Consensus Under Fuzziness by Keith Lehrer (auth.), Janusz Kacprzyk, Hannu Nurmi, Mario

By Keith Lehrer (auth.), Janusz Kacprzyk, Hannu Nurmi, Mario Fedrizzi (eds.)

We dwell, regrettably, in turbulent and tough instances laid low with a number of political, fiscal, and social difficulties, in addition to via ordinary mess ups around the world. structures turn into a growing number of advanced, and this matters all degrees, exemplified first via international political alliances, teams of nations, areas, etc., and secondly, by way of multinational (global) organisations and corporations of all sizes. those similar matters impact all social teams. This all makes choice tactics very complex. In almost all selection techniques in those advanced platforms, there are lots of actors (decision makers) who symbolize person topics (persons, nations, businesses, etc.) and their respective curiosity teams. to arrive a significant (good) determination, evaluations of all such actors has to be taken into consideration or a given determination can be rejected and never carried out. preferably, a choice will be made after a consensus among the events concerned have been attained. So, consensus is a truly fascinating state of affairs. In such a lot real-world instances there's substantial uncertainty relating all elements of the choice making procedure. furthermore, evaluations, pursuits, constraints, and so forth. are typically imprecisely identified. This makes the choice making approach tough as one can't hire traditional "hard" tools.

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The Shannon entropy is defined for an arbitrary proba- 43 bility distribution function p on X by the formula S (P) = - L: p (x) log2P (x). 2) xEX As the majority of other measures of uncertainty, the Shannon entropy measures uncertainty in bits, it has the range [0, log2IXI], it is subadditive, and it is additive for independent marginal probability distributions. It was axiomatically proven in several different ways that the Shannon entropy is the only reasonable measure of uncertainty in probability theory [1, 39].

As pointed out by Barrett and Pattanaik (1985), with such reinterpretation, it will be possible to use the formal structure of the theory of stochastic social preference and choice to develop models of vague social or individual preferences and optimality. The interpretation and intuitive justification for such models will be similar to those for models based on fuzzy notions of preference and optimality. REFERENCES Arrow, K. J. (1963), Social Choice and Individual Wiley and Sons. Values; second edition, New York: John Barbera, S.

Plenum Press, New York, 1988. [9] J. F. Geer and G. J. Klir. Discord in possibility theory. International Journal of General Systems, 19(2):119-132, 1991. [10] T. George and N. R. Pal. Quantification of conflict in Dempster-Shafer framework: a new approach. International Journal of General Systems, 24(4):407-423, 1996. [11] M. A. Gil. Fuzziness and loss of information in statistical problems. IEEE- Transaction on Systems, Man, and Cybernetics, 17(6):1016-1025, 1987. [12] D. Harmanec. Toward a characterization of uncertainty measure for the Dempster-Shafer theory.

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