

MTH591 Analysis I
Introductory course in analysis covering properties of Euclidian spaces and their applications to functions. 

Free Software Downloads

Free Software Downloads

Some of the following software implements algorithms described in the above textbook, others were developed for research purposes. The authors grant you the right to download and execute it for your personal use or for non-profit instructional use. Any other use, including copying, distributing or modifying the work for commercial purposes, is subject to the restrictions of U.S. Copyright Law and the Berne International Copyright Convention.

These programs will only run in the Microsoft Windows environment. You may need to install the .Net 2.0 framework from Microsoft to run these programs

         FuzzyController Mark J. Wierman. A .Net program.  Backs a truck up to a dock.

         FuzzyCluster Mark J. Wierman.  A .Net program.  Clusters data set.

         FuzzyCluster.New (Version 3) Mark J. Wierman. A .Net program. Clusters data set. Some graphing ability.

         FuzzyVoter Mark J. Wierman. A .Net program.  Calculates Max-Sets and Pareto-Sets for Three Actors with a Granularity of Five levels.

 

Free software for the Fuzzy Math program is available at the following address: 

http://duck.creighton.edu/index.php?selection=2&subselection=3

Free Textbook

Free Textbook

An Introduction to the Mathematics of Uncertainty 1st edition

Mark J Wierman, Professor, Creighton University

Copyright 2010-2012, Mark J. Wierman. All rights reserved.

This book is an introduction to Fuzzy Set Theory and Evidence Theory oriented toward undergraduate students. It may be downloaded without charge.

Please note that this material is copyrighted under U.S. Copyright Law. The authors grant you the right to download and print it for your personal use or for non-profit instructional use. Any other use, including copying, distributing or modifying the work for commercial purposes, is subject to the restrictions of U.S. Copyright Law and the Berne International Copyright Convention.

         Download the Textbook