In this article, we propose an axiomatic system for fuzzy “cardinality” measures (referred to as fuzzy c-measures for short) assigning to each finite fuzzy set a generalized cardinal that expresses the number of elements that the fuzzy set contains. The system generalizes an axiomatic system introduced by J. Casasnovas and J. Torrens (2003). We show that each fuzzy c-measure is determined by tw...

Fuzzy measures are a generalization of probability measures for which additivity is removed and monotonicity is imposed instead. These measures have become a powerful tool in Decision Theory (see e.g. 12, the work of Schmeidler 21 and 3); moreover, the Choquet Expected Utility model generalizes the Expected Utility one, and this model offers a simple theoretical foundation for explaining phenom...

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...

in recent years, the balanced score card (bsc) has been the focus of considerable methodology for strategic cost management in management accounting area since it was originally proposed by kaplan ,r.s. and norton, d.p. in 1992. bsc is an approach to performance measurement based on both financial and nonfinancial information from four perspectives which are called financial, customer, internal...

As a measure of information shared between two fuzzy pattern vectors, the fuzzy information proximity measure (FIPM) plays an important part in fuzzy pattern recognition, fuzzy clustering analysis and fuzzy approximate reasoning. In this paper, two novel FIPMs are set up. Firstly, an axiom theory about the FIPM is given, and different expressions of the FIPM are discussed. A new FIPM is then pr...

In case of fuzzy reasoning in sparse fuzzy rule bases, the question of selecting the suitable fuzzy similarity measure is essential. The rule antecedents of the sparse fuzzy rule bases are not fully covering the input universe therefore fuzzy reasoning methods applied for sparse fuzzy rule bases requires similarity measures able to distinguish the similarity of non-overlapping fuzzy sets, too. ...

In multicriteria decision making, the study of attribute contributions is crucial to attain correct decisions. Fuzzy measures allow a complete description of the joint behavior of attribute subsets. However, the determination of fuzzy measures is often hard. A common way to identify fuzzy measures is HLMS (Heuristic Least Mean Squares) algorithm. In this paper, the convergence of the HLMS algor...

The paper deals with the well-known notion of similarity measures between fuzzy sets and proposes a variety of similarity measures for fuzzy sets. Moreover, the paper proves that the proposed measures satisfy the properties of the axiomatic definition for similarity measures and introduces several theorems. Several illustrative and practical examples from the areas of pattern recognition, decis...