We introduce notions of soft rough m-polar fuzzy sets and m-polar fuzzy soft rough sets as novel hybrid models for soft computing, and investigate some of their fundamental properties. We discuss the relationship between m-polar fuzzy soft rough approximation operators and crisp soft rough approximation operators. We also present applications of m-polar fuzzy soft rough sets to decision-making.

The hybridization of rough sets and fuzzy sets has focused on creating an end product that extends both contributing computing paradigms in a conservative way. As a result, the hybrid theory inherits their respective strengths, but also exhibits some weaknesses. In particular, although they allow for gradual membership, fuzzy rough sets are still abrupt in a sense that adding or omitting a sing...

This study describes application of some approximate reasoning methods to analysis of hydrocyclone performance. In this manner, using a combining of Self Organizing Map (SOM), Neuro-Fuzzy Inference System (NFIS)-SONFISand Rough Set Theory (RST)-SORST-crisp and fuzzy granules are obtained. Balancing of crisp granules and non-crisp granules can be implemented in close-open iteration. Using differ...

In this paper we define rough intuitionistic fuzzy sets (analogous to the definition of rough fuzzy sets introduced by Dubois and Prade [8] ) and study their properties. Some propositions in this notion are proved.

Classification based on fuzzy logic techniques can handle uncertainty to a certain extent as it provides only the fuzzy membership of an element in a set. This paper implements the extension of fuzzy logic: Neutrosophic logic to handle indeterminacy, uncertainty effectively. Classification is done on various techniques based on Neutrosophic logic i.e. Neutrosophic soft set, rough Neutrosophic s...

Granular computing deals with information representation in the form of a number of entities or information granules. Information granules are made up of a collection of entities, usually of numeric level, joined due to their similarity, functional adjacency, indistinguishability, coherence or alikeness. The granular computing is associated to sets concepts, such as fuzzy sets, rough sets, inte...

This paper discusses the relationship between probability and fuzziness based on the process of perception. As a generalization of crisp set, fuzzy set is used to model fuzzy event as proposed by Zadeh. Similarly, we may consider rough set to represent rough event in terms of probability measure. Special attention will be given to conditional probability of fuzzy event as well as conditional pr...

Since upper and lower approximations could be induced from the rough set structures, rough sets are considered as approximations. The concept of fuzzy rough sets was proposed by replacing crisp binary relations with fuzzy relations by Dubois and Prade. In this paper, we introduce and investigate some properties of intuitionistic fuzzy rough approximation operators and intuitionistic fuzzy relat...

Rough set theory is an important approach to granular computing. Type-1 fuzzy set theory permits the gradual assessment of the memberships of elements in a set. Hybridization of these assessments results in a fuzzy rough set theory. Type-2 fuzzy sets possess many advantages over type-1 fuzzy sets because their membership functions are themselves fuzzy, which makes it possible to model and minim...

Just like rough set theory, fuzzy set theory addresses the topic of dealing with imperfect knowledge. Recent investigations have shown how both theories can be combined into a more flexible, more expressive framework for modelling and processing incomplete information in information systems. At the same time, intuitionistic fuzzy sets have been proposed as an attractive extension of fuzzy sets,...