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220 results on '"Ramík, Jaroslav"'

3. Generalized Hukuhara-Clarke Derivative of Interval-valued Functions and its Properties

Author

Chauhan, Ram Surat, Ghosha, Debdas, Ramik, Jaroslav, and Debnath, Amit Kumar

Subjects
Mathematics - Optimization and Control, 90C30, 65K05
Abstract

In this article, the notion of gH-Clarke derivative for interval-valued functions is proposed. To define the concept of gH-Clarke derivatives, the concepts of limit superior, limit inferior, and sublinear interval-valued functions are studied in the sequel. The upper gH-Clarke derivative of a gH-Lipschitz interval-valued function (IVF) is observed to be a sublinear IVF. It is found that every gH-Lipschitz continuous function is upper gH-Clarke differentiable. For a convex and gH-Lipschitz IVF, it is shown that the upper gH-Clarke derivative coincides with the gH-directional derivative. The entire study is supported by suitable illustrative examples., Comment: 24 pages

Published
2020

7. When is the condition of order preservation met?

Author

Kulakowski, Konrad, Mazurek, Jiri, Ramik, Jaroslav, and Soltys, Michael

Subjects
Computer Science - Discrete Mathematics
Abstract

This article explores a relationship between inconsistency in the pairwise comparisons method and conditions of order preservation. A pairwise comparisons matrix with elements from an alo-group is investigated. This approach allows for a generalization of previous results. Sufficient conditions for order preservation based on the properties of elements of pairwise comparisons matrix are derived. A numerical example is presented., Comment: 19 pages

Published
2018
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9. Applications in Practical Decision-Making Methods: PROMETHEE and TOPSIS

Author

Ramík, Jaroslav, Beckmann, M., Founding Editor, Künzi, H. P., Founding Editor, Fandel, Günter, Editor-in-Chief, Trockel, Walter, Editor-in-Chief, Dawid, Herbert, Series Editor, Dimitrov, Dinko, Series Editor, Gerber, Anke, Series Editor, Haake, Claus-Jochen, Series Editor, Hofmann, Christian, Series Editor, Pfeiffer, Thomas, Series Editor, Slowiński, Roman, Series Editor, Zijm, W. H. M., Series Editor, and Ramík, Jaroslav

Published
2020
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10. Applications in Decision-Making: Analytic Hierarchy Process—AHP Revisited

Author

Ramík, Jaroslav, Beckmann, M., Founding Editor, Künzi, H. P., Founding Editor, Fandel, Günter, Editor-in-Chief, Trockel, Walter, Editor-in-Chief, Dawid, Herbert, Series Editor, Dimitrov, Dinko, Series Editor, Gerber, Anke, Series Editor, Haake, Claus-Jochen, Series Editor, Hofmann, Christian, Series Editor, Pfeiffer, Thomas, Series Editor, Slowiński, Roman, Series Editor, Zijm, W. H. M., Series Editor, and Ramík, Jaroslav

Published
2020
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11. Pairwise Comparisons Matrices on Alo-Groups in Decision-Making

Author

Ramík, Jaroslav, Beckmann, M., Founding Editor, Künzi, H. P., Founding Editor, Fandel, Günter, Editor-in-Chief, Trockel, Walter, Editor-in-Chief, Dawid, Herbert, Series Editor, Dimitrov, Dinko, Series Editor, Gerber, Anke, Series Editor, Haake, Claus-Jochen, Series Editor, Hofmann, Christian, Series Editor, Pfeiffer, Thomas, Series Editor, Slowiński, Roman, Series Editor, Zijm, W. H. M., Series Editor, and Ramík, Jaroslav

Published
2020
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12. Pairwise Comparison Matrices in Decision-Making

Author

Ramík, Jaroslav, Beckmann, M., Founding Editor, Künzi, H. P., Founding Editor, Fandel, Günter, Editor-in-Chief, Trockel, Walter, Editor-in-Chief, Dawid, Herbert, Series Editor, Dimitrov, Dinko, Series Editor, Gerber, Anke, Series Editor, Haake, Claus-Jochen, Series Editor, Hofmann, Christian, Series Editor, Pfeiffer, Thomas, Series Editor, Slowiński, Roman, Series Editor, Zijm, W. H. M., Series Editor, and Ramík, Jaroslav

Published
2020
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13. Stochastic Approaches to Pairwise Comparisons Matrices in Decision-Making

Author

Ramík, Jaroslav, Beckmann, M., Founding Editor, Künzi, H. P., Founding Editor, Fandel, Günter, Editor-in-Chief, Trockel, Walter, Editor-in-Chief, Dawid, Herbert, Series Editor, Dimitrov, Dinko, Series Editor, Gerber, Anke, Series Editor, Haake, Claus-Jochen, Series Editor, Hofmann, Christian, Series Editor, Pfeiffer, Thomas, Series Editor, Slowiński, Roman, Series Editor, Zijm, W. H. M., Series Editor, and Ramík, Jaroslav

Published
2020
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14. Pairwise Comparisons Matrices with Fuzzy and Intuitionistic Fuzzy Elements in Decision-Making

Author

Ramík, Jaroslav, Beckmann, M., Founding Editor, Künzi, H. P., Founding Editor, Fandel, Günter, Editor-in-Chief, Trockel, Walter, Editor-in-Chief, Dawid, Herbert, Series Editor, Dimitrov, Dinko, Series Editor, Gerber, Anke, Series Editor, Haake, Claus-Jochen, Series Editor, Hofmann, Christian, Series Editor, Pfeiffer, Thomas, Series Editor, Slowiński, Roman, Series Editor, Zijm, W. H. M., Series Editor, and Ramík, Jaroslav

Published
2020
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15. Preliminaries

Author

Ramík, Jaroslav, Beckmann, M., Founding Editor, Künzi, H. P., Founding Editor, Fandel, Günter, Editor-in-Chief, Trockel, Walter, Editor-in-Chief, Dawid, Herbert, Series Editor, Dimitrov, Dinko, Series Editor, Gerber, Anke, Series Editor, Haake, Claus-Jochen, Series Editor, Hofmann, Christian, Series Editor, Pfeiffer, Thomas, Series Editor, Slowiński, Roman, Series Editor, Zijm, W. H. M., Series Editor, and Ramík, Jaroslav

Published
2020
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18. Why We Need Desirable Properties in Pairwise Comparison Methods?

Author

Perzina, Radomír and Ramík, Jaroslav

Subjects
ANALYTIC hierarchy process, LEAST squares, ERROR functions, TOPSIS method, SOFTWARE development tools
Abstract

Pairwise comparison matrices (PCMs) are inevitable tools in some important multiple‐criteria decision‐making methods, for example AHP/ANP, TOPSIS, PROMETHEE and others. In this paper, we investigate some important properties of PCMs which influence the generated priority vectors for the final ranking of the given alternatives. The main subproblem of the Analytic Hierarchy Process (AHP) is to calculate the priority vectors, that is, the weights assigned to the elements of the hierarchy (criteria, sub‐criteria, and/or alternatives or variants), by using the information provided in the form of a pairwise comparison matrix. Given a set of elements, and a corresponding pairwise comparison matrix, whose entries evaluate the relative importance of the elements with respect to a given criterion, the final ranking of the given alternatives is evaluated. We investigate some important and natural properties of PCMs called the desirable properties, particularly, the non‐dominance, consistency, intensity and coherence, which influence the generated priority vectors. Usually, the priority vector is calculated based on some well‐known method, for example, the Eigenvector Method, the Arithmetic Mean Method, the Geometric Mean Method, the Least Square Method, and so forth. The novelty of our approach is that the priority vector is calculated as the solution of an optimization problem where an error objective function is minimised with respect to constraints given by the desirable properties. The properties of the optimal solution are discussed and some illustrating examples are presented. The corresponding software tool has been developed and demonstrated in some examples. [ABSTRACT FROM AUTHOR]

Published
2024
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22. Interval Eigenproblem in Max-Min Algebra

Author

Gavalec, Martin, Ramík, Jaroslav, Zimmermann, Karel, Fandel, Günter, Editor-in-chief, Trockel, Walter, Editor-in-chief, Dawid, Herbert, Series editor, Dimitrov, Dinko, Series editor, Gerber, Anke, Series editor, Haake, Claus-Jochen, Series editor, Hofmann, Christian, Series editor, Pfeiffer, Thomas, Series editor, Slowiński, Roman, Series editor, Zijm, W.H.M., Series editor, Gavalec, Martin, Ramík, Jaroslav, and Zimmermann, Karel

Published
2015
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23. Eigenproblem in Max-Drast and Max-Łukasiewicz Algebra

Author

Gavalec, Martin, Ramík, Jaroslav, Zimmermann, Karel, Fandel, Günter, Editor-in-chief, Trockel, Walter, Editor-in-chief, Dawid, Herbert, Series editor, Dimitrov, Dinko, Series editor, Gerber, Anke, Series editor, Haake, Claus-Jochen, Series editor, Hofmann, Christian, Series editor, Pfeiffer, Thomas, Series editor, Slowiński, Roman, Series editor, Zijm, W.H.M., Series editor, Gavalec, Martin, Ramík, Jaroslav, and Zimmermann, Karel

Published
2015
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24. Pairwise Comparison Matrices in Decision Making

Author

Gavalec, Martin, Ramík, Jaroslav, Zimmermann, Karel, Fandel, Günter, Editor-in-chief, Trockel, Walter, Editor-in-chief, Dawid, Herbert, Series editor, Dimitrov, Dinko, Series editor, Gerber, Anke, Series editor, Haake, Claus-Jochen, Series editor, Hofmann, Christian, Series editor, Pfeiffer, Thomas, Series editor, Slowiński, Roman, Series editor, Zijm, W.H.M., Series editor, Gavalec, Martin, Ramík, Jaroslav, and Zimmermann, Karel

Published
2015
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25. Preference Matrices with Fuzzy Elements in Decision Making

Author

Gavalec, Martin, Ramík, Jaroslav, Zimmermann, Karel, Fandel, Günter, Editor-in-chief, Trockel, Walter, Editor-in-chief, Dawid, Herbert, Series editor, Dimitrov, Dinko, Series editor, Gerber, Anke, Series editor, Haake, Claus-Jochen, Series editor, Hofmann, Christian, Series editor, Pfeiffer, Thomas, Series editor, Slowiński, Roman, Series editor, Zijm, W.H.M., Series editor, Gavalec, Martin, Ramík, Jaroslav, and Zimmermann, Karel

Published
2015
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26. Optimization Problems Under Max-Min Separable Equation and Inequality Constraints

Author

Gavalec, Martin, Ramík, Jaroslav, Zimmermann, Karel, Fandel, Günter, Editor-in-chief, Trockel, Walter, Editor-in-chief, Dawid, Herbert, Series editor, Dimitrov, Dinko, Series editor, Gerber, Anke, Series editor, Haake, Claus-Jochen, Series editor, Hofmann, Christian, Series editor, Pfeiffer, Thomas, Series editor, Slowiński, Roman, Series editor, Zijm, W.H.M., Series editor, Gavalec, Martin, Ramík, Jaroslav, and Zimmermann, Karel

Published
2015
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27. Preliminaries

Author

Gavalec, Martin, Ramík, Jaroslav, Zimmermann, Karel, Fandel, Günter, Editor-in-chief, Trockel, Walter, Editor-in-chief, Dawid, Herbert, Series editor, Dimitrov, Dinko, Series editor, Gerber, Anke, Series editor, Haake, Claus-Jochen, Series editor, Hofmann, Christian, Series editor, Pfeiffer, Thomas, Series editor, Slowiński, Roman, Series editor, Zijm, W.H.M., Series editor, Gavalec, Martin, Ramík, Jaroslav, and Zimmermann, Karel

Published
2015
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33. Ranking Alternatives by Pairwise Comparisons Matrix and Priority Vector

Author

Ramík Jaroslav

Subjects
pairwise comparisons matrix, priority vector, ranking alternatives, analytic hierarchy process, AHP, C44, Business, HF5001-6182
Abstract

The decision making problem considered here is to rank n alternatives from the best to the worst, using information given by the decision maker(s) in the form of an n×n pairwise comparisons (PC) matrix. We investigate pairwise comparisons matrices with elements from a real interval which is a traditional multiplicative approach used in Analytic hierarchy process (AHP). Here, we deal with two essential elements of AHP: measuring consistency of PC matrix and the method of eliciting the priority vector by which the final ranking of alternatives is derived. Classical approaches introduced by T. Saaty in AHP are compared with later approaches based on the AHP criticism published in the literature. Advantages and disadvantages of both approaches are highlighted and discussed.

Published
2017
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39. Fuzzy Sets

Author

Ramík, Jaroslav, Vlach, Milan, Hillier, Frederick S., editor, Ramík, Jaroslav, and Vlach, Milan

Published
2002
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44. Preliminaries

Author

Ramík, Jaroslav, Vlach, Milan, Hillier, Frederick S., editor, Ramík, Jaroslav, and Vlach, Milan

Published
2002
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