The most popular approach to decision-making in the setting of fuzzy sets is the maximin ranking of solutions. This method is natural when interpreting the fuzzy sets as flexible constraints that cannot compensate with one another. However the obtained ranking of solutions is very coarse. Two kinds of refinements to this ordering are introduced: a partial ordering according to the least satisfi...

Many ranking methods have been proposed so far. The fuzzy number defuzzification method with continuous weighted quasi-arithmetic means was proposed by Yoshida in the domain (−∞,+∞) . Recently in [22], the researcher used this method with the ordinary fuzzy set in a compact interval, that all the conclusions can be extended to the ordinary fuzzy set in [24] directly. This parameterized defuzzif...

in this paper, we consider the production possibility set with n production units such that the following four principles that governs: inclusion observations, conceivability, immensity and convexity. our goal is to estimate the output of a same and new production unit with existing production possibility and amount of input is specified. so, initially we find the interval changes of each input...

It is well known fact that binary relations are generalized mathematical functions. Contrary to functions from domain to range, binary relations may assign to each element of domain two or more elements of range. Some basic operations on functions such as the inverse and composition are applicable to binary relations as well. Depending on the domain or range or both are fuzzy value fuzzy set, i...

The methods of fuzzy decision-making use the comparison of fuzzy numbers or sets to choose among alternatives. The linear ordering of real numbers does not extend to fuzzy numbers and fuzzy numbers can only be partially ordered and hence they cannot be compared. However, when fuzzy numbers are used in practical applications their comparison becomes necessary. Several methods of comparing fuzzy ...

In voting theory the well-known Gibbard-Satterthwaite theorem is about the manipulability of aggregators which consists of the aggregation of individual preferences expressed as a complete ordering over the set of alternatives. This paper deals with the generalization of such a theorem in a context where each individual expresses a fuzzy preference (weak) ordering. This extension is called H-ma...

When dealing with multi-criteria decision making problems, the concept of Pareto-optimality and Pareto-dominance may be inefficient (e.g. generally multiple solutions exist), especially when there is a large number of criteria. Our paper considers the fuzzy multi-criteria decision making problem based on Zadeh’s linguistic approach to P-optimality and P-dominance. The construction, analysis and...

Ordering-based modifiers can be particularly useful in fuzzy control and other fields related to fuzzy systems. This paper deals with the construction of such modifiers by means of hull operators with respect to fuzzy orderings.

The basic paradigm of simulation is the probabilistic approach to describing real world uncertainty. However, in many cases we do not have an information that would be precise enough to build the corresponding probabilistic model or there are some human factors that prevent doing so. In such situations the mathematical tools of fuzzy set theory may be successfully used. It seems that the simple...