Iranian Journal of Fuzzy Systems
Year:2007 | Volume:4 | Issue:2|Papers Count:8

We use the basic binomial option pricing method but allow some or all the parameters in the model to be uncertain and model this uncertainty using fuzzy numbers. We show that with the fuzzy model we can, with a reasonably small number of steps, consider almost all possible future stock prices; whereas the crisp model can consider only n + 1 prices after n steps.

In this paper, the finitely many constraints of a fuzzy relation inequalities problem are studied and the linear objective function on the region defined by a fuzzy max-average operator is optimized. A new simplification technique which accelerates the resolution of the problem by removing the components having no effect on the solution process is given together with an algorithm and a numerical example to illustrate the steps of the problem resolution process.

There are several methods for solving fuzzy linear programming (FLP) problems. When the constraints and/or the objective function are fuzzy, the methods proposed by Zimmermann, Verdegay, Chanas and Werners are used more often than the others. In the Zimmerman method (ZM) the main objective function cx is added to the constraints as a fuzzy goal and the corresponding linear programming (LP) problem with a new objective (l) is solved. When this new LP has alternative optimal solutions (AOS), ZM may not always present the "best" solution. Two cases may occur: cx may have different bounded values for the AOS or be unbounded. Since all of the AOS have the samel, they have the same values for the new LP. Therefore, unless we check the value of cx for all AOS, it may be that we do not present the best solution to the decision maker (DM); it is possible that cx is unbounded but ZM presents a bounded solution as the optimal solution. In this note, we propose an algorithm for eliminating these difficulties.

We study interior operators and interior structures in a fuzzy setting. We investigate systems of "almost open" fuzzy sets and the relationships to fuzzy interior operators and fuzzy interior systems.

Notions of strongly regular, regular and left (right) regular G-semi groups are introduced. Equivalent conditions are obtained through fuzzy notion for a G-semi group to be either strongly regular or regular or left regular.  

The concept of right (left) quotient (or residual) of an ideal h by an ideal v of an L-subring m of a ring R is introduced. The right (left) quotients are shown to be ideals of m. It is proved that the right quotient [h:r v] of an ideal of h by an ideal v of an L-subring m is the largest ideal of m such that [h:r v]v Íh. Most of the results pertaining to the notion of quotients (or residual) of an ideal of ordinary rings are extended to L-ideal theory of L-subrings.

In this paper, we study some properties of the near SR-compactness in L-topological spaces, where L is a fuzzy lattice. The near SR-compactness is a kind of compactness between Lowen's fuzzy compactness' and SR-compactness, and it preserves desirable properties of compactness in general topological spaces.

In this paper, the concept of countably near PS-compactness in L-topological spaces is introduced, where L is a completely distributive lattice with an order-reversing involution. Countably near PS-compactness is defined for arbitrary L-subsets and some of its fundamental properties are studied.