{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T14:06:02Z","timestamp":1760709962956,"version":"3.41.2"},"reference-count":40,"publisher":"Emerald","issue":"9","license":[{"start":{"date-parts":[[2019,10,7]],"date-time":"2019-10-07T00:00:00Z","timestamp":1570406400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["K"],"published-print":{"date-parts":[[2019,10,7]]},"abstract":"<jats:sec><jats:title content-type=\"abstract-subheading\">Purpose<\/jats:title><jats:p>With respect to multiple attribute group decision-making (MAGDM) in which the assessment values of alternatives are denoted by normal discrete fuzzy variables (NDFVs) and the weight information of attributes is incompletely known, this paper aims to develop a novel fuzzy stochastic MAGDM method based on credibility theory and fuzzy stochastic dominance, and then applies the proposed method for selecting the most desirable investment alternative under uncertain environment.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Design\/methodology\/approach<\/jats:title><jats:p>First, by aggregating the membership degrees of an alternative to a scale provided by all decision-makers into a triangular fuzzy number, the credibility degree and expect the value of a triangular fuzzy number are calculated to construct the group fuzzy stochastic decision matrix. Second, based on determining the credibility distribution functions of NDFVs, the fuzzy stochastic dominance relations between alternatives on each attribute are obtained and the fuzzy stochastic dominance degree matrices are constructed by calculating the dominance degrees that one alternative dominates another on each attribute. Subsequently, calculating the overall fuzzy stochastic dominance degrees of an alternative on each attribute, a single objective non-linear optimization model is established to determine the weights of attributes by maximizing the relative closeness coefficients of all alternatives to positive ideal solution. If the information about attribute weights is completely unknown, the idea of maximizing deviation is used to determine the weights of attributes. Finally, the ranking order of alternatives is determined according to the descending order of corresponding relative closeness coefficients and the best alternative is determined.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Findings<\/jats:title><jats:p>This paper proposes a novel fuzzy stochastic MAGDM method based on credibility theory and fuzzy stochastic dominance, and a case study of investment alternative selection problem is provided to illustrate the applicability and sensitivity of the proposed method and its effectiveness is demonstrated by comparison analysis with the proposed method with the existing fuzzy stochastic MAGDM method. The result shows that the proposed method is useful to solve the MAGDM problems in which the assessment values of alternatives are denoted by NDFVs and the weight information of attributes is incompletely known.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Originality\/value<\/jats:title><jats:p>The contributions of this paper are that to describe the dominance relations between fuzzy variables reasonably and quantitatively, the fuzzy stochastic dominance relations between any two fuzzy variables are redefined and the concept of fuzzy stochastic dominance degree is proposed to measure the dominance degree that one fuzzy variable dominate another; Based on credibility theory and fuzzy stochastic dominance, a novel fuzzy stochastic MAGDM method is proposed to solve MAGDM problems in which the assessment values of alternatives are denoted by NDFVs and the weight information of attributes is incompletely known. The proposed method has a clear logic, which not only can enrich and develop the theories and methods of MAGDM but also provides decision-makers a novel method for solving fuzzy stochastic MAGDM problems.<\/jats:p><\/jats:sec>","DOI":"10.1108\/k-08-2018-0438","type":"journal-article","created":{"date-parts":[[2019,7,8]],"date-time":"2019-07-08T08:53:03Z","timestamp":1562575983000},"page":"2030-2064","source":"Crossref","is-referenced-by-count":6,"title":["A novel fuzzy stochastic MAGDM method based on credibility theory and fuzzy stochastic dominance with incomplete weight information"],"prefix":"10.1108","volume":"48","author":[{"given":"Xiaoyue","family":"Liu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaolu","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Li","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qinghua","family":"Zeng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"140","reference":[{"issue":"11","key":"key2019092314475994800_ref001","doi-asserted-by":"crossref","first-page":"3037","DOI":"10.1007\/s00500-015-1989-6","article-title":"Soft consensus measures in group decision making using unbalanced fuzzy linguistic information","volume":"21","year":"2017","journal-title":"Soft Computing"},{"issue":"4","key":"key2019092314475994800_ref002","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1007\/s13042-016-0589-9","article-title":"An approach to interval-valued intuitionistic stochastic multi-criteria decision-making using set pair analysis","volume":"9","year":"2018","journal-title":"International Journal of Machine Learning and Cybernetics"},{"volume-title":"Fuzzy Sets and Systems: Theory and Applications","year":"1980","key":"key2019092314475994800_ref003"},{"issue":"3","key":"key2019092314475994800_ref004","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/0020-0255(83)90025-7","article-title":"Ranking fuzzy numbers in the setting of possibility theory","volume":"30","year":"1983","journal-title":"Information Sciences"},{"issue":"3","key":"key2019092314475994800_ref005","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1016\/0165-0114(87)90028-5","article-title":"The mean value of a fuzzy number","volume":"24","year":"1987","journal-title":"Fuzzy Sets and Systems"},{"volume-title":"Possibility Theory","year":"1988","key":"key2019092314475994800_ref006"},{"issue":"1","key":"key2019092314475994800_ref007","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/0165-0114(92)90062-9","article-title":"The expect value of a fuzzy number","volume":"47","year":"1992","journal-title":"Fuzzy Sets and Systems"},{"issue":"1","key":"key2019092314475994800_ref008","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/j.ejor.2015.06.047","article-title":"Interval-valued intuitionistic hesitant fuzzy choquet integral based TOPSIS method for multi-criteria group decision making","volume":"248","year":"2016","journal-title":"European Journal of Operational Research"},{"volume-title":"Introduction to Theory of Fuzzy Subsets","year":"1975","key":"key2019092314475994800_ref009"},{"issue":"3","key":"key2019092314475994800_ref010","doi-asserted-by":"crossref","first-page":"498","DOI":"10.1016\/S0377-2217(98)00040-X","article-title":"Interactive group decision making procedure under incomplete information","volume":"116","year":"1999","journal-title":"European Journal of Operational Research"},{"issue":"10","key":"key2019092314475994800_ref011","doi-asserted-by":"crossref","first-page":"887","DOI":"10.1016\/0898-1221(88)90124-1","article-title":"Comparison of fuzzy numbers based on the probability measure of fuzzy events","volume":"15","year":"1988","journal-title":"Computer and Mathematics with Applications"},{"issue":"3","key":"key2019092314475994800_ref012","first-page":"197","article-title":"On distance of fuzzy variables","volume":"19","year":"2008","journal-title":"Journal of Intelligent and Fuzzy Systems"},{"key":"key2019092314475994800_ref013","unstructured":"Li, X. and Liu, B.D. (2006), \u201cMaximum variance theorems for various types of uncertain variable\u201d, Technical Report."},{"issue":"3","key":"key2019092314475994800_ref014","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/0165-0114(92)90223-Q","article-title":"Ranking fuzzy numbers with integral value","volume":"50","year":"1992","journal-title":"Fuzzy Sets and Systems"},{"volume-title":"Uncertainty Theory: An Introduction to Its Axiomatic Foundations","year":"2004","key":"key2019092314475994800_ref015"},{"key":"key2019092314475994800_ref016","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/j.eswa.2016.01.059","article-title":"Decision making for the selection of cloud vendor: an improved approach under group decision-making with integrated weights and objective\/subjective attributes","volume":"55","year":"2016","journal-title":"Expert Systems with 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