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A Quantitative View on Fuzzy Numbers

József Mezei, A Quantitative View on Fuzzy Numbers. TUCS Dissertations 142. Turku Centre for Computer Science, 2011.

Abstract:

Since its introduction, fuzzy set theory has become a useful tool in the mathematical modelling of problems in Operations Research and many other fields. The number of applications is growing continuously. In this thesis we investigate a special type of fuzzy set, namely fuzzy numbers. Fuzzy numbers (which will be considered in the thesis as possibility distributions) have been widely used in quantitative analysis in recent decades.

In this work two measures of interactivity are defined for fuzzy numbers, the possibilistic correlation and correlation ratio. We focus on both the theoretical and practical applications of these new indices. The approach is based on the level-sets of the fuzzy numbers and on the concept of the joint distribution of marginal possibility distributions. The measures possess similar properties to the corresponding probabilistic correlation and correlation ratio. The connections to real life decision making problems are emphasized focusing on the financial applications.

We extend the definitions of possibilistic mean value, variance, covariance and correlation to quasi fuzzy numbers and prove necessary and sufficient conditions for the finiteness of possibilistic mean value and variance. The connection between the concepts of probabilistic and possibilistic correlation is investigated using an exponential distribution.

The use of fuzzy numbers in practical applications is demonstrated by the Fuzzy Pay-Off method. This model for real option valuation is based on findings from earlier real option valuation models. We illustrate the use of number of different types of fuzzy numbers and mean value concepts with the method and provide a real life application.

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BibTeX entry:

@PHDTHESIS{phdMezei11a,
  title = {A Quantitative View on Fuzzy Numbers},
  author = {Mezei, József},
  number = {142},
  series = {TUCS Dissertations},
  school = {Turku Centre for Computer Science},
  year = {2011},
  ISBN = {978-952-12-2670-0},
}

Belongs to TUCS Research Unit(s): Institute for Advanced Management Systems Research (IAMSR)

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