On the Extension of Pseudo-Boolean Functions for the Aggregation of Interacting Criteria
نویسندگان
چکیده
The paper presents an analysis on the use of integrals defined for non-additive measures (or capacities) as the Choquet and the Šipoš integral, and the multilinear model, all seen as extensions of pseudoBoolean functions, and used as a means to model interaction between criteria in a multicriteria decision making problem. The emphasis is put on the use, besides classical comparative information, of information about difference of attractiveness between acts, and on the existence, for each point of view, of a “neutral level”, allowing to introduce the absolute notion of attractive or repulsive act. It is shown ∗Corresponding author. On leave from Thomson-CSF, Corporate Research Lab, 91404 Orsay Cedex, France
منابع مشابه
ON THE FUZZY SET THEORY AND AGGREGATION FUNCTIONS: HISTORY AND SOME RECENT ADVANCES
Several fuzzy connectives, including those proposed by Lotfi Zadeh, can be seen as linear extensions of the Boolean connectives from the scale ${0,1}$ into the scale $[0,1]$. We discuss these extensions, in particular, we focus on the dualities arising from the Boolean dualities. These dualities allow to transfer the results from some particular class of extended Boolean functions, e.g., from c...
متن کاملThe influence of variables on pseudo-Boolean functions with applications to game theory and multicriteria decision making
The power of players in a collective decision process is a central issue in game theory. For this reason, the concept of influence of players on a simple game has been introduced. More generally, the influence of variables on Boolean functions has been defined and studied. We extend this concept to pseudo-Boolean functions, thus making it possible to appraise the degree of influence of any coal...
متن کاملMATRIX VALUATION PSEUDO RING (MVPR) AND AN EXTENSION THEOREM OF MATRIX VALUATION
Let R be a ring and V be a matrix valuation on R. It is shown that, there exists a correspondence between matrix valuations on R and some special subsets ?(MVPR) of the set of all square matrices over R, analogous to the correspondence between invariant valuation rings and abelian valuation functions on a division ring. Furthermore, based on Malcolmson’s localization, an alternative proof for t...
متن کاملThe Arity Gap of Aggregation Functions and Further Extensions
The aim of this paper is to completely classify all aggregation functions based on the notion of arity gap. We first establish explicit descriptions of the arity gap of the Lovász extensions of pseudo-Boolean functions and, in particular, of the Choquet integrals. Then we consider the wider class of order-preserving functions between arbitrary, possibly different, posets, and show that similar ...
متن کاملمکانیابی محل دفن پسماند جامد شهر ایلام با استفاده از رویههای بولین و ترکیب خطی وزنی در محیط GIS
Abstract Background and purpose: Urban developments and population growth have dramatically increased all kinds of municipal solid waste (MSW) generation. Hence, treatment and disposal of municipal waste is one of the main concerns in urban environmental management. The aim of this study was to determine suitable locations for landfill based on environmental criteria using Boolean and Weight...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- European Journal of Operational Research
دوره 148 شماره
صفحات -
تاریخ انتشار 2003