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,...

A fuzzy rough set approach has been proposed without using any fuzzy logical connectives. By this approach, gradual decision rules are induced from a given decision table. Fuzzy-rough modus ponens and fuzzy-rough modus tollens have been formulated based on the gradual decision rules. The equivalence condition between fuzzy-rough modus ponens and fuzzy-rough modus tollens is discussed. The condi...

–Rough set theory is a powerful tool to extract classification rules from a database that usually is given in the form of information system in which information is expressed by attributes and their values. In this paper, we first evaluate every example data (tuple) using, not a singleton but, a fuzzy number (or, suppose the original information system is along with such fuzzy numbers), due to ...

Decision-theoretic rough set theory (DTRS) is becoming one of the important research directions for studying set approximations using Bayesian decision procedure and probability theory in rough set community. In this paper, a novel model, fuzzy multigranulation decision-theoretic rough set model (FM-DTRS), is proposed in terms of inclusion measure of fuzzy rough sets in the viewpoint of fuzzy m...