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

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 IJFSA.2017010106.m01 is called a vague soft set over U where IJFSA.2017010106.m02 is a mapping given by IJFSA.2017010106.m03 and IJFSA.2017010106.m04 is the power set of vague sets over U. Every set IJFSA.2017010106.m05 for all IJFSA.2017010106.m06, from this family may be considered as the set of e-approximate elements of the vague soft set IJFSA.2017010106.m07. Hence the vague soft set sIJFSA.2017010106.m08 can be viewed as consisting of a collection of approximations of the following form for all IJFSA.2017010106.m09 and for all IJFSA.2017010106.m10:

    IJFSA.2017010106.m11

  • Definition 2.2: (Alhazaymeh & Hassan, 2012). A pair IJFSA.2017010106.m12 is called an interval-valued vague soft set over U, where IJFSA.2017010106.m13 is a mapping given by IJFSA.2017010106.m14, where IJFSA.2017010106.m15 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 IJFSA.2017010106.m16 and IJFSA.2017010106.m17 over a universe U, denoted by IJFSA.2017010106.m18 is an interval-valued vague soft set IJFSA.2017010106.m19, where IJFSA.2017010106.m20 and for all IJFSA.2017010106.m21:

    IJFSA.2017010106.m22

and:

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