{"title":"A Markov Chain-Based Group Consensus Method with Unknown Parameters","authors":"Chao Fu, Wenjun Chang","doi":"10.1007/s10726-024-09876-y","DOIUrl":null,"url":null,"abstract":"<p>Group consensus (GC) is important for generating a group solution satisfactory or acceptable to most decision-makers in a group. Its convergency usually depends on several rounds of iterations and becomes more difficult with unknown parameters because GC is usually associated with parameters. To address the GC with unknown parameters, this paper proposes a Markov chain-based GC method, in which criterion weights and expert weights are considered as parameters. Given the interval-valued assessments of decision-makers, the GC at the alternative and global levels is defined. Based on the Markov chain, a two-hierarchical randomization algorithm is designed with unknown criterion weights to determine the transition probability matrix used to generate the stable GC. To accelerate the stable GC’s convergency, criteria significantly contributing negatives to the stable GC are identified and suggestions on helping renew decision-makers’ assessments on the identified criteria are provided. On the condition that the stable GC is definitely satisfied, a GC-based two-hierarchical randomization algorithm is designed based on the Markov chain to determine the transition probability matrix for generating the stable ranking value distribution of each alternative. The proposed method is employed to analyze a development mode selection problem. It is compared with the stochastic multicriteria acceptability analysis and simple additive weighting methods based on the problem by calculation and principle.</p>","PeriodicalId":47553,"journal":{"name":"Group Decision and Negotiation","volume":null,"pages":null},"PeriodicalIF":3.6000,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Group Decision and Negotiation","FirstCategoryId":"91","ListUrlMain":"https://doi.org/10.1007/s10726-024-09876-y","RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MANAGEMENT","Score":null,"Total":0}
引用次数: 0
Abstract
Group consensus (GC) is important for generating a group solution satisfactory or acceptable to most decision-makers in a group. Its convergency usually depends on several rounds of iterations and becomes more difficult with unknown parameters because GC is usually associated with parameters. To address the GC with unknown parameters, this paper proposes a Markov chain-based GC method, in which criterion weights and expert weights are considered as parameters. Given the interval-valued assessments of decision-makers, the GC at the alternative and global levels is defined. Based on the Markov chain, a two-hierarchical randomization algorithm is designed with unknown criterion weights to determine the transition probability matrix used to generate the stable GC. To accelerate the stable GC’s convergency, criteria significantly contributing negatives to the stable GC are identified and suggestions on helping renew decision-makers’ assessments on the identified criteria are provided. On the condition that the stable GC is definitely satisfied, a GC-based two-hierarchical randomization algorithm is designed based on the Markov chain to determine the transition probability matrix for generating the stable ranking value distribution of each alternative. The proposed method is employed to analyze a development mode selection problem. It is compared with the stochastic multicriteria acceptability analysis and simple additive weighting methods based on the problem by calculation and principle.
期刊介绍:
The idea underlying the journal, Group Decision and Negotiation, emerges from evolving, unifying approaches to group decision and negotiation processes. These processes are complex and self-organizing involving multiplayer, multicriteria, ill-structured, evolving, dynamic problems. Approaches include (1) computer group decision and negotiation support systems (GDNSS), (2) artificial intelligence and management science, (3) applied game theory, experiment and social choice, and (4) cognitive/behavioral sciences in group decision and negotiation. A number of research studies combine two or more of these fields. The journal provides a publication vehicle for theoretical and empirical research, and real-world applications and case studies. In defining the domain of group decision and negotiation, the term `group'' is interpreted to comprise all multiplayer contexts. Thus, organizational decision support systems providing organization-wide support are included. Group decision and negotiation refers to the whole process or flow of activities relevant to group decision and negotiation, not only to the final choice itself, e.g. scanning, communication and information sharing, problem definition (representation) and evolution, alternative generation and social-emotional interaction. Descriptive, normative and design viewpoints are of interest. Thus, Group Decision and Negotiation deals broadly with relation and coordination in group processes. Areas of application include intraorganizational coordination (as in operations management and integrated design, production, finance, marketing and distribution, e.g. as in new products and global coordination), computer supported collaborative work, labor-management negotiations, interorganizational negotiations, (business, government and nonprofits -- e.g. joint ventures), international (intercultural) negotiations, environmental negotiations, etc. The journal also covers developments of software f or group decision and negotiation.