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Power Average Operators of Trapezoidal Cubic Fuzzy Numbers and Application to Multi-attribute Group Decision Making

Authors
  • Fahmi, Aliya1
  • Amin, Fazli1
  • Abdullah, Saleem2
  • Shakeel, Muhammad1
  • 1 Hazara University Mansehra, Pakistan , (Pakistan)
  • 2 Abdul Wali Khan University Mardan, Pakistan , (Pakistan)
Type
Published Article
Journal
Journal of Intelligent Systems
Publisher
De Gruyter
Publication Date
Dec 24, 2019
Volume
29
Issue
1
Pages
1643–1661
Identifiers
DOI: 10.1515/jisys-2018-0122
Source
De Gruyter
Keywords
License
Green

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.

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