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Trapezoidal interval type-2 fuzzy soft stochastic set and its application in stochastic multi-criteria decision-making

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Abstract

Trapezoidal interval type-2 fuzzy soft set (TrIT2FSS) (Zhang and Zhang, Appl Math Model 37:4948–4971, 2013) is a delicious generalization of soft set theory where the performance of the alternatives over some parameters is assigned by means of trapezoidal interval type-2 fuzzy numbers (TrIT2FNs). Zhang and Zhang (2013) proposed an approach to multi-criteria group decision-making (MCGDM) problems under trapezoidal interval type-2 fuzzy soft set. However, due to the increasing complexity of decision-making problems, the performance of the alternatives may be determined randomly with respect to some possible states related to the decision-making problems which are known as stochastic multi-criteria decision-making (SMCDM) problems. To handle such type of SMCDM problems based on trapezoidal interval type-2 fuzzy soft set, no research exists till now. To fill up this lacuna, here we have formulated a new generalization of TrIT2FSS to solve the MCDM problems under stochastic environment. First, we have introduced the notion of trapezoidal interval type-2 fuzzy soft stochastic set (TrIT2FSSS). Second, we deal with the obligatory definition of expected trapezoidal interval type-2 fuzzy soft set (ETrIT2FSS). Finally, we have proposed a methodology for handling the trapezoidal interval type-2 fuzzy soft stochastic set (TrIT2FSSS) based stochastic MCDM problems. Additionally, in this model we have assumed that the weights of each of the parameters are partially known. We have proposed a process to obtain the weights of the parameters using signed distance measurement. An application of our proposed approach regarding the selection of the best company for investment of a bank has also been given to describe the feasibility and effectiveness of our proposed approach.

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Acknowledgements

The authors are very thankful to the editors and anonymous reviewers for providing very thoughtful comments which have lead to an improved version of this paper. This work is supported by the Department of Science and Technology(DST), New Delhi, India, through the letter No.DST/INSPIRE/03/2014/003326.

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Authors and Affiliations

  1. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, WB, 721102, India

    Soumi Manna & Shyamal Kumar Mondal

  2. Department of Pure & Applied Science, Midnapore City College, Kuturia, Bhadutala, Paschim Medinipur, WB, 721129, India

    Tanushree Mitra Basu

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  1. Soumi Manna
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  2. Tanushree Mitra Basu
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  3. Shyamal Kumar Mondal
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Correspondence to Soumi Manna.

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Manna, S., Basu, T.M. & Mondal, S.K. Trapezoidal interval type-2 fuzzy soft stochastic set and its application in stochastic multi-criteria decision-making. Granul. Comput. 4, 585–599 (2019). https://doi.org/10.1007/s41066-018-0119-0

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