Abstract
Abstract Trapezoidal cubic fuzzy numbers (TzCFNs) are an extraordinary cubic fuzzy set on a real number set. TzCFNs are useful for dealing with well-known quantities in decision data and decision making problems themselves. This paper is about multi-attribute group decision making problems in which the attribute values are stated with TzCFNs, which are solved by developing a new decision method based on power average operators of TzCFNs. The new operation laws for TzCFNs are given. Hereby, the power average operator of real numbers is extended to four kinds of power average operators of TzCFNs, involving the power average operator of TzCFNs, the weighted power average operator of TzCFNs, the power ordered weighted average operator of TzCFNs, and the power hybrid average operator of TzCFNs. In the proposed group decision method, the individual overall evaluation values of alternatives are generated by using the power average operator of TzCFNs. Applying the hybrid average operator of TzCFNs, the specific general evaluation standards of alternatives are then combined into the collective ones, which are used to rank the alternatives. The example analysis shows the practicality and effectiveness of the proposed method.
Highlights
Fuzzy sets were presented by Zadeh [60] to describe fuzzy problems with the membership function
This paper is about multi-attribute group decision making problems in which the attribute values are stated with Trapezoidal cubic fuzzy numbers (TzCFNs), which are solved by developing a new decision method based on power average operators of TzCFNs
This paper considers the multi-attribute group decision making (MAGDM) problem, in which the attribute values are in the form of TzCFNs, and a new MAGDM method is offered
Summary
Fuzzy sets were presented by Zadeh [60] to describe fuzzy problems with the membership function. Fahmi et al.: Power Average Operators of Trapezoidal Cubic Fuzzy Numbers. A. Fahmi et al.: Power Average Operators of Trapezoidal Cubic Fuzzy Numbers | 1645 weighted geometric Bonferroni mean operator, and some of their properties are investigated. Liu et al [29] extended the Bonferroni mean operator based on the Dombi operations to propose the IF Dombi Bonferroni mean operator, the IF weighted Dombi Bonferroni mean operator, the IF Dombi geometric Bonferroni mean operator, and the IF weighted Dombi geometric Bonferroni mean operator for dealing with the aggregation of IFNs, and proposed some MAGDM methods. Fahmi et al [9] developed the Hamming distance for triangular cubic fuzzy number and weighted averaging operator.
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