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Interval-valued probabilistic hesitant fuzzy set for multi-criteria group decision-making.

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Title: Interval-valued probabilistic hesitant fuzzy set for multi-criteria group decision-making.
Authors: Krishankumar, R.1 (AUTHOR), Ravichandran, K. S.1 (AUTHOR), Kar, Samarjit2 (AUTHOR) dr.samarjitkar@gmail.com, Gupta, Pankaj3 (AUTHOR), Mehlawat, Mukesh Kumar3 (AUTHOR)
Source: Soft Computing - A Fusion of Foundations, Methodologies & Applications. Nov2019, Vol. 23 Issue 21, p10853-10879. 27p.
Subjects: Group decision making, Fuzzy sets, Aggregation operators, Probability theory, Geometry
Abstract: As a powerful extension to fuzzy set, hesitant fuzzy set (HFS) attracted many scholars in the recent times. The HFS had the ability to accept multiple membership values for a specific instance, which helped in handling uncertainty to a certain extent. However, the previous studies on the hesitant fuzzy theory consider only single occurring probability value for each element which is problematic for decision-makers (DMs) to associate an accurate occurring probability with each element. To alleviate this issue, in this paper, a new concept called interval-valued probabilistic hesitant fuzzy set (IVPHFS) is proposed. Some desirable properties of IVPHFS are also investigated. Further, a new aggregation operator called simple interval-valued probabilistic hesitant fuzzy weighted geometry (SIVPHFWG) is presented and some interesting properties are discussed. Following this, a new extension of statistical variance (SV) is put forward under IVPHFS for calculating the weights of each criterion. A new extension to the popular VIKOR (VlseKriterijumskaOptimizacijaKompromisnoResenje) method is also presented under IVPHFS for ranking objects. The practicality of the proposed decision framework is analyzed by presenting two illustrative examples, viz., supplier selection problem and smartphone selection problem. Finally, the strength and weakness of the proposed decision framework are realized by comparison with other methods. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
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Abstract:As a powerful extension to fuzzy set, hesitant fuzzy set (HFS) attracted many scholars in the recent times. The HFS had the ability to accept multiple membership values for a specific instance, which helped in handling uncertainty to a certain extent. However, the previous studies on the hesitant fuzzy theory consider only single occurring probability value for each element which is problematic for decision-makers (DMs) to associate an accurate occurring probability with each element. To alleviate this issue, in this paper, a new concept called interval-valued probabilistic hesitant fuzzy set (IVPHFS) is proposed. Some desirable properties of IVPHFS are also investigated. Further, a new aggregation operator called simple interval-valued probabilistic hesitant fuzzy weighted geometry (SIVPHFWG) is presented and some interesting properties are discussed. Following this, a new extension of statistical variance (SV) is put forward under IVPHFS for calculating the weights of each criterion. A new extension to the popular VIKOR (VlseKriterijumskaOptimizacijaKompromisnoResenje) method is also presented under IVPHFS for ranking objects. The practicality of the proposed decision framework is analyzed by presenting two illustrative examples, viz., supplier selection problem and smartphone selection problem. Finally, the strength and weakness of the proposed decision framework are realized by comparison with other methods. [ABSTRACT FROM AUTHOR]
ISSN:14327643
DOI:10.1007/s00500-018-3638-3