scholarly journals Practical Algorithms for Multi-Stage Voting Rules with Parallel Universes Tiebreaking

2019 ◽  
Vol 33 ◽  
pp. 2189-2196 ◽  
Author(s):  
Jun Wang ◽  
Sujoy Sikdar ◽  
Tyler Shepherd ◽  
Zhibing Zhao ◽  
Chunheng Jiang ◽  
...  
Keyword(s):  
Machine Learning ◽  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Search Algorithms ◽  
Voting Rules ◽  
Practical Algorithms ◽  
Multi Stage ◽  
Parallel Universes ◽  
Np Complete

STV and ranked pairs (RP) are two well-studied voting rules for group decision-making. They proceed in multiple rounds, and are affected by how ties are broken in each round. However, the literature is surprisingly vague about how ties should be broken. We propose the first algorithms for computing the set of alternatives that are winners under some tiebreaking mechanism under STV and RP, which is also known as parallel-universes tiebreaking (PUT). Unfortunately, PUT-winners are NP-complete to compute under STV and RP, and standard search algorithms from AI do not apply. We propose multiple DFS-based algorithms along with pruning strategies, heuristics, sampling and machine learning to prioritize search direction to significantly improve the performance. We also propose novel ILP formulations for PUT-winners under STV and RP, respectively. Experiments on synthetic and realworld data show that our algorithms are overall faster than ILP.

APPROACHES TO MULTI-STAGE MULTI-ATTRIBUTE GROUP DECISION MAKING

2011 ◽  
Vol 10 (01) ◽  
pp. 121-146 ◽  
Author(s):  
ZESHUI XU
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Investment Decision ◽  
Weight Vector ◽  
Interval Uncertainty ◽  
Weighted Averaging ◽  
Multi Stage ◽  
Investment Decision Making ◽  
Magdm Problems

Multi-stage multi-attribute group decision making (MS-MAGDM) as a familiar decision activity that usually occurs in our daily life, such as multi-stage investment decision making, medical diagnosis, personnel dynamic examination, military system efficiency dynamic evaluation, etc. The aim of this paper is to investigate MS-MAGDM problems in which both the weight information on a collection of predefined attributes and the decision information on a finite set of alternatives with respect to the attributes are collected at different stages. We first propose a Poisson distribution based method to determine the weight vector associated with a time-weighted averaging (TWA) operator. Furthermore, we use a hybrid weighted aggregation (HWA) operator to fuse all individual decision information into group opinions at different stages, and then utilize the TWA operator to aggregate the derived group opinions at different stages into the complex group ones so as to rank the given alternatives. After that, we further investigate MS-MAGDM problems where all decision information at different stages cannot be given in exact numerical values, but value ranges can be obtained. An approach based on the uncertain time-weighted averaging (UTWA) operator and the uncertain hybrid weighted aggregation (UHWA) operator is developed for solving MS-MAGDM problems under interval uncertainty. Finally, a practical example is provided to illustrate the developed approaches.

A multi-stage group decision making for strategic supplier selection based on prospect theory with interval-valued q-rung orthopair fuzzy linguistic sets

2021 ◽  
pp. 1-17
Author(s):  
Shunsheng Guo ◽  
Yuji Gao ◽  
Jun Guo ◽  
Zhijie Yang ◽  
Baigang Du ◽  
...  
Keyword(s):  
Decision Making ◽  
Prospect Theory ◽  
Group Decision Making ◽  
Supplier Selection ◽  
Group Decision ◽  
Weighted Averaging ◽  
Multi Stage ◽  
Fuzzy Linguistic ◽  
Interval Valued

With the aggravation of market competition, strategic supplier is becoming more and more critical for the success of manufacturing enterprises. Suppler selection, being the critical and foremost activity must ensure that selected suppliers are capable of supporting the long-term development of organizations. Hence, strategic supplier selection must be restructures considering the long-term relationships and prospects for sustainable cooperation. This paper proposes a novel multi-stage multi-attribute group decision making method under an interval-valued q-rung orthopair fuzzy linguistic set (IVq-ROFLS) environment considering the decision makers’ (DMs) psychological state in the group decision-making process. First, the initial comprehensive fuzzy evaluations of DMs are represented as IVq-ROFLS. Subsequently, two new operators are proposed for aggregating different stages and DMs’ preferences respectively by extending generalized weighted averaging (GWA) to IVq-ROFLS context. Later, a new hamming distance based linear programming method based on entropy measure and score function is introduced to evaluate the unknown criteria weights. Additionally, the Euclidean distance is employed to compute the gain and loss matrix, and objects are prioritized by extending the popular Prospect theory (PT) method to the IVq-ROFLS context. Finally, the practical use of the proposed decision framework is validated by using a strategic supplier selection problem, as well as the effectiveness and applicability of the framework are discussed by using comparative analysis with other methods.

scholarly journals Favoring Consensus and Penalizing Disagreement in Group Decision Making

2008 ◽  
Vol 12 (5) ◽  
pp. 416-421 ◽  
Author(s):  
José Luis García-Lapresta ◽  
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operator ◽  
Weak Order ◽  
Decision Makers ◽  
Multi Stage ◽  
Linguistic Categories

In this paper we introduce a multi-stage decision making procedure where decision makers' opinions are weighted by their contribution to the agreement after they sort alternatives into a fixed finite scale given by linguistic categories, each one having an associated numerical score. We add scores obtained for each alternative using an aggregation operator. Based on distances among vectors of individual and collective scores, we assign an index to decision makers showing their contributions to the agreement. Opinions of negative contributors are excluded and the process is reinitiated until all decision makers contribute positively to the agreement. To obtain the final collective weak order on the set of alternatives, we weigh the scores that decision makers assign to alternatives by indices corresponding to their contribution to the agreement.

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