Abstract Capillary rise within rough structures is a wetting phenomenon that fundamental to survival in biological organisms, deterioration of our built environment, and performance numerous innovations, from 3D microfluidics carbon capture. Here, accurately predict capillary rise, we must couple two phenomena: hemiwicking. Experiments, simulations, theory demonstrate how this coupling challeng...

This paper presents an expressive language for representing knowledge about vague concepts. It is based on the rough set formalism and it caters for implicit definition of rough relations by combining different regions (e.g. upper approximation, lower approximation, boundary) of other rough relations. The semantics of the proposed language is obtained by translating it to the language of extend...

In order to involve user knowledge in determining equality of sets, which may not be equal in the mathematical sense, three types of approximate (rough) equalities were introduced by Novotny and Pawlak ([8, 9, 10]). These notions were generalized by Tripathy, Mitra and Ojha ([13]), who introduced the concepts of approximate (rough) equivalences of sets. Rough equivalences capture equality of se...

Soft rough sets which are a hybrid model combining rough sets with soft sets are defined by using soft rough approximation operators. Soft rough sets can be seen as a generalized rough set model based on soft sets. The present paper aims to combine the covering soft set with rough set, which gives rise to the new kind of soft rough sets. Based on the covering soft sets, we establish soft coveri...

Multi–granulation is an improvement of the classical rough set theory since it uses a family of binary relations instead of of a single indiscernibility relation for the constructing of approximation. In this paper, the multi–granulation rough set approach is further generalized into fuzzy environment. A family of fuzzy T–similarity relations are used to define the optimistic and pessimistic fu...

Structure of Rough Approximations Based on Molecular Lattices p. 69 Rough Approximations under Level Fuzzy Sets p. 78 Fuzzy-Rough Modus Ponens and Modus Tollens as a Basis for Approximate Reasoning p. 84 Logic and Rough Sets Rough Truth, Consequence, Consistency and Belief Revision p. 95 A Note on Ziarko's Variable Precision Rough Set Model and Nonmonotonic Reasoning p. 103 Fuzzy Reasoning Base...

Abstract: Rule based systems store knowledge as a set of rules and reason over them to solve problems. A new hype rough net approach for rule generation, representation and reasoning of knowledge-based system using rough sets and Petri nets is presented in this paper. A Rough Petri Net (RPN) is proposed for representing knowledge and formalism for the verification of rule-based systems. The mai...

Support vector techniques were proposed by Vapnik as an alternative to neural networks for solving non-linear problems. The concepts of margins in support vector techniques provides a natural relationship with the rough set theory. This chapter describes rough set theoretic extensions of support vector technologies for classification, prediction, and clustering. The theoretical formulations of ...