Application of Wald Function to OR and AND Fuzzy Operations in No- Data Problems

Authors

  • Houju Hori Jr. Houju Hori Jr. Mie University (Former Professor)
  • Yukio Matsumoto The Institute of Statistical Mathematics

DOI:

https://doi.org/10.6000/2371-1647.2016.02.09

Keywords:

Subjective qualifier, fuzzy event, membership function, subjective probability distribution, OR-conjunction, AND-conjunction

Abstract

Subjective qualifiers of Wald's theory of decision functions are the fuzzy events of the subsequent fuzzy set theory. Wald's notion of subjective qualifiers involves applying integral transforms to convert states of nature into fuzzy events. Probabilities of fuzzy events and arithmetic formulas for fuzzy utility function values are readily derived from Wald's integral transforms. We have applied Zadeh's extension principle to Wald's integral transforms and demonstrated that fuzzy mathematics is effective when applied to multiple subjective probability distributions conjoined by OR and AND operations. In this paper, we focus on no-data problems and construct a fuzzy Bayes' theorem for cases in which a membership function and multiple subjective probability distributions conjoined by OR or AND operations are given. In addition, we devise a formulation for the corresponding decision making problem.

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Published

2016-11-28

How to Cite

Houju Hori Jr., H. H. J., & Matsumoto, Y. (2016). Application of Wald Function to OR and AND Fuzzy Operations in No- Data Problems. Journal of Advances in Management Sciences & Information Systems, 2, 107–110. https://doi.org/10.6000/2371-1647.2016.02.09

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Articles