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VSOP fuzzy numbers and their fuzzy ordering
Fuzzy Sets and Systems, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kiyomitsu Horiuchi, Naoyuki Tamura
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The orders of intuitionistic fuzzy numbers
Journal of Intelligent & Fuzzy Systems, 2015In many applications of intuitionistic fuzzy sets, comparing or ranking intuitionistic fuzzy numbers (IFNs) plays an important role. In this paper, the orders of intuitionistic fuzzy numbers are discussed. The orders of IFNs have undesired mathematical properties. By using a special function, a new order of IFNs is proposed.
Zhao Zhang, Zeshui Xu
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On the properties of orderings of extensional fuzzy numbers
2020 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2020The article stems from distinct studies on arithmetics of fuzzy numbers, orderings of fuzzy numbers, and metrics on fuzzy numbers. Trying to capture the existing knowledge in the mentioned areas and putting them together, we motivate the construction of metric-like spaces on fuzzy numbers by desirable connection to their arithmetics.
Martin Stepnicka +2 more
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Orderings of Extensional Fuzzy Numbers
2019 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2019This article follows the arithmetics of extensional fuzzy numbers that are based on the transitive closure of the used similarity relations and that form particular MI-prefields. The direction of the contribution goes towards defining the ordering of extensional fuzzy numbers in order to construct further notions from the mathematical analysis in the ...
Martin Stepnicka +2 more
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Fuzzy Portfolio Diversification with Ordered Fuzzy Numbers
2017In this paper, we consider a multi-objective portfolio diversification problem under real constraints in fuzzy environment, where the objective is to minimize the variance of portfolio and maximize expected return rate of portfolio. The return rates of assets are modeled using concept of Ordered Fuzzy Candlesticks, which are Ordered Fuzzy Numbers.
Adam Marszalek, Tadeusz Burczynski
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2015
This chapter describes different methods for comparing and ordering fuzzy numbers. Theoretically, fuzzy numbers can only be partially ordered, and hence cannot be compared. However, in practical applications, such as decision making, scheduling, market analysis or optimisation with fuzzy uncertainties, the comparison of fuzzy numbers becomes crucial.
Beata Basiura +6 more
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This chapter describes different methods for comparing and ordering fuzzy numbers. Theoretically, fuzzy numbers can only be partially ordered, and hence cannot be compared. However, in practical applications, such as decision making, scheduling, market analysis or optimisation with fuzzy uncertainties, the comparison of fuzzy numbers becomes crucial.
Beata Basiura +6 more
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An index for ordering fuzzy numbers
Fuzzy Sets and Systems, 1993Abstract A new index that is useful for ordering (ranking) of fuzzy numbers is proposed. To use this index the membership functions of fuzzy numbers need not be normal or convex. Properties of this index and its relationship to the 1981 Yager's index are explained.
F. Choobineh, Huishen Li
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The majority order of fuzzy numbers
Proceedings Joint 9th IFSA World Congress and 20th NAFIPS International Conference (Cat. No. 01TH8569), 2002Majority order is defined to determine ranking orders between fuzzy numbers. Some reasonable properties of the derived order relations are investigated in detail. In particular, the approaches are mathematically interpreted by means of the Lebesgue measure.
null Jinsheng Liu +2 more
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Transitive fuzzy orderings of fuzzy numbers
Fuzzy Sets and Systems, 1989In this well-organized paper a generalization of the Baas-Kwakernaak index [\textit{S. M. Baas} and \textit{H. Kwakernaak}, Automatica 13, 47-58 (1977; Zbl 0363.90010)] is presented by replacing the min operation in their definition by a t-norm. Essential properties of the thus defined induced fuzzy ordering are established.
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On the admissibility of the alpha-order for fuzzy numbers
Computational and Applied MathematicszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Diego García-Zamora +5 more
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