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Rough approximation of a fuzzy set in semigroups based on soft relations

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Abstract

Binary relations play an important role in both mathematics and information sciences. In this paper, we focus our discussion on a fuzzy set which is approximated in the sense of the aftersets and foresets. To this end, a soft binary relation has been used. A new approach is being introduced to get two sets of fuzzy soft sets, called the lower approximation and upper approximation regarding the aftersets and foresets. We applied these concepts on semigroups and approximations of fuzzy subsemigroups, fuzzy left (right) ideals, fuzzy interior ideals and fuzzy bi-ideals of semigroups are studied.

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  1. Rani Sumaira Kanwal & Muhammad Shabir

    Present address: Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan

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    1. Rani Sumaira Kanwal
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    2. Muhammad Shabir
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    Correspondence to Rani Sumaira Kanwal.

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    Communicated by Anibal Tavares de Azevedo.

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    Kanwal, R.S., Shabir, M. Rough approximation of a fuzzy set in semigroups based on soft relations. Comp. Appl. Math. 38, 89 (2019). https://doi.org/10.1007/s40314-019-0851-3

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