Possibility Interval-Valued Vague Soft Expert Sets and Its Similarity Measure

Possibility Interval-Valued Vague Soft Expert Sets and Its Similarity Measure

Ganeshsree Selvachandran (UCSI University, Kuala Lumpur, Malaysia) and Sunil Jacob John (National Institute of Technology Calicut, Calicut, India)
Copyright: © 2017 |Pages: 14
DOI: 10.4018/IJFSA.2017010106
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Abstract

In this paper, the authors aim to extend the notion of interval-valued vague soft sets to establish the concept of possibility interval-valued vague soft expert sets. The set theoretic operations of this concept and other related concepts are introduced. The algebraic properties of this notion such as the laws of commutativity, associativity and De Morgan are established and verified. Lastly, the similarity measure between this set is introduced and illustrated using a hypothetical example related to texture synthesis.
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Preliminaries

In this section, we provide the definitions of some important concepts.

  • Definition 2.1: (Xu et al., 2010). A pair is called a vague soft set over U where is a mapping given by and is the power set of vague sets over U. Every set for all , from this family may be considered as the set of e-approximate elements of the vague soft set . Hence the vague soft set s can be viewed as consisting of a collection of approximations of the following form for all and for all :

  • Definition 2.2: (Alhazaymeh & Hassan, 2012). A pair is called an interval-valued vague soft set over U, where is a mapping given by , where is the power set of interval-valued vague sets on U. In other words, an interval-valued vague soft set over U is a parameterized family of interval-valued vague sets of U.

  • Definition 2.3: (Alhazaymeh & Hassan, 2012). The union (intersection) of two interval-valued vague soft sets and over a universe U, denoted by is an interval-valued vague soft set , where and for all :

and:

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