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Open AccessArticle

Evaluation of Investment Policy Based on Multi-Attribute Decision-Making Using Interval Valued T-Spherical Fuzzy Aggregation Operators

1
Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan
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School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Selangor, Malaysia
3
Department of Management and Marketing, Faculty of Economics and Management, Universiti Putra Malaysia, Serdang 43400, Selangor, Malaysia
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(3), 357; https://doi.org/10.3390/sym11030357
Received: 20 January 2019 / Revised: 24 February 2019 / Accepted: 4 March 2019 / Published: 9 March 2019
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)
Expressing the measure of uncertainty, in terms of an interval instead of a crisp number, provides improved results in fuzzy mathematics. Several such concepts are established, including the interval-valued fuzzy set, the interval-valued intuitionistic fuzzy set, and the interval-valued picture fuzzy set. The goal of this article is to enhance the T-spherical fuzzy set (TSFS) by introducing the interval-valued TSFS (IVTSFS), which describes the uncertainty measure in terms of the membership, abstinence, non-membership, and the refusal degree. The novelty of the IVTSFS over the pre-existing fuzzy structures is analyzed. The basic operations are proposed for IVTSFSs and their properties are investigated. Two aggregation operators for IVTSFSs are developed, including weighted averaging and weighted geometric operators, and their validity is examined using the induction method. Several consequences of new operators, along with their comparative studies, are elaborated. A multi-attribute decision-making method in the context of IVTSFSs is developed, followed by a brief numerical example where the selection of the best policy, among a list of investment policies of a multinational company, is to be evaluated. The advantages of using the framework of IVTSFSs are described theoretically and numerically, hence showing the limitations of pre-existing aggregation operators. View Full-Text
Keywords: aggregation operators; interval-valued T-spherical fuzzy set; multi-attribute decision-making; T-spherical fuzzy set aggregation operators; interval-valued T-spherical fuzzy set; multi-attribute decision-making; T-spherical fuzzy set
MDPI and ACS Style

Ullah, K.; Hassan, N.; Mahmood, T.; Jan, N.; Hassan, M. Evaluation of Investment Policy Based on Multi-Attribute Decision-Making Using Interval Valued T-Spherical Fuzzy Aggregation Operators. Symmetry 2019, 11, 357.

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