RAMÍK, Jaroslav. Extended Fuzzy Intervals and their Application in Optimal Allocation Problem Under Uncertainty. Transactions on Fuzzy Sets and Systems. 2023, vol. 2, No 1, p. 1-14. ISSN 2821-0131. Available from: https://dx.doi.org/10.30495/tfss.2022.1964124.1043.
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Basic information
Original name Extended Fuzzy Intervals and their Application in Optimal Allocation Problem Under Uncertainty.
Authors RAMÍK, Jaroslav.
Edition Transactions on Fuzzy Sets and Systems, 2023, 2821-0131.
Other information
Original language English
Type of outcome Article in a journal
Country of publisher Czech Republic
Confidentiality degree is not subject to a state or trade secret
WWW URL
Organization unit School of Business Administration in Karvina
Doi http://dx.doi.org/10.30495/tfss.2022.1964124.1043
Keywords in English Optimal allocation problem, Division scheme, Interval valued functions, Interval coeffcients, Extended fuzzy interval coeffcients
Links GA21-03085S, research and development project.
Changed by Changed by: prof. RNDr. Jaroslav Ramík, CSc., učo 48844. Changed: 20/12/2022 15:33.
Abstract
In this paper we dene a special interval uncertainty by extending the well known concept of fuzzy intervals (or, fuzzy numbers), dening a new concept of extended fuzzy interval and its subspace: extended linear fuzzy interval. We present some examples and derive basic properties. Then we demonstrate an application of the new concept by formulating the well known Optimal Allocation Problem (OAP) and its solution under uncertainty. We formulate the corresponding optimization problem with the extended fuzzy interval coecients and also extended fuzzy interval variables and derive its optimal solution in the form of extended fuzzy intervals. Two numerical examples are presented in order to illustrate particular problems and solution concepts. The main innovation highlights of this paper may be formulated as follows: We generalize the well known concept of the fuzzy interval, i.e. fuzzy set of the real numbers R with triangular or trapezoidal membership function, by dening the new concept of extended fuzzy interval - EFI. Then we dene a special subspace of extended fuzzy intervals with piece-wise linear membership functions called extended linear fuzzy interval - ELFI. We derive basic properties of the newly dened concepts and present some examples illustrating particular new properties. We demonstrate application possibilities and advantages of the new concept by an optimal allocation problem with the extended fuzzy interval coecients as well as variables. We present two numerical examples illustrating a particular problem of allocation type and corresponding solution concepts.
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