Bi-capacities have been presented recently by the authors as a natural generalization of capacities (fuzzy measures). Usual concepts as Möbius transform, Shapley value and interaction index, Choquet integral, kadditivity can be generalized. We present formulas of the Choquet integral w.r.t. the Möbius transform, and w.r.t. the interaction index for 2-additive bi-capacities.

In this paper, a new class of bi-cooperative games with fuzzy bi-coalitions is proposed in multilinear extension form. The extension is shown to be unique. The solution concept discussed in [3] is investigated and characterized for this class of games.

Digital age today has shown increasing reliance on digital media and rapid distribution of digital contents. The issues of piracy and copyright are of immense concern in this exponentially increasing digital revolution. In this paper, authors propose use of bi-orthogonal wavelet transform as an effective tool to address copyright infringement issues. A synergistic combination of bi-orthogonal w...

This paper develops a bi-objective portfolio selection problem that maximizes returns and minimizes a risk measure called conditional Drawdown (CDD). The drawdown measures include the maximal Drawdown and Average Drawdown as its limiting case. The CDD family of risk functional is similar to conditional value at Risk (CVaR). In this paper, the fuzzy method has been used to solve the bi-objec...

The major activity of Business Intelligence (BI) is to dig out the various trends and patterns from variety of authentic sources that helps the managers to take appropriate decision in framing the policies for business plans accordingly. Surveys are considered to be an essential part of BI. Surveys conducted amongst different or same groups by different team may yield conflicting reports. Moreo...

‎Let $G$ be a finite group‎. ‎An element $gin G$ is called non-vanishing‎, ‎if for‎ ‎every irreducible complex character $chi$ of $G$‎, ‎$chi(g)neq 0$‎. ‎The bi-Cayley graph ${rm BCay}(G,T)$ of $G$ with respect to a subset $Tsubseteq G$‎, ‎is an undirected graph with‎ ‎vertex set $Gtimes{1,2}$ and edge set ${{(x,1),(tx,2)}mid xin G‎, ‎ tin T}$‎. ‎Let ${rm nv}(G)$ be the set‎ ‎of all non-vanishi...

The uncertainty of a financial market is traditionally dealt with probabilistic approaches. However, there are many non-probabilistic factors that affect the financial markets such that the return rate of risky assets may be regarded as fuzzy number, which is a powerful tool used to describe an uncertain environment with vagueness and ambiguity and some type of fuzziness. In this paper, the con...

One of the most important elements in a lattice are the irreducible elements. For example, when the lattice is finite, which is usual in the computational case, it forms a base from which the complete lattice is obtained. These elements are also important in Formal Concept Analysis, since they are the basic information of a relational system. In the general fuzzy framework of multi-adjoint conc...

The business environment is full of uncertainties. Investing in various asset classes may lower the risk of overall portfolio and increase the potential for greater returns. In this paper, we propose a bi-objective mixed asset portfolio selection model involving projects as well as securities. Furthermore, based on fuzzy decision theory, a fuzzy mixed projects and securities portfolio selection...