This paper aims to apply the concept of rough sets Pythagorean fuzzy in UP-algebras. Then we introduce fifteen types UP-algebras and study their generalization. In addition, will also discuss $t$-level subsets relationships between

In this paper, the notion of an interval valued intuitionistic fuzzy subsemiring (ideal) of a semiring with respect to t−norm T and s−norm S is given and the characteristic properties are described. The homomorphic image and inverse image are investigated. In particular, by the help of the congruence relations on semirings, new interval valued intuitionistic (S, T )−fuzzy subsemirings (ideals) ...

The paper presents a new hybridization methodology involving Neural, Fuzzy and Rough Computing. A Rough Sets based approximation technique has been proposed based on a certain Neuro – Fuzzy architecture. A New Rough Neuron composition consisting of a combination of a Lower Bound neuron and a Boundary neuron has also been described. The conventional convergence of error in back propagation has b...

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...

For the generality of fuzzy ideals in TM-algebra, a cubic ideal this algebra has been studied, such as and T-ideals. Some properties these are investigated. Also, we show that T-ideal is ideal, but converse not generally valid. In addition, sub-algebra defined, new relations between level subset discussed. After that, T-ideals under homomorphism image (pre-image) Finally, Cartesian product TM-a...

The rough-set theory proposed by Pawlak, has been widely used in dealing with data classification problems. The original rough-set model is, however, quite sensitive to noisy data. Tzung thus proposed deals with the problem of producing a set of fuzzy certain and fuzzy possible rules from quantitative data with a predefined tolerance degree of uncertainty and misclassification. This model allow...

Various expanded rough set models based on tolerance relations enlarge the application fields of rough set theory. Through generating tolerance relations to fuzzy tolerance relations and combining with dominance relations, a tolerance class of a fuzzy tolerance relation is further decomposed into a positive fuzzy tolerance class, a negative fuzzy tolerance class and a purely fuzzy tolerance cla...

This paper presents a general framework for the study of fuzzy rough sets in which both constructive and axiomatic approaches are used. In constructive approach, a pair of lower and upper generalized approximation operators is defined. The connections between fuzzy relations and fuzzy rough approximation operators are examined. In axiomatic approach, various classes of fuzzy rough approximation...

A rough set is a formal approximation of a crisp set which gives lower and upper approximation of original set to deal with uncertainties. The concept of neutrosophic set is a mathematical tool for handling imprecise, indeterministic and inconsistent data. In this paper, we introduce the concepts of Rough Fuzzy Neutrosophic Sets and Fuzzy Neutrosophic Rough Sets and investigate some of their pr...