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Spherical fuzzy power partitioned Maclaurin Symmetric Mean Operators and their application in Multiple Attribute Group Decision Making

Zhang Huiyuan, Cai Qiang, Wei Guiwu

Archives of Control Sciences

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2023

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Vol. 33, No. 1

179--238

EN

Spherical fuzzy sets (SFSs) provide more free space for decision makers (DMs) to express preference information from four aspects: approval, objection, abstention and refusal. The partitioned Maclaurin symmetric mean (PMSM) operator is an effective information fusion tool, which can fully capture the interrelationships among any multiple attributes in the same block whereas attributes in different block are unrelated. Therefore, in this paper, we first extend PMSM operator to spherical fuzzy environment and develop spherical fuzzy PMSM (SFPMSM) operator as well as spherical fuzzy weighted PMSM (SFWPMSM) operator. Meanwhile, we discuss some properties and special cases of these two operators. To diminish the impact of extreme evaluation values on decision-making results, then we integrate power average (PA) operator and PMSM operator to further develop spherical fuzzy power PMSM (SFPPMSM) operator and spherical fuzzy weighted power PMSM (SFWPPMSM) operator and also investigate their desirable properties. Subsequently, a new multiple attribute group decision making (MAGDM) method is established based on SFWPPMSM operator under spherical fuzzy environment. Finally, two numerical examples are used to illustrate the proposed method, and comparative analysis with the existing methods to further testy the validity and superiority of the proposed method.

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Group decision making using interval-valued intuitionistic fuzzy soft matrix and confident weight of experts

Das S., Kar S., Pal T.

Journal of Artificial Intelligence and Soft Computing Research

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2014

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Vol. 4, No. 1

57--77

EN

This article proposes an algorithmic approach for multiple attribute group decision making (MAGDM) problems using interval-valued intuitionistic fuzzy soft matrix (IVIFSM) and confident weight of experts. We propose a novel concept for assigning confident weights to the experts based on cardinals of interval-valued intuitionistic fuzzy soft sets (IVIFSSs). The confident weight is assigned to each of the experts based on their preferred attributes and opinions, which reduces the chances of biasness. Instead of using medical knowledgebase, the proposed algorithm mainly relies on the set of attributes preferred by the group of experts. To make the set of preferred attributes more important, we use combined choice matrix, which is combined with the individual IVIFSM to produce the corresponding product IVIFSM. This article uses IVIFSMs for representing the experts’ opinions. IVIFSM is the matrix representation of IVIFSS and IVIFSS is a natural combination of interval-valued intuitionistic fuzzy set (IVIFS) and soft set. Finally, the performance of the proposed algorithm is validated using a case study from real life.

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A multiple attribute group decision making method based on generalized interwal-valued trapezoidal fuzzy numbers

Liu P., Wang Y.

Control and Cybernetics

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2011

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Vol. 40, no 1

163-184

EN

A ranking approach based on grey correlative coefficient is presented to solve the multiple attribute decision making problems in which the attribute values and the weights take the form of the generalized interval-valued trapezoidal fuzzy number (GIYTFN). Firstly, the concept and the calculation rules of GIYTFN are introduced, the distance of GIYTFN is proposed. Secondly, the method of linguistic terms transformed into GIYTFN and the normalization method of GIYTFN is illustrated, and a grey relational decision making method based on the GIYTFN is presented in detail. The alternatives are ranked based on the grey correlative coefficient. Finally, an illustrative example is given to show the effectiveness of this method and the decision making steps.