Mathematical Preliminaries

  • Masatoshi Sakawa
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 48)


This chapter is devoted to mathematical preliminaries, which will be used in the remainder of this book. Starting with several basic definitions involving fuzzy sets, operations on fuzzy sets, especially fuzzy numbers, are outlined. Bellman and Zadeh’s approach to decision making in a fuzzy environment, called fuzzy decision, is then examined. Fundamental notions and methods of multiobjective, interactive multiobjective, and interactive fuzzy multiobjective linear programming are briefly reviewed. A brief discussion of genetic algorithms is also given.


Membership Function Fuzzy Number Pareto Optimal Solution Fuzzy Decision Fuzzy Goal 
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Copyright information

© Physica-Verlag Heidelberg 2000

Authors and Affiliations

  • Masatoshi Sakawa
    • 1
  1. 1.Department of Industrial and Systems EngineeringFaculty of Engineering Hiroshima UniversityHigashi-HiroshimaJapan

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