Vagueness and Roughness

The paper proposes a new formal approach to vagueness and vague sets taking inspirations from Pawlak’s rough set theory. Following a brief introduction to the problem of vagueness, an approach to conceptualization and representation of vague knowledge is presented from a number of different perspectives: those of logic, set theory, algebra, and computer science. The central notion of the vague set, in relation to the rough set, is defined as a family of sets approximated by the so called lower and upper limits. The family is simultaneously considered as a family of all denotations of sharp terms representing a suitable vague term, from the agent’s point of view. Some algebraic operations on vague sets and their properties are defined. Some important conditions concerning the membership relation for vague sets, in connection to Blizard’s multisets and Zadeh’s fuzzy sets, are established as well. A classical outlook on a logic of vague sentences (vague logic) based on vague sets is also discussed

Literature Review on Vague Set Theory in Different Domains

Problem of decision making is a crucial task in every business. This decision making job is found very difficult when it is depends on the imprecise and vague environment, which is frequent in recent years. Vague sets are an extension of Fuzzy sets. In the fuzzy sets, each object is assigned a single value in the interval [0,1] reflecting its grade of membership. This single value does not allow a separation of evidence for membership and evidence against membership. Gau et al. proposed the notion of vague sets, where each object is characterized by two different membership functions: a true membership function and a false membership function. This kind of reasoning is also called interval membership, as opposed to point membership in the context of fuzzy sets. In this paper, reviews the related works on the decision making by using vague sets in different fields

(α,β,T)-Convex vague sets

By using vague sets we generalize the notion of convex sets and introduce the notion of (α, β ,T )-convex vague sets and study their properties, where T is a triangular norm on [0, 1].

Vague BCK/BCI-algebras

In this note, by using the concept of vague sets, the notion of vague $BCK/BCI$-algebra is introduced. And the notions of $\alpha$-cut and vague-cut are introduced and the relationships between these notions and crisp subalgebras are studied

An Application of Neutrosophic Bipolar Vague On Multi-Criteria Decision Making Problems

In this paper, we studied the concept of neutrosophic bipolar vague set and some of its operations. Also, we propose score, certainty and accuracy functions to compare the neutrosophic bipolar vague sets

Web analytics in the workplace: What Amazon and web newsrooms have in common – and where they differ.

The Politics of Data series continues with an investigation of how data-driven performance measurements operate in the workplace. What can we learn from the case of clicks in online news? Drawing from her ethnographic research shadowing web journalists, Angèle Christin illuminates the ambiguous and rather vague sets of meanings associated with clicks and web metrics that have become so omnipresent in online journalism

A Novel Distance between Vague Sets and Its Applications in Decision Making

A novel distance between vague sets (VSs) is presented after the inadequacies of existing distance measures between vague sets are analyzed by artificial vague sets. The proposed method investigates the assignment of degree of hesitation to the membership and nonmembership degree, and the properties are also discussed. The performances of the new method are illustrated by pattern classification problem. Finally, the proposed method is applied into multicriteria fuzzy decision making, where the linear programming method is taken to generate optimal weights for every criterion and the best alternative is obtained by the weighted sum of distance measures between each alternative and the idea alternative with respect to a set of criteria. The experimental results show the effectiveness of the proposed method

I-Vague Vector Spaces

The notions of I-vague vector spaces of vector spaces with membership and non-membership functions taking values in an involutary dually residuated lattice ordered semigroup are introduced which generalizes the notions with truth values in a Boolean algebra as well as those usual vague sets whose membership and non-membership functions taking values in the unit interval [0, 1]. We discuss some properties of I-vague vector spaces

Uncertain Query Processing using Vague Set or Fuzzy Set: Which One Is Better?

In this paper we attempt to make a theoretical comparison between fuzzy sets and vague sets in processing uncertain queries. We have designed an architecture to process uncertain i.e. fuzzy or vague queries. In the architecture we have presented an algorithm to find the membership value that generates the fuzzy or vague representation of the attributes with respect to the given uncertain query. Next, a similarity measure is used to get each tuples similarity value with the uncertain query for both fuzzy and vague sets. Finally, a decision maker will supply a threshold or α-cut value based on which a corresponding SQL statement is generated for the given uncertain query. This SQL retrieves different result sets from the database for fuzzy or vague data. It has been shown with examples that vague sets give more accurate  result in comparison with fuzzy sets for any uncertain query