In this paper, we take a GL-quantale as the truth value table to study a new rough set model—L-valued fuzzy rough sets. The three key components of this model are: an L-fuzzy set A as the universal set, an L-valued relation of A and an L-fuzzy set of A (a fuzzy subset of fuzzy sets). Then L-valued fuzzy rough sets are completely characterized via both constructive and axiomatic approaches.

Our aim of this paper is to introduce the concept of L-double fuzzy rough sets in which both constructive and axiomatic approaches are used. In constructive approach, a pair of L-double fuzzy lower (resp. upper) approximation operators is defined and the basic properties of them are studied. From the viewpoint of the axiomatic approach, a set of axioms is constructed to characterize the L double fuzzy upper (resp. lower) approximation of L-double fuzzy rough sets. Finally, from L- double fuzzy approximation operators, we generated Alexandrov L-double fuzzy topology.

Today, recommender systems, according to their special performance, are widely utilized in several scientific issues. Fuzzy recommender systems are the type of systems in which they are combined with fuzzy theory and give more flexibility to recommender systems. Nonetheless, in this article a new combination method from fuzzy rough set collaborative filtering is presented in which the distance is calculated based on Euclidean distance measure. In fact, by using fuzzy rough sets the applicants’ data are used regarding to have better prediction. This combination method via fuzzy rough sets increases the accuracy of prediction. Since, implemented experiments on test data depict recommended method has better validation in comparison with other reputed methods.

In this research work, a wholesaler-retailer-customer supply chain model for a deteriorating item is considered, where the retailer's warehouse in the market place has a limited capacity. The retailer can rent an additional warehouse (rented warehouse) if needed, with a higher rent compared to the existing warehouse (own warehouse). The customers' demand of the item is linearly influenced by the stock level and in case of shortages the base demand is partially backlogged. Being the leader of the supply chain, the retailer introduces some promotional cost to boost the base demand of the item. To participate in joint marketing decision, the wholesaler shares a compromise part of this promotional cost. Goal of this research work is to maximize the individual profits (when the retailer is the leader and the wholesaler is the follower) as well as the channel profit (when the retailer and the wholesaler jointly make marketing decision) of the system. It is established that if the wholesaler shares a part of the promotional cost, then the channel profit as well as the individual profits increase. The supply chain model is also considered in imprecise environment, where different inventory parameters are fuzzy/rough in nature. In this case, the individual profits as well as the channel profit become fuzzy/rough in nature. As optimization of fuzzy/rough objective is not well defined, following credibility/trust measure of fuzzy/rough event, an approach is followed for comparison of fuzzy/rough objectives and a Particle Swarm Optimization algorithm is implemented to find the marketing decisions. Efficiency of the algorithm in solving the problem is statistically established. The existence of the joint marketing decision is established analytically and numerically (with illustration) in crisp as well as in imprecise environments.

Web robots are software programs that traverse the internet autonomously. Their most important task is to fetch information and send it to the origin server. The high consumption of network bandwidth by them and server performance reduction, have caused the web robot detection problem. In this paper, fuzzy rough set theory has been used for web robot detection. The proposed method includes 4 phases. In the first phase, user sessions have identified using fuzzy rough set clustering. In the second phase, a vector of 10 features is extracted for each session. In the third phase, the identified sessions are labeled using a heuristic method. In the fourth phase, these labels are improved using fuzzy rough set classification. The proposed method performance has been evaluated on a real world dataset. The experimental results have been compared with state-of-the-art methods, and show the superiority of the proposed method in terms of F-measure.

High dimensional microarray datasets are difficult to classify since they have many features with small number ofinstances and imbalanced distribution of classes. This paper proposes a filter-based feature selection method to improvethe classification performance of microarray datasets by selecting the significant features. Combining the concepts ofrough sets, weighted rough set, fuzzy rough set and hesitant fuzzy sets for developing an effective algorithm is the maincontribution of this paper. The mentioned method has two steps, in the first step, four discretization approaches areapplied to discretize continuous datasets and selects a primary subset of features by combining of weighted rough setdependency degree and information gain via hesitant fuzzy aggregation approach. In the second step, a significancemeasure of features (defined by fuzzy rough concepts) is employed to remove redundant features from primary set.The Wilcoxon Signed Ranked tes (A Non-parametric statistical test) is conducted for comparing the presented methodwith ten feature selection methods across seven datasets. The results of experiments show that the proposed methodis able to select a significant subset of features and it is an effective method in the literature in terms of classificationperformance and simplicity.

The evaluation information mainly relies on expert’s subjective judgment, which is imprecise and uncertain, and this issue is also true in the supplier selection. In order to improve and achieve reliable results, this study provides a systematic framework for selecting suppliers based on sustainability dimensions in which a hybrid fuzzy- rough AHP-WASPAS approach is proposed for sustainable supplier selection. The effectiveness of the proposed methodology is illustrated through its application in Kurdistan Gas Company supplier selection. First, the sustainable supplier selection criteria are determined by reviewing previous research. After screening the sustainable supplier selection criteria with the fuzzy Delphi method, AHP based on fuzzy rough numbers is used to determine the weights of criteria. Finally, a developed version of Waspas method, namely the Waspas method based on rough-fuzzy numbers, is introduced which can be applied in the environment of vague and uncertain decision making. This proposed approach is used to rank sustainable suppliers of Kurdistan Gas Company.

The rough set model was constructed in fuzzy approximation space. In this study, we first introduce the fuzzy relation, relative sets, and fuzzy equivalence class. Then, we prove some properties of the fuzzy equivalence class. Thereafter, the concept of fuzzy rough set is proposed over fuzzy relation and inverse fuzzy relation in fuzzy approximation space by means of relative sets and fuzzy equivalence class sets, and some propositions are proved. Also, some examples and dentitions are presented in this study.

$L$-fuzzy rough sets are extensions of the classical rough sets by relaxing the equivalence relations to $L$-relations. The topological structures induced by $L$-fuzzy rough sets have opened up the way for applications of topological facts and methods in granular computing. In this paper, we firstly prove that each arbitrary $L$-relation can generate an Alexandrov $L$-topology. Based on this fact, we introduce the topological similarity of $L$-relations, denote it by T-similarity, and we give intuitive characterization of T-similarity. Then we introduce the variations of a given $L$-relation and investigate the relationship among them. Moreover, we prove that each $L$-relation is uniquely topological similar to an $L$-preorder. Finally, we investigate the related algebraic structures of different sets of $L$-relations on the universe.

In real-world data deluge, due to insignificant information and high dimension, irrelevant and redundant attributes reduce the ability of experts both in predictive accuracy and speed, respectively. Attribute selection is the notion of selecting those attributes that are essential as well as enough to specify the target knowledge preferably. Fuzzy rough set-based approaches play a crucial role in selecting relevant and less redundant attributes from a high-dimensional dataset. Intuitionistic fuzzy set-based approaches can handle uncertainty as it gives an additional degree of freedom when compared to fuzzy approaches. So, it has a more flexible and practical ability to deal with vagueness and noise available in the information system. In this paper, we introduce two new robust approaches for attribute selection based on intuitionistic fuzzy rough set theory using the concepts of Different Classes ratio and Laplace Summation operator. Firstly, Different Classes ratio and Laplace Summation operator based lower andupper approximations are established based on intuitionistic fuzzy rough set concept. Moreover, we present algorithms and illustrative examples for a better understanding of our approaches. Finally, experimental analysis is performed on some real-valued datasets for attribute selection and classification accuracies.