Fuzzy rule interpolation is an important technique for performing inferences with sparse rule bases. Even when given observations have no overlap with the antecedent values of any rule, fuzzy rule interpolation may still derive a conclusion. Nevertheless, fuzzy rule interpolation can only handle fuzziness but not roughness. Rough set theory is a useful tool to deal with incomplete knowledge, wh...

Disease forecasting using soft computing techniques is major area of research in data mining in recent years. To classify heart and diabetes diseases, this paper proposes a diagnosis system using cuckoo search optimized rough sets based attribute reduction and fuzzy logic system. The disease prediction is done as per the following steps 1) feature reduction using cuckoo search with rough set th...

There exists a direct relation between fuzzy rough sets and fuzzy preorders. On the other hand, it is well known the existing parallelism between Formal Concept Analysis and Rough Set Theory. In both cases, Galois connections play a central role. In this work, we focus on adjunctions (also named isotone Galois connections) between fuzzy preordered sets; specifically, we study necessary conditio...

Among the huge number of attributes or features present in real-life data sets, only a small fraction of them are effective to represent the data set accurately. Prior to analysis of the data set, selecting or extracting relevant and significant features is an important preprocessing step used for pattern recognition, data mining, and machine learning. In this regard, a novel dimensionality red...

A color image segmentation technique which exploits a novel definition of rough fuzzy sets and the rough–fuzzy product operation is presented. The segmentation is performed by partitioning each block in multiple rough fuzzy sets that are used to build a lower and a upper histogram in the HSV color space. For each bin of the lower and upper histograms a measure, called τ index, is computed to fi...

In many fields, especially in environmetrics and social sciences, it is impossible to obtain exact quantitative data about a variable of interest. Many researchers have suggested that vague, non-precise observations should be described by fuzzy sets. Fuzzy set theory originated by Zadeh (1965) relies on ordering relations that express intensity (degree) of membership of an object in a set. Appl...

Rough set theory can be generalized by induced topology through equivalence relations. Motivated the work of generalization rough via topology, concept and properties $ \tau-\mathfrak{K} $-fuzzy open (closed) sets are proposed. Considering sets, we have obtained lower upper approximations also proved their properties. represented as $-open \alpha level sets. The fuzzy on basis binary relation c...

By means of Dubois and Prade’s idea, we introduce the concept of rough fuzzy normal subgroups and investigate some related properties. Combining rough sets and soft sets, rough soft normal subgroups with respect to a normal subgroup of groups in Pawlak approximation spaces are introduced. Moreover, we investigate the relationships between lower and upper rough soft normal subgroups with respect...

Combining rough sets and fuzzy soft sets, we propose an algorithm to obtain the optimal decision program. In this algorithm, firstly, according to fuzzy soft sets, we build up information systems; secondly, we compute the significance of each parameter according to rough set theory; thirdly, combining subjective bias, we give an algorithm to obtain the comprehensive weight of each parameter; at...