Fuzzy numbers revisited: operations on extensional fuzzy numbers
Fuzzy numbers are commonly represented with fuzzy sets. Their objective is to better represent imprecise data. However, operations on fuzzy numbers are not as straightforward as maths on crisp numbers. Commonly, the Zadeh's extension rule is applied to elaborate a result. This can produce two problems: (1) high computational complexity and (2) for some fuzzy sets and some operations the results is not a fuzzy set with the same features (eg. multiplication of two triangular fuzzy sets does not produce a triangular fuzzy set). One more problem is the fuzzy spread -- fuzziness of the result increases with the number of operations. These facts can severely limit the application field of fuzzy numbers. In this paper we would like to revisite this problem with a different kind of fuzzy numbers -- extensional fuzzy numbers. The paper defines operations on extensional fuzzy numbers and relational operators (=, >, >=, <, <=) for them. The proposed approach is illustrated with several applicational examples. The C++ implementation is available from a public GitHub repository.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Analytical Formulations for the Level Based Weighted Average Value of Discrete Trapezoidal Fuzzy Numbers
In fuzzy decision-making processes based on linguistic information, operations on discrete fuzzy numbers are commonly performed. Aggregation and defuzzification operations are some of these often used operations. Many ag…
Decision MakingSolution of Rectangular Fuzzy Games by Principle of Dominance Using LR-type Trapezoidal Fuzzy Numbers
Fuzzy Set Theory has been applied in many fields such as Operations Research, Control Theory, and Management Sciences etc. In particular, an application of this theory in Managerial Decision Making Problems has a remarka…
Decision MakingManagementTrapezoidal Fuzzy Numbers for the Transportation Problem
Transportation Problem is an important problem which has been widely studied in Operations Research domain. It has been often used to simulate different real life problems. In particular, application of this Problem in N…
Simulation of Random LR Fuzzy Intervals
Random fuzzy variables join the modeling of the impreciseness (due to their ``fuzzy part'') and randomness. Statistical samples of such objects are widely used, and their direct, numerically effective generation is there…
A Dynamic Survey of Fuzzy, Intuitionistic Fuzzy, Neutrosophic, Plithogenic, and Extensional Sets
Real-world phenomena often exhibit vagueness, partial truth, and incomplete information. To model such uncertainty in a mathematically rigorous way, many generalized set-theoretic frameworks have been introduced, includi…