Next Article in Journal
A Hybrid Data Hiding Method for Strict AMBTC Format Images with High-Fidelity
Next Article in Special Issue
Type 2 Fuzzy Inference-Based Time Series Model
Previous Article in Journal
Symmetry Breaking in Interacting Ring-Shaped Superflows of Bose–Einstein Condensates
Previous Article in Special Issue
Solving Triangular Intuitionistic Fuzzy Matrix Game by Applying the Accuracy Function Method
Open AccessArticle

Group Decision-Making Based on the VIKOR Method with Trapezoidal Bipolar Fuzzy Information

Department of Mathematics, University of the Punjab, New Campus, Lahore 54590, Pakistan
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80219, Jeddah 21589, Saudi Arabia
BORDA Research Unit and IME, University of Salamanca, 37007 Salamanca, Spain
Author to whom correspondence should be addressed.
Symmetry 2019, 11(10), 1313;
Received: 2 October 2019 / Revised: 14 October 2019 / Accepted: 17 October 2019 / Published: 19 October 2019
The VIKOR methodology stands out as an important multi-criteria decision-making technique. VIKOR stands for “VIekriterijumsko KOmpromisno Rangiranje”, a Serbian term for “multi-criteria optimization and compromise solution”. It has been adapted to sources of information with sundry formats. We contribute to that strand on literature with a design of a new multiple-attribute group decision-making method called the trapezoidal bipolar fuzzy VIKOR method. It consists of a suitable redesign of the VIKOR approach so that it can use information with bipolar configurations. Bipolar fuzzy sets (and numbers) establish a symmetrical trade-off between two judgmental constituents of human thinking. The agents acquire uncertain and vague information in the form of linguistic variables parameterized by trapezoidal bipolar fuzzy numbers. Trapezoidal bipolar fuzzy numbers are considered by decision-makers for assigning the preference information of alternatives with respect to different attributes. Our non-trivial adaptation necessitates several steps. The ranking function of bipolar fuzzy numbers is employed to make a simple decision matrix with real numbers as its entries. Shannon’s entropy concept is applied to evaluate the normalized weights for attributes that may be either partially or completely unknown to the decision-makers. The ordering of the alternatives is obtained by assorting the maximum group utility and the individual regret of the opponent in an ascending manner. For illustration, the proposed technique is applied to two group decision-making problems, namely, the selection of waste treatment methods and the site to plant a thermal power station. A comparison of this method with the trapezoidal bipolar fuzzy TOPSIS method is also presented. View Full-Text
Keywords: trapezoidal bipolar fuzzy numbers; VIKOR; TOPSIS; entropy measure trapezoidal bipolar fuzzy numbers; VIKOR; TOPSIS; entropy measure
Show Figures

Figure 1

MDPI and ACS Style

Shumaiza; Akram, M.; Al-Kenani, A.N.; Alcantud, J.C.R. Group Decision-Making Based on the VIKOR Method with Trapezoidal Bipolar Fuzzy Information. Symmetry 2019, 11, 1313.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

Back to TopTop