In this note the notion of interval-valued fuzzy BF -algebras (briefly, i-v fuzzy BF -algebras), the level and strong level BF -subalgebra is introduced. Then we state and prove some theorems which determine the relationship between these notions and BF -subalgebras. The images and inverse images of i-v fuzzy BF -subalgebras are defined, and how the homomorphic images and inverse images of i-v ...

We introduce the category IVRel(H) consisting of interval-valued H-fuzzy relational spaces and relation preserving mappings between them and we study structures of the category IVRel(H) in the viewpoint of the topological universe introduced by Nel. Thus we show that IVRel(H) satisfies all the conditions of a topological universe over Set except the terminal separator property and IVRel(H) is C...

The concept of the rough set was originally proposed by Pawlak as a formal tool for modelling and processing incomplete information in information systems, then in 1990, Dubois and Prade first introduced the rough fuzzy sets and fuzzy rough sets as a fuzzy extension of the rough sets. The aim of this paper is to present a new extension of the rough set theory by means of integrating the classic...

Interval-valued fuzzy sets involve more uncertainties than ordinary fuzzy sets and can be used to capture imprecise or uncertain decision information in fields that require multiple-criteria decision analysis (MCDA). This paper takes the simple additive weighting (SAW) method and the technique for order preference by similarity to an ideal solution (TOPSIS) as the main structure to deal with in...

Based on the Choquet integral and the generalized Shapley function, two new induced Atanassov’s interval-valued intuitionistic fuzzy hybrid aggregation operators are defined, which are named as the induced generalized Shapley Atanassov’s interval-valued intuitionistic fuzzy hybrid Choquet arithmetical averaging (IGS-IVIFHCAA) operator and the induced generalized Shapley Atanassov’s interval-val...

In many practical situation, some of the attribute values for an object may be interval and set-valued. This paper introduces the interval and set-valued information systems and decision systems. According to the semantic relation of attribute values, interval and set-valued information systems can be classified into two categories: disjunctive (Type 1) and conjunctive (Type 2) systems. In this...

In this paper the concept of interval valued intuitionistic fuzzy soft set relations (IVIFSS-relations for short) is proposed. Our relations on interval valued intuitionistic fuzzy soft sets is an extension of the relations on intuitionistic fuzzy soft sets, introduced by Mukherjee and Chakraborty in 2009. The basic properties of the IVIFSS-relations are also presented and discussed. It is seen...

in this paper, we introduce a function in order to measure the distancebetween two order intervals of fuzzy numbers, and show that this function isa metric. we investigate some properties of this metric, and finally presentan application. we think that this study could provide a more generalframework for researchers studying on interval analysis, fuzzy analysis andfuzzy decision making.