The Problem of a Function Maximization on a Type-2 Fuzzy Set

  • S. O. Mashchenko
  • D. O. Kapustian
Part of the Understanding Complex Systems book series (UCS)


The article focuses on generalizing the concept of the maximizing alternative in the case of the objective function maximization problem on the type-2 fuzzy set (T2FS) of feasible alternatives. An extension of the natural order relation to the class of fuzzy sets is used for comparison of fuzzy sets of alternatives membership degrees. It is shown that such a fuzzy preference relation provides fuzzy sets of membership degrees of T2FSs of feasible alternatives to be normal. With the help of this preference relation a fuzzy set of non-dominated alternatives is constructed. The notion of α-level non-dominated alternative is introduced. It is shown that this is a solution to the optimization problem. In this problem the objective function is maximized with a bounded secondary membership degree of the T2FS of feasible alternatives. The problem of choosing alternatives according to the two criteria (the objective function and secondary degrees of membership to the T2FS of feasible alternatives) is formulated. Its Pareto optimal solutions are called the effective maximizing alternatives. Their properties are investigated.


Type-2 Fuzzy Sets (T2FS) Fuzzy Preference Relations (FPR) Pareto Optimal Solutions Secondary Degrees Function Maximization Problem 
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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© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • S. O. Mashchenko
    • 1
  • D. O. Kapustian
    • 1
  1. 1.Taras Shevchenko National University of KyivKyivUkraine

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