{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,7]],"date-time":"2026-01-07T05:41:09Z","timestamp":1767764469650,"version":"3.48.0"},"reference-count":37,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T00:00:00Z","timestamp":1767139200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, the Multistage Bipolar method is developed. The paper presents a synthesis of three streams related to multiple criteria decision-making: the reference point-based approach, the interactive approach and multistage decision processes. A significant problem, the solution of which is a prerequisite for the application of the Multistage Bipolar method, is the determination of the sets of reference objects for subsequent stages. This paper addresses the question of how to utilize an interactive multi-criteria approach to select subsets of \u2018good\u2019 and \u2018bad\u2019 objects for each stage of the considered process, which the decision-maker will accept as sets of reference objects. Its objective is to propose an interactive procedure for generating these sets. The approach proposed in this paper is illustrated by the utilization of stage sets of reference points, generated via the proposed interactive procedure, within a mathematical model for resource allocation in a multistage regional development planning problem. The problem addressed constitutes a mathematical economics model, while simultaneously demonstrating that multi-criteria methods are widely applicable in management. Of fundamental importance here is the expenditure of public funds in a manner that yields maximum benefits for citizens.<\/jats:p>","DOI":"10.3390\/e28010054","type":"journal-article","created":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T16:34:23Z","timestamp":1767198863000},"page":"54","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Interactive Selection of Reference Sets in Multistage Bipolar Method"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8561-3863","authenticated-orcid":false,"given":"Maciej","family":"Nowak","sequence":"first","affiliation":[{"name":"Department of Operations Research, University of Economics in Katowice, 40-287 Katowice, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5581-0922","authenticated-orcid":false,"given":"Tadeusz","family":"Trzaskalik","sequence":"additional","affiliation":[{"name":"Department of Operations Research, University of Economics in Katowice, 40-287 Katowice, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,12,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"936","DOI":"10.1287\/mnsc.19.8.936","article-title":"A Class of Solutions for Group Decision Problems","volume":"19","author":"Yu","year":"1973","journal-title":"Manag. 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