Next Article in Journal
Optimization of Mass Concrete Construction Using a Twofold Parallel Genetic Algorithm
Previous Article in Journal
Dynamic Relaxation Method for Load Capacity Analysis of Reinforced Concrete Elements
Article Menu
Issue 3 (March) cover image

Export Article

Open AccessArticle

Hesitant Probabilistic Multiplicative Preference Relations in Group Decision Making

1
Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan
2
Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan
3
Faculty of Economics and Management, University of Szczecin, 71-101 Szczecin, Poland
4
Department of Artificial Intelligence Method and Applied Mathematics in the Faculty of Computer Science and Information Technology, West Pomeranian University of Technology, 71-210 Szczecin, Poland
5
Department of Computer Science, School of Engineering, Computer and Mathematical Sciences, Auckland University of Technology, Auckland 1010, New Zealand
*
Author to whom correspondence should be addressed.
Appl. Sci. 2018, 8(3), 398; https://doi.org/10.3390/app8030398
Received: 30 January 2018 / Revised: 28 February 2018 / Accepted: 4 March 2018 / Published: 8 March 2018
  |  
PDF [4318 KB, uploaded 9 March 2018]
  |  

Abstract

The preference of one alternative over another is a useful way to express the opinion of the decision-maker. In the process of group decision-making, preference relations are used in preference modeling of the alternatives under given criteria. The probability is an important tool to deal with uncertainty and, in many scenarios of decision-making problems, the probabilities of different events affect the decision-making process directly. In order to deal with this issue, the hesitant probabilistic multiplicative preference relation (HPMPR) is defined in this paper. Furthermore, consistency of the HPMPR and consensus among decision makers are studied here. In this respect, many algorithms are developed to achieve consistency of HPMPRs, reasonable consensus between decision-makers and a final algorithm is proposed comprehending all other algorithms, presenting a complete decision support model for group decision-making. Lastly, we present a case study with complete illustration of the proposed model and discuss the effects of probabilities on decision-making validating the importance of the introduction of probability in hesitant multiplicative preference relations. View Full-Text
Keywords: decision support system; hesitant fuzzy sets; multi-criteria group decision-making; hesitant multiplicative set; hesitant probabilistic multiplicative set decision support system; hesitant fuzzy sets; multi-criteria group decision-making; hesitant multiplicative set; hesitant probabilistic multiplicative set
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Bashir, Z.; Rashid, T.; Wątróbski, J.; Sałabun, W.; Malik, A. Hesitant Probabilistic Multiplicative Preference Relations in Group Decision Making. Appl. Sci. 2018, 8, 398.

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.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Appl. Sci. EISSN 2076-3417 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top