New Fuzzy Extensions on Binomial Distribution Article Swipe
Gia Sirbiladze
,
Janusz Kacprzyk
,
Teimuraz Manjafarashvili
,
Bidzina Midodashvili
,
Bidzina Matsaberidze
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.3390/axioms11050220
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.3390/axioms11050220
The use of discrete probabilistic distributions is relevant to many practical tasks, especially in present-day situations where the data on distribution are insufficient and expert knowledge and evaluations are the only instruments for the restoration of probability distributions. However, in such cases, uncertainty arises, and it becomes necessary to build suitable approaches to overcome it. In this direction, this paper discusses a new approach of fuzzy binomial distributions (BDs) and their extensions. Four cases are considered: (1) When the elementary events are fuzzy. Based on this information, the probabilistic distribution of the corresponding fuzzy-random binomial variable is calculated. The conditions of restrictions on this distribution are obtained, and it is shown that these conditions depend on the ratio of success and failure of membership levels. The formulas for the generating function (GF) of the constructed distribution and the first and second order moments are also obtained. The Poisson distribution is calculated as the limit case of a fuzzy-random binomial experiment. (2) When the number of successes is of a fuzzy nature and is represented as a fuzzy subset of the set of possible success numbers. The formula for calculating the probability of convolution of binomial dependent fuzzy events is obtained, and the corresponding GF is built. As a result, the scheme for calculating the mathematical expectation of the number of fuzzy successes is defined. (3) When the spectrum of the extended distribution is fuzzy. The discussion is based on the concepts of a fuzzy-random event and its probability, as well as the notion of fuzzy random events independence. The fuzzy binomial upper distribution is specifically considered. In this case the fuzziness is represented by the membership levels of the binomial and non-binomial events of the complete failure complex. The GF of the constructed distribution and the first-order moment of the distribution are also calculated. Sufficient conditions for the existence of a limit distribution and a Poisson distribution are also obtained. (4) As is known, based on the analysis of lexical material, the linguistic spectrum of the statistical process of word-formation becomes two-component when switching to vocabulary. For this, two variants of the hybrid fuzzy-probabilistic process are constructed, which can be used in the analysis of the linguistic spectrum of the statistical process of word-formation. A fuzzy extension of standard Fuchs distribution is also presented, where the fuzziness is reflected in the growing numbers of failures. For better representation of the results, the examples of fuzzy BD are illustrated in each section.
Related Topics
Concepts
Mathematics
Fuzzy number
Fuzzy logic
Multinomial distribution
Negative binomial distribution
Probability distribution
Cumulative distribution function
Binomial distribution
Binomial (polynomial)
Fuzzy set
Beta-binomial distribution
Applied mathematics
Poisson distribution
Statistics
Probability density function
Computer science
Artificial intelligence
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.3390/axioms11050220
- https://www.mdpi.com/2075-1680/11/5/220/pdf?version=1652420355
- OA Status
- gold
- Cited By
- 9
- References
- 25
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4229448406
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W4229448406Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.3390/axioms11050220Digital Object Identifier
- Title
-
New Fuzzy Extensions on Binomial DistributionWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2022Year of publication
- Publication date
-
2022-05-09Full publication date if available
- Authors
-
Gia Sirbiladze, Janusz Kacprzyk, Teimuraz Manjafarashvili, Bidzina Midodashvili, Bidzina MatsaberidzeList of authors in order
- Landing page
-
https://doi.org/10.3390/axioms11050220Publisher landing page
- PDF URL
-
https://www.mdpi.com/2075-1680/11/5/220/pdf?version=1652420355Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
goldOpen access status per OpenAlex
- OA URL
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https://www.mdpi.com/2075-1680/11/5/220/pdf?version=1652420355Direct OA link when available
- Concepts
-
Mathematics, Fuzzy number, Fuzzy logic, Multinomial distribution, Negative binomial distribution, Probability distribution, Cumulative distribution function, Binomial distribution, Binomial (polynomial), Fuzzy set, Beta-binomial distribution, Applied mathematics, Poisson distribution, Statistics, Probability density function, Computer science, Artificial intelligenceTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
9Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 2, 2024: 4, 2023: 3Per-year citation counts (last 5 years)
- References (count)
-
25Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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