Weighted Constraints in Fuzzy Optimization

Many practical optimization problems are characterized by some flexibility in the problem constraints, where this flexibility can be exploited for additional trade-off between improving the objective function and satisfying the constraints. Especially in decision making, this type of flexibility could lead to workable solutions, where the goals and the constraints specified by different parties involved in the decision making are traded off against one another and satisfied to various degrees. Fuzzy sets have proven to be a suitable representation for modeling this type of soft constraints. Conventionally, the fuzzy optimization problem in such a setting is defined as the simultaneous satisfaction of the constraints and the goals. No additional distinction is assumed to exist amongst the constraints and the goals. This report proposes an extension of this model for satisfying the problem constraints and the goals, where preference for different constraints and goals can be specified by the decision-maker. The difference in the preference for the constraints is represented by a set of associated weight factors, which influence the nature of trade-off between improving the optimization objectives and satisfying various constraints. Simultaneous weighted satisfaction of various criteria is modeled by using the recently proposed weighted extensions of (Archimed

Use of idempotent functions in the aggregation of different filters for noise removal

The majority of existing denoising algorithms obtain good results for a specific noise model, and when it is known previously. Nonetheless, there is a lack in denoising algorithms that can deal with any unknown noisy images. Therefore, in this paper, we study the use of aggregation functions for denoising purposes, where the noise model is not necessary known in advance; and how these functions affect the visual and quantitative results of the resultant images

Fuzzy Multi-objective Supplier Selection Problem: Possibilistic Programming Approach

In this paper, a multi-objective mathematical model is developed in fuzzy environment in which the vagueness in aspiration level of objectives and data imprecision regarding the selection criteria and related constraints are con- sidered simultaneously as a source of fuzziness. In the model, such data impreci- sion is presented based on the estimation of its possibility distribution to better capture the uncertainty. Finally, a fuzzy solution methodology is constructed by the aid of weighted additive aggregation function to derive optimal solution. As pre- liminary investigation, we report that the proposed model is more flexible and con- venient than the previous models whose imprecise parameters are treated as a given single estimated value

The Complexity of Manipulating kk-Approval Elections

An important problem in computational social choice theory is the complexity of undesirable behavior among agents, such as control, manipulation, and bribery in election systems. These kinds of voting strategies are often tempting at the individual level but disastrous for the agents as a whole. Creating election systems where the determination of such strategies is difficult is thus an important goal. An interesting set of elections is that of scoring protocols. Previous work in this area has demonstrated the complexity of misuse in cases involving a fixed number of candidates, and of specific election systems on unbounded number of candidates such as Borda. In contrast, we take the first step in generalizing the results of computational complexity of election misuse to cases of infinitely many scoring protocols on an unbounded number of candidates. Interesting families of systems include $k$-approval and $k$-veto elections, in which voters distinguish $k$ candidates from the candidate set. Our main result is to partition the problems of these families based on their complexity. We do so by showing they are polynomial-time computable, NP-hard, or polynomial-time equivalent to another problem of interest. We also demonstrate a surprising connection between manipulation in election systems and some graph theory problems