Dynamic weights allocation according to uncertain evaluation information

ABSTRACT

Weights allocation methods are critical in Multi-Criteria Decision Making. Given numerical importances for each involved criterion, direct normalizing those numerical importances to obtain weights for those criteria is plain, lack of flexibility, and thus cannot well model some more types of subjective preferences of different decision makers like Dominance Strength as defined in this study. We show that concave RIM quantifier Q based OWA weights allocation method can well handle and model such preference. However, in real decision making those numerical importances are very often embodied by uncertain information such as independent random variables with discrete or continuous distributions, statistic information and interval numbers. In any of those circumstances, simple RIM quantifier Q based OWA weights allocation cannot work. Therefore, in this study, we will propose some special dynamic weights allocation methods to gradually allocate weights and accumulate allocated parts to each criterion, and finally, obtain a total weights collection. When the uncertain numerical importances become equivalent to general real numbers, the method automatically degenerates into general RIM quantifier based OWA weights allocation. The innovative weight allocations have discrete and continuous versions: the former can be well programmed while the latter has neat and succinct mathematical expression. The method can also be widely used in many other applications like some economic problems including investment quota allocation for one’s favorite stocks, and the dynamic OWA aggregation for interval numbers.

KEYWORDS:

• Decision making
• Multi-Criteria Decision Making
• OWA operator
• probability distribution
• uncertain information
• weights allocation

Additional information

Funding

This work was supported by the VEGA grant agency under [grant number 1/0420/15]; Science and Technology Assistance Agency under [grant number APVV-14-0013]; National Natural Science Foundation of China (NSFC) under [Project 71701158]; and MOE (Ministry of Education in China) Project of Humanities and Social Sciences under [grant number 17YJC630114].

Notes on contributors

LeSheng Jin

LeSheng Jin is a Lecture in Nanjing Normal University. His research interests are information fusion and fuzzy systems. He has published/coauthored about 30 papers.

Radko Mesiar

Radko Mesiar is a full professor in the Faculty of Civil Engineering, Slovak University of Technology, Bratislava, Slovakia. He has published/coauthored over 300 papers and serves as Area Editor in over 7 journals.

Ronald Yager

Ronald Yager is an IEEE life Fellow, and a full professor in Machine Intelligence Institute, Iona College, New York, USA. He has published/coauthored over 600 papers.

JinDong Qin

JinDong Qin is an associated professor in the School of Management, Wuhan University of Technology, Wuhan, China. He has published/coauthored near 30 papers.