We present the concept of bi-capacity as a generalization of capacities (or fuzzy measures). The Choquet integral w.r.t. bi-capacities is defined, and is a generalization of Cumulative Prospect Theory models. This new model can bring much more flexibility in representing preferences. Lastly, we introduce the Möbius transform of bi-capacities.

In this paper some types of decomposable signed fuzzy measures have been presented. We discuss properties of 6-and ⊕decomposable signed fuzzy measures. We consider their relationship with bi-capacities.

Customers are realizing the importance and benefits of shopping online such as convenience, comparison, product research, larger selection, and lower prices. The dynamic nature of e-commerce evokes online businesses to make alterations in their business processes and decisions making to satisfy customers’ needs. Online businesses are adopting Business Intelligence (BI) tools and systems with th...

and Applied Analysis 3 Definition 1.4 see 18, 20–23 . 1 The intersection of all fuzzy α-closed resp., semiclosed, preclosed, γ-closed, semi-preclosed, β-closed sets containing a fuzzy set A is called a fuzzy α-closure resp., semiclosure, preclosure, γ-closure, semi-preclosure, β-closure of A. 2 The union of all fuzzy α-open resp., semiopen, preopen, γ-open, semi-preopen, β-open sets contained i...

In recent years, geometric-mean averaging operators (GMA operators) have been proposed to overcome the drawbacks of the existing T-operators and averaging operators for handling the Boolean “AND” and “OR” operations in fuzzy information retrieval. However, the GMA operators can not deal with queries represented by generalized fuzzy numbers. In this paper, we present generalized fuzzy number geo...

In this paper, we introduce the concept of anti M-fuzzy sub-bigroup of an M-bigroup and bi lower level subset of an anti M-fuzzy sub-bigroup and discussed some of its properties.

In this paper, we present a new prioritization method for information fusion under fuzzy environment. We propose a new measure to measure the similarity between generalized trapezoidal fuzzy numbers. Based on the proposed similarity measure, we develop an utility function of generalized trapezoidal fuzzy numbers. With the utility function of generalized trapezoidal fuzzy numbers, we propose a n...

In this paper, we present the induced generalized intuitionistic fuzzy ordered weighted averaging (IGIFOWA) operator. It is a new aggregation operator that generalized the IFOWA operator, including all the characteristics of both the generalized IFOWA and the induced IFOWA operators. It provides a very general formulation that includes as special cases a wide range of aggregation operators for ...

In this work we introduce the concept of Generalized Atanassov’s Intuitionistic Fuzzy Index. We characterize it in terms of fuzzy implication operators and we propose a construction method with automorphisms. Finally, we study some special properties of the generalized Atanassov’s intuitionistic fuzzy index. Keywords— Atanassov’s Intuitionistic Fuzzy Index, Fuzzy Implication Operator, Automorph...