in this paper, a novel approach for ranking fuzzy numbers based on the angle measure is introduced. several left and right spreads at each chosen levels of fuzzy numbers is used to determine center of mass points(cmps) and then, the angels between the cmps and the horizontal axis is calculated. the total angle is determined by averaging the computed angles and finally, the novel method is compa...

The starting point of this paper is the introduction of a new measure of inclusion of fuzzy set A in fuzzy set B. Previously used inclusion measures take values in the interval [0,1]; the inclusion measure proposed here takes values in a Boolean lattice. In other words, inclusion is viewed as an Lfuzzy valued relation between fuzzy sets. This relation is reflexive, antisymmetric and transitive,...

In the present communication, we review the existing measures of fuzzy information. We define and characterize two fuzzy information measures which are sub additive and different from known measures of fuzzy information. We also study monotonic behavior and particular cases of these fuzzy information measures. 2000 Mathematics Subject Classification: 94A17 and 94 D 05

When there are interactions among the independent variables, the performances of the most often used multiple regression models and ridge regression model are not well enough. In contrast, the Choquet integral takes into account the interactions among independent variables, the discrete Choquet integral regression models based on some non-negative valued fuzzy measures or monotonic measure can ...

The notion of a signed measure arises if a measure is allowed to take on both positive and negative values. A set that is both positive and negative with respect to a signed measure is termed as a null set. Some concepts in measure theory can be generalized by means of classes of null sets. An abstract formulation and proof of the Lebesgue decomposition theorem using the concept of null sets is...

Measures A (set) function μ : K → [0,∞], with ∅ ∈ K ⊂ 2 and μ(∅) = 0 is called additive or finitely additive if A,B ∈ K, with A ∪ B ∈ K and A ∩ B = ∅ imply μ(A ∪ B) = μ(A) + μ(B). Similarly, μ is called σ-additive or countably additive if Ai ∈ K, with ⋃∞ i=1 Ai = A ∈ K and Ai ∩ Aj = ∅ for i 6= j imply μ(A) = ∑∞ i=1 μ(Ai). It is clear that if μ is σ-additive then μ is also additive, but the conv...

We present an axiomatic approach to conditional measures of fuzzy events which is inspired by the Dupré–Tipler argument for Bayesianism. Unlike there or in the older and related Cox argument, although we are able to derive additive probabilities other non-additive solutions exist. Our motivation is to show that Bayesian foundational arguments are based on Boolean logic but they do not require i...

The fuzzy modeling technology, which uses a rule-based description of the relationship between variables, is discussed. We then turn to the problem of the simultaneous solution of relationships involving fuzzy models. We illustrate this problem by considering the equilibrium problem in economics. In this case we have two relationships, one between price and supply and the other between price an...