4.7 Article

Power geometric operators of trapezoidal intuitionistic fuzzy numbers and application to multi-attribute group decision making

Journal

APPLIED SOFT COMPUTING
Volume 29, Issue -, Pages 153-168

Publisher

ELSEVIER SCIENCE BV
DOI: 10.1016/j.asoc.2014.12.031

Keywords

Multi-attribute group decision making; Trapezoidal intuitionistic fuzzy number; Weighted possibility mean; Power geometric operator

Funding

  1. National Natural Science Foundation of China [71061006, 11461030, 61263018]
  2. Humanities Social Science Programming Project of Ministry of Education of China [09YGC630107]
  3. Natural Science Foundation of Jiangxi Province of China [20114BAB201012, 20142BAB201011]
  4. Twelve five Programming Project of Jiangxi Province Social Science [13GL17]
  5. Excellent Young Academic Talent Support Program of Jiangxi University of Finance and Economics

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As a special intuitionistic fuzzy set on a real number set, trapezoidal intuitionistic fuzzy numbers (TrIFNs) have the better capability to model ill-known quantities. The purpose of this paper is to develop some power geometric operators of TrIFNs and apply to multi-attribute group decision making (MAGDM) with TrIFNs. First, the lower and upper weighted possibility means of TrIFNs are introduced as well as weighted possibility means. Hereby, a new lexicographic method is developed to rank TrIFNs. The Minkowski distance between TrIFNs is defined. Then, four kinds of power geometric operators of TrIFNs are investigated including the power geometric operator of TrIFNs, power weighted geometric operator of TrIFNs, power ordered weighted geometric operator of TrIFNs and power hybrid geometric operator of TrIFNs. Their desirable properties are discussed. Four methods for MAGDM with TrIFNs are respectively proposed for the four cases whether the weight vectors of attributes and DMs are known or unknown. In these methods, the individual overall attribute values of alternatives are generated by using the power geometric or power weighted geometric operator of TrIFNs. The collective overall attribute values of alternatives are determined through constructing the multi-objective optimization model, which is transformed into the goal programming model to solve. Thus, the ranking order of alternatives is obtained according to the collective overall attribute values of alternatives. Finally, the green supplier selection problem is illustrated to demonstrate the application and validation of the proposed method. (C) 2015 Elsevier B.V. All rights reserved.

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