In this paper, we define a binary relation for general collective choice situations, the needing relation, that captures one notion of dependence between alternatives with respect to inclusion in several popular solution concepts, including the top-cycle set, the uncovered set, the Banks set, and the minimal covering set. After defining the relation and relating it to a graph theoretical view o...

Coalitional game theory is a sub-area of game theory that models situations where agents can benefit from cooperation. Its representations and solution concepts are NP-hard in the general case. I describe some of the major solution concepts and survey two papers that deal with this general-case intractability. The first studies a specific well-motivated coalitional game and finds that two solut...

a‎s we know, developing mathematical models and numerical procedures that would appropriately treat and solve systems of linear equations where some of the system's parameters are proposed as fuzzy numbers is very important in fuzzy set theory. for this reason, many researchers have used various numerical methods to solve fuzzy linear systems. in this paper, we define the concepts of midpoint a...

Many research on primary school children in Malaysia indicate an over reliance on the written symbols representation (Munirah, 2001; Parmjit, 2005; Munirah& Noor Azlan, 2002; Chinappan & Ambigapathy, 2009; Mohini & Jacinta, 2010). This is a cause for concern as researchers draw strong connections between the representations children use and their understanding (Lamon, 2001). Janvier (1987) desc...

A‎s we know, developing mathematical models and numerical procedures that would appropriately treat and solve systems of linear equations where some of the system's parameters are proposed as fuzzy numbers is very important in fuzzy set theory. For this reason, many researchers have used various numerical methods to solve fuzzy linear systems. In this paper, we define the concepts of midpoint a...

Theoretical research on claims problems has concentrated on normative properties and axiomatizations of solution concepts. We complement these analyses by empirical evidence on the predictability of three classical solution concepts in a bankruptcy problem. We examine both people’s impartial normative evaluations as well as their actual negotiation behavior in a bargaining with claims environme...

Kohlberg and Mertens (1986) argued that a solution concept to a game should be invariant under the addition or deletion of an equivalent strategy and not require the use of weakly dominated strategies. In this paper we study which of these requirements are satisfied by Kalai and Samet’s (1984) concepts of persistent equilibria and persistent retracts. While none of these concepts has all the in...

Most haemodialysis patients are, even when treated ‘adequately’ according to current standards, exposed to the so-called unphysiology of dialysis, which was described more than 25 years ago [1]. They are still at high risk of being overhydrated and dehydrated, hypertensive and hypotensive, acidotic and alkalotic, or hyperkaliaemic and hypokaliaemic thrice weekly. Furthermore, most patients are ...