Fuzzy vectors as a tool for modeling uncertain multidimensional quantities
Pages 1585 - 1603
Abstract
The paper deals with modeling uncertain multidimensional quantities by means of fuzzy vectors. In connection with possible interactions among variables, the separability of fuzzy vectors is discussed in detail. For the case when interconnections among variables are given by a crisp relation, a more general form of separability of fuzzy vectors-the separability on a given relation (e.g. on a probability simplex) is introduced. Properties of fuzzy vectors separable on a given relation are studied, and ways of convenient setting of such fuzzy vectors are proposed. Finally, fuzzy extensions of real-valued functions and real-vector-valued functions to general input fuzzy vectors are investigated.
References
[1]
Dubois, D., Ostasiewicz, W. and Prade, H., Fuzzy sets: history and basic notions. In: Dubois, D., Prade, H. (Eds.), Fundamentals of Fuzzy Sets, Kluwer Academic Publishers, Boston, London, Dordrecht. pp. 21-124.
[2]
Dubois, D. and Prade, H., Additions of interactive fuzzy numbers. IEEE Trans. Automat. Control. vAC-26 i4. 926-936.
[3]
Fullér, R. and Majlender, P., On interactive fuzzy numbers. Fuzzy Sets and Systems. v143. 355-369.
[4]
Inuiguchi, M., Necessity measure optimization in linear programming problems with fuzzy polytopes. Fuzzy Sets and Systems. v158 i17. 1882-1891.
[5]
Inuiguchi, M., Ramík, J. and Tanino, T., Oblique fuzzy vectors and their use in possibilistic linear programming. Fuzzy Sets and Systems. v135. 123-150.
[6]
Inuiguchi, M. and Tanino, T., Fuzzy linear programming with interactive uncertain parameters. Reliable Comput. v10 i5. 357-367.
[7]
Inuiguchi, M. and Tanino, T., Possibilistic linear programming with fuzzy if--then rule coefficients. Fuzzy Optim. Decision Making. v1 i1. 65-91.
[8]
Constrained fuzzy arithmetic: basic questions and some answers. Soft Comput. v2. 100-108.
[9]
Negoita, C.V. and Ralescu, D.A., Representation theorems for fuzzy concepts. Kybernetes. v4. 169-174.
[10]
O. Pavlačka, Fuzzy methods of decision making, Dissertation Thesis, Palacký University Olomouc, 2007 (in Czech.).
[11]
O. Pavlačka, J. Talašová, Application of the fuzzy weighted average of fuzzy numbers in decision making models, in: U. Bodenhofer, V. Novák, M. Štěpnička, (Eds.), New Dimensions in Fuzzy Logic and Related Technologies, Vol II, Proc. 5th EUSFLAT Conf., Ostrava, Czech Republic, Ostravská univerzita, Ostrava, September 11--14, 2007, pp. 455--462.
[12]
Pavlačka, O. and Talašová, J., Fuzzy vectors of normalized weights and their application in decision making models. APLIMAT---J. Appl. Math. v1 i1. 451-462.
[13]
Talašová, J. and Pavlačka, O., Fuzzy probability spaces and their applications in decision making. Austrian J. Statist. v35 i2&3. 347-356.
[14]
Viertl, R., Statistical Methods for Non-Precise Data. 1996. CRC Press, Boca Raton, FL.
[15]
Zadeh, L.A., Fuzzy sets. Inform. Control. v8. 338-353.
[16]
Zadeh, L.A. and Zadeh, L.A., Concept of a linguistic variable and its application to approximate reasoning I, II. Inform. Sci. v8. 199-249.
Index Terms
- Fuzzy vectors as a tool for modeling uncertain multidimensional quantities
Index terms have been assigned to the content through auto-classification.
Recommendations
On fuzzy n-cell numbers and n-dimension fuzzy vectors
Fuzzy n-cell numbers are a kind of special n-dimension fuzzy numbers, whose sets of cuts are all hyperrectangles. n-dimension fuzzy vectors are the Cartesian products of n one-dimension fuzzy numbers. In this paper, we show that the fuzzy n-cell number ...
Oblique fuzzy vectors and their use in possibilistic linear programming
Special issue: Interfaces between fuzzy set theory and interval analysisIn this paper, we propose oblique fuzzy vectors to treat the interactivity among fuzzy numbers. Oblique fuzzy vectors are extensions of fuzzy numbers and vectors of non-interactive fuzzy numbers. The interactivity among fuzzy numbers can be treated by a ...
Modeling uncertain variables of the weighted average operation by fuzzy vectors
The paper deals with the fuzzy extension of the weighted average operation. First, we study the convenient ways how uncertain weights and weighted values can be modeled by fuzzy vectors. We show that, in comparison to a tuple of fuzzy numbers that have ...
Comments
Information & Contributors
Information
Published In
Copyright © Elsevier B.V. © 2010.
Publisher
Elsevier North-Holland, Inc.
United States
Publication History
Published: 01 June 2010
Author Tags
Qualifiers
- Article
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- 0Total Citations
- 0Total Downloads
- Downloads (Last 12 months)0
- Downloads (Last 6 weeks)0
Reflects downloads up to 27 Jul 2024
Other Metrics
Citations
Cited By
View allView Options
View options
Get Access
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in