Operational Risk Assessment of Distribution Network Equipment Based on Rough Set and D-S Evidence Theory

With the increasing complication, compaction, and automation of distribution network equipment, a small failure will cause an outbreak chain reaction and lead to operational risk in the power distribution system, even in the whole power system. Therefore, scientific assessment of power distribution equipment operation risk is significant to the security of power distribution system. In order to get the satisfactory assessment conclusions from the complete and incomplete information and improve the assessment level, an operational risk assessment model of distribution network equipment based on rough set and D-S evidence theory was built. In this model, the rough set theory was used to simplify and optimize the operation risk assessment indexes of distribution network equipment and the evidence D-S theory was adopted to combine the optimal indexes. At last, the equipment operational risk level was obtained from the basic probability distribution decision. Taking the transformer as an example, this paper compared the assessment result obtained from the method proposed in this paper with that from the ordinary Rogers ratio method and discussed the application of the proposed method. It proved that the method proposed in this paper is feasible, efficient, and provides a new way to assess the distribution network equipment operational risk

On Rough Sets and Hyperlattices

In this paper, we introduce the concepts of upper and lower rough hyper fuzzy ideals (filters) in a hyperlattice and their basic properties are discussed. Let $\theta$ be a hyper congruence relation on $L$. We show that if $\mu$ is a fuzzy subset of $L$, then $\overline{\theta}()=\overline{\theta}()$ and $\overline{\theta}(\mu^*) =\overline{\theta}((\overline{\theta}(\mu))^*)$, where is the least hyper fuzzy ideal of $L$ containing $\mu$ and \mu^*(x) = sup\{\alpha \in [0, 1]: x \in I( \mu_{\alpha} )\}$$ for all $x \in L$. Next, we prove that if $\mu$ is a hyper fuzzy ideal of $L$, then $\mu$ is an upper rough fuzzy ideal. Also, if $\theta$ is a $\wedge-$complete on $L$ and $\mu$ is a hyper fuzzy prime ideal of $L$ such that $\overline{\theta}(\mu)$ is a proper fuzzy subset of $L$, then $\mu$ is an upper rough fuzzy prime ideal. Furthermore, let $\theta$ be a $\vee$-complete congruence relation on $L$. If $\mu$ is a hyper fuzzy ideal, then $\mu$ is a lower rough fuzzy ideal and if $\mu$ is a hyper fuzzy prime ideal such that $\underline{\theta}(\mu)$ is a proper fuzzy subset of $L$, then $\mu$ is a lower rough fuzzy prime ideal

Fuzzy Techniques for Decision Making 2018

Zadeh's fuzzy set theory incorporates the impreciseness of data and evaluations, by imputting the degrees by which each object belongs to a set. Its success fostered theories that codify the subjectivity, uncertainty, imprecision, or roughness of the evaluations. Their rationale is to produce new flexible methodologies in order to model a variety of concrete decision problems more realistically. This Special Issue garners contributions addressing novel tools, techniques and methodologies for decision making (inclusive of both individual and group, single- or multi-criteria decision making) in the context of these theories. It contains 38 research articles that contribute to a variety of setups that combine fuzziness, hesitancy, roughness, covering sets, and linguistic approaches. Their ranges vary from fundamental or technical to applied approaches