Construction of Fuzzy Numbers via Cumulative Distribution Function

Georgios Souliotis, Yousif Alanazi and Basil Papadopoulos ()
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Georgios Souliotis: Department of Civil Engineering Section of Mathematics and Informatics, Democritus University of Thrace, 67100 Kimeria, Greece
Yousif Alanazi: Department of Mathematics, College of Science, Kuwait University, Kuwait City 13060, Kuwait
Basil Papadopoulos: Department of Civil Engineering Section of Mathematics and Informatics, Democritus University of Thrace, 67100 Kimeria, Greece

Mathematics, 2022, vol. 10, issue 18, 1-10

Abstract: The first person to introduce possibility theory was Lotfi A. Zadeh, in 1977. It was, of course, of no coincidence that he directly combined it with the theory of fuzzy sets. Later, several researchers dealt with the mathematical foundations of the theory of possibilities. They introduced possibility distribution as a concept, and they directly combined it with fuzzy numbers. A fuzzy number corresponds to a possibility distribution and vice versa. This correspondence gave a key advantage to possibility theory over probability theory. This advantage is the facility of operations. However, there is also a basic: problem how is a possibility distribution generated? In this paper, we introduce a method of constructing a possibility distribution via a cumulative probability function. The advantage of this method is the simplicity of construction, which is nothing more than the construction of a fuzzy triangular or trapezoidal number via a cumulative probability function. This construction introduces a way to determine a fuzzy number without relying on the experience or intuition of the researcher. We should, of course, emphasize that this specific construction is within the framework of a theoretical model. We do not apply it to specific data. We also considered that the theoretical construction model should be presented through the theory of possibilities, thus avoiding the theory of probabilities.

Keywords: fuzzy numbers; possibility measure; necessity measure; cumulative distribution function; possibility distributions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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