On the polytope of fuzzy measures
نویسندگان
چکیده
In this paper we deal with the problem of studying some mathematical aspects regarding the polytope of fuzzy measures when the referential set is finite. More concretely, we study whether two extreme points are adjacent; for general polytopes, this is a NP-hard problem. However, for the case of fuzzy measures, we give a necessary and sufficient condition for two extreme points to be adjacent. This allows us to prove that it is possible to find out in polynomial time (in the number of minimal subsets) whether two extremes are adjacent. These results can be extended to the polytope given by the convex hull of monotone boolean functions.
منابع مشابه
On the Structure of the k-Additive Fuzzy Measures
The family of k-additive measures has been introduced as a midterm between probabilities and general fuzzy measures and finds a wide number of applications in practice. However, its structure is different from other families of fuzzy measures and is certainly more complex (for instance, its vertices are not always {0, 1}valued), so it has not been yet fully studied. In this paper we present som...
متن کاملON TRUNCATED MEASURES OF INCOME INEQUALITY FROM A FUZZY PERSPECTIVE
In most statistical analysis, inequality or extent of variation in income isrepresented in terms of certain summary measures. But some authors arguedthat the concept of inequality is vague and thus cannot be measured as anexact concept. Therefore, fuzzy set theory provides naturally a useful toolfor such circumstances. In this paper we have introduced a real-valued fuzzymethod of illustrating t...
متن کاملINFORMATION MEASURES BASED TOPSIS METHOD FOR MULTICRITERIA DECISION MAKING PROBLEM IN INTUITIONISTIC FUZZY ENVIRONMENT
In the fuzzy set theory, information measures play a paramount role in several areas such as decision making, pattern recognition etc. In this paper, similarity measure based on cosine function and entropy measures based on logarithmic function for IFSs are proposed. Comparisons of proposed similarity and entropy measures with the existing ones are listed. Numerical results limpidly betoken th...
متن کاملIntuitionistic Fuzzy Information Measures with Application in Rating of Township Development
Predominantly in the faltering atmosphere, the precise value of some factors is difficult to measure. Though, it can be easily approximated by intuitionistic fuzzy linguistic term in the real-life world problem. To deal with such situations, in this paper two information measures based on trigonometric function for intuitionistic fuzzy sets, which are a generalized version of the fuzzy informat...
متن کاملA note on decision making in medical investigations using new divergence measures for intuitionistic fuzzy sets
Srivastava and Maheshwari (Iranian Journal of Fuzzy Systems 13(1)(2016) 25-44) introduced a new divergence measure for intuitionisticfuzzy sets (IFSs). The properties of the proposed divergence measurewere studied and the efficiency of the proposed divergence measurein the context of medical diagnosis was also demonstrated. In thisnote, we point out some errors in ...
متن کامل