Ternary Kleenean Non-additive Measures

  • Tomoyuki Araki
  • Masao Mukaidono
  • Fujio Yamamoto
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 114)


The theory of non-additive measures and integral calculus with respect to them is rich and has been developed in many streams. In this paper, the authors focus on and extend one special non-additive measure, which is called fuzzy measure. Then they focus on and extend an item from the integral calculus, called the Sugeno integral. This expansion enables us to treat concepts such as “negation” and “unknown” in the field of fuzzy measures—these concepts have never been treated well in the field. To achieve it, the authors attempt to translate the vagueness of fuzzy set theory and fuzzy logic to the ambiguity of fuzzy measure by considering the fact that the Sugeno integral in fuzzy measure theory can be represented using fuzzy switching functions with constants in fuzzy logic. Then, we attempt to apply the facts clarified in fuzzy logic to fuzzy measure. Consequently, two new concepts: “Ternary Kleenean Non-additive Measure” and “Kleene-Sugeno integral” are proposed.


Fuzzy Logic Switching Function Logic Formula Fuzzy Measure Boolean Lattice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Tomoyuki Araki
    • 1
  • Masao Mukaidono
    • 2
  • Fujio Yamamoto
    • 3
  1. 1.Department of Electronics and Photonic Systems EngineeringHiroshima Institute of TechnologyJapan
  2. 2.Department of Computer ScienceMeiji UniversityJapan
  3. 3.Department of Information and Computer SciencesKanagawa Institute of TechnologyJapan

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