یک الگوریتم جدید در تصمیم‌گیری گروهی فازی بر مبنای توافق گروهی؛ مطالعه کاربردی: مدیریت منابع آبهای زیرزمینی

نوع مقاله : مقاله پژوهشی

نویسندگان

1 کارشناس ارشد/ دانشکده عمران، دانشگاه علم و صنعت

2 استاد/ دانشکده عمران، دانشگاه علم و صنعت.

چکیده

تصمیم‌گیری یک امر ضروری در بسیاری از زمینه‌ها از جمله: مالی، مهندسی، پزشکی و ... است. تصمیم‌گیری چند معیاره و تصمیم‌گیری گروهی دو روش قوی و پرکاربرد برای حل مسائل تصمیم‌گیری و انتخاب بهترین گزینه از بین گزینه‌های موجود است. تصمیم‌گیری گروهی نظر شرکت‌کننده‌های مختلف را اخذ و این نظرات را برای رسیدن به یک اجماع گروهی مناسب با یکدیگر تجمیع می‌کند.
در این مقاله ضمن بررسی تصمیم‌گیری گروهی فازی، یک الگوریتم جدید جهت تصمیم‌گیری گروهی فازی بر مبنای توافق گروهی ارائه می‌گردد. با استفاده از این الگوریتم تصمیم‌گیران قادرند نظرات و ارزیابی‌های خود از گزینه‌ها و همچنین اهمیت شاخص‌ها را به چهار صورت مختلف: 1- رتبه‌بندی گزینه‌ها 2- رابطه اولویت فازی 3- رابطه اولویت چندگانه 4- تابع مطلوبیت ارائه نمایند. در این الگوریتم، نظرات مختلف شرکت‌کنندگان پس از همگن‌سازی، با استفاده از یک عملگر تجمیعی  با یکدیگر تجمیع شده و پس از برآورد میزان توافق گروهی، گزینه برتر انتخاب می‌گردد. علاوه براین، تصمیم‌گیران قادرند نظرات و ارزیابی‌های خود از گزینه‌ها و اهمیت شاخص‌ها را در هر مرحله تا رسیدن به توافق گروهی مناسب، مورد بازنگری و اصلاح قرار داده و تصمیم نهایی را بر اساس توافق گروهی بین کلیه اعضاء انتخاب نمایند. کارائی این الگوریتم در مدیریت و برنامه‌ریزی منابع آب، با استفاده از یک مطالعه کاربردی در انتخاب بهترین گزینه از بین 13 گزینه، برای تأمین آب یک منطقه با استفاده از منابع آبهای زیرزمینی مورد بررسی قرار گرفته است. کاربرد الگوریتم مزبور در اولویت بندی 13 گزینه استحصال منابع آب زیرزمینی نشان داد که با تعامل بین تصمیم‌گیران و بازنگری تصمیم‌گیران با کمترین درجه توافق، می‌توان به یک تصمیم جمعی با درجه توافق معقول و از پیش تعیین شده دست یافت.

کلیدواژه‌ها


عنوان مقاله [English]

A New Consensus-based Fuzzy Group Decision-Making Algorithm Case Study: Groundwater Resource Management

نویسندگان [English]

  • H Mianabadi 1
  • A Afshar 2
1 Dept. of Civil Engineering, Iran Univ. of Science and Technology
2 Professor, Dept. of Civil Engineering, Iran Univ. of Science and Technology
چکیده [English]

Decision-making is an essential process in many financial, engineering, and medical fields. Multi Criteria Decision Making (MCDM) and Group Decision-Making (GDM) are among well practiced approaches in solving decision making problems. Group Decision-Making basically combines professional judgments into a coherent group decision.
This paper surveys Fuzzy Group Decision Making (FGDM) and develops a newconsensus-based fuzzy group decision making algorithm. Decision Makers (DMs) may express their opinions about alternatives and importance of each criterion in four different formats as follow: (1) preference ordering, (2) utility values, (3) fuzzy preference relations; and (4) multiplicative preference relations. In this proposed algorithm, unifying the evaluations of each expert, results in an aggregated score for each alternative. The third step is to rank the linguistic labels or fuzzy sets and select the preferred alternatives based on this sorting. Finally, the decision manager assesses the consensus level and the individual contribution to the group decision and selects the final solution. To illustrate the application of the model in the real decision making processes, this algorithm is used to a groundwater development project to select the most preference alternative for a regional water supply system. Results indicate that the proposed Fuzzy Group Decision Making approach is a relevant approach to aggregate the individual expert’s opinion in order to reach a reasonable and determinate consensus level among DMs .

کلیدواژه‌ها [English]

  • Fuzzy Group Decision Making
  • consensus
  • Groundwater resource management
  • OWA aggregation operator
Abrishamchi, A., Ebrahimian. A., Tajrishi, M., Marino. M.A., (2005), “Case Study: Application of Multicriteria Decision Making to Urban Water Supply”. Journal of Water Resources planning and Management, v 131, n 4, pp. 326–335.
Ben-Arieh D. and Chen Z., (2004), “A new linguistic labels aggregation and Consensus in group decision making“, Conference of IERC, Houston, Texas, USA.
Bodily, S.E., (1985), “Modern decision making: a guide to modeling with decision support systems”. McGraw-Hill Book Company, New York.
Bordogna G., Fedrizzi M., Pasi G., (1997), “Linguistic modeling of consensus in group decision making based on OWA operators”, IEEE Transactions on Systems, Man, and Cybernetics Part A: Systems and Humans, v 27, n 1, pp. 126–133.
Bryson, N., (1996), “Group decision-making and the analytic hierarchy process: exploring the consensus-relevant information content”, Computers & Operations Research, v 23, pp. 27– 35.
Bullen, P.S., Mitrinovic, D.S., Vasic, P. M., (1988), “Means and their inequalities”, Mathematics and its Applications, 31, D. Reidel Publishing Co., Dordrecht.
Carlsson, C., R.Full´er and S.Full´er, (1997), “OWA operators for doctoral student selection problem”, in: R.R.Yager and J.Kacprzyk eds., The ordered weighted averaging operators: Theory, Methodology, and Applications, Kluwer Academic Publishers, Boston, pp. 197-178.
Chang P.-T. Lee E. S., (1994), “Ranking of fuzzy sets based on the concept of existence”, Computers Mathematics Application, v 27, n 9/10, pp. 1-21.
Chen S-J., Hwang C-L, (1989), “Fuzzy multiple attribute decision making”, Springer-Verlag.
Chen, Z., (2005), “Consensus in group decision making under linguistic assessments”, PhD Thesis, Department of Industrial and Manufacturing Systems Engineering, College of Engineering Kansas State University, Manhattan.
Cheng C-H., (1999), “A simple fuzzy group decision making method”, IEEE International Conference on Fuzzy Systems, v 2, pp. 910-915.
Chiclana F., Herrera F., Herrera-Viedma E., (1998), “Integrating three representation, models in fuzzy multipurpose decision making based on fuzzy preference relations”, Fuzzy Sets and Systems, v 97, pp. 277-291.
Chiclana F., Herrera F., Herrera-Viedma E., (2001), “Integrating Multiplicative Preference Relations in a Multipurpose Decision-making Model Based on Fuzzy Preference Relations”, Fuzzy Sets and Systems, v122, pp. 277-291.
Choudhurya, A.K., Shankarb, R., Tiwari, M.K., (2005), “Consensus-based intelligent group decision-making model for the selection of advanced technology.” J. Decision Support Systems, Article In Press.
Das, A.B., (2001), “Application of optimization techniques in groundwater quality management”, Sad hana, v 26, n 4, pp. 293-316.
Dubois, D., Fargier, H., Prade, H., (1996), “Refinements of the maximin approach to decision-making in a fuzzy environment”, Fuzzy Sets and Systems, v 81, n 1, pp. 103-122.
Duckstein, L., Treichel, W., El Magnouni, S., (1994), “Ranking ground-water management alternatives by multicriterion analysis.”J.Water Resource Planning and Management, v 120, n 4, pp. 546–565.
El Magnouni, S., Treichel, W., (1992), “A multi-criteria approach to ground water resources assessment.” BRGM Tech. Note No. 48 EAUHN92. Burean de Recherché Geologique et Miniere (BRGM), Orleans, France.
Fedrizzi M., Pereira R. A. M., Zorat A., (1995), ‘Dynamical model for reaching consensus in group decision making”, Proceedings of the ACM Symposium on Applied Computing, pp. 493-496.
Herrera F., Herrera-Viedma E., Verdegay J. L., (1996a), “Model of consensus in group decision making under linguistic assessments”, Fuzzy Sets and Systems, v 78, n 1, 73 p.
Herrera F., Herrera-Viedma E., Verdegay J. L., (1996b), “Direct approach processes in group decision making using linguistic OWA operators”, Fuzzy Sets and Systems, v 79, n 2, pp. 175-190.
Herrera-Viedma E., Herrera F., Chiclana F., (2002), “A consensus model for multiperson decision making with different preference structures”, Systems, Man
 
      and Cybernetics, Part A, IEEE Transactions on, v 32, n 3, pp. 394 -402.
Hwang C-L., Lin M-J., (1987), “Group decision making under multiple criteria: methods and applications”. Berlin, New York: Springer-Verlag.
Jiang H, Eastman JR., (2000), “Application of fuzzy measures in multi-criteria evaluation in GIS”. International journal Geography Information Systems. v 14, n 2, pp. 173–184.
Kacprzyk J., Fedrizzi M., Nurmi H., (1992), “Group decision making and consensus under fuzzy preferences and fuzzy majority”, Fuzzy Sets and Systems, v 49, pp. 21-31.
Kickert WJM., (1978), “Fuzzy theories of decision-making”. Martin us Nijhoff, Lei den.
Lee E. S., Li R. -J., (1988), ‘Comparison of fuzzy numbers based on the probability measure of fuzzy events”, Computers & Mathematics with Applications, v 15, n 10, pp. 87-896.
Lee-Kwang H., Lee J., (1999), “Method for ranking fuzzy numbers and its application to decision-making”,IEEE Transactions on Fuzzy Systems, v 7, n 6, pp. 677-685.
Malczewski, J., Rinner, (2005), “Exploring multicriteria decision strategies in GIS with linguistic quantifiers: A case study of residential quality evaluation”. J.Geograph System, v 7, pp. 249-268.
Mellers. B, Chang. S., (1994), “Representations of risk judgments”. Organ Behav Hum Dec .v 52, n 7, pp. 167–184.
Munda, G., (1995), “Multicriteria evaluation in a fuzzy environment: theory and applications in ecological economics”. Physica-Verlag, Heidelberg.
Ng K.-C, Abramson B, (1992), “Consensus diagnosis: a simulation study”, Systems, Man and Cybernetics, IEEE Transactions on, v 22, n 5, pp. 916 – 928.
Pohekar, S.D., Ramachandran, M., (2004), “Application of multi-criteria decision making to sustainable energy planning-A review”, Renewable and Sustainable Energy Reviews, v 8, pp. 365–381.
Pasi, G., Yager, R.R., (2006), “Modeling the concept of majority opinion in group decision making”. Information Sciences, v 176, pp. 390-414.
Regan H., Olyvan M., Markovchick L., (2005), “A formal model for consensus and negotiation in environmental management”, Journal of Environmental Management, Article in press, pp.1-10.
Robertson, W, A., (2002), “A comparison of three group decision-making strategies and their effects on the group decision-making process.” PhD Thesis, Virginia Polytechnic Institute and StateUniversity.
Smolíková R., Wachowiak M.P., (2002), “Aggregation operators for selection problems”, Fuzzy Sets and Systems, v 131, n 1, pp. 23-34.
Sugeno, M., (1974), “Theory of fuzzy integrals and its applications”, PhD thesis, Tokyo Institute of Technology, Tokyo.
Xu, Z.S., (2004), “A method based on linguistic aggregation operators for group decision making with linguistic preference relations”, Information Science, v 116, pp. 19-30.
Xu, Z., (2006), “Induced uncertain linguistic OWA operators applied to group decision making”. Information Fusion, v 7, pp.231-238.
Xu, Z.S., Chen, J., (2006), “An interactive method for fuzzy multiple attribute group decision making “, Information Science, Article in Press.
Yager, R.R., (1988), “On ordered weighted averaging aggregation operators in multi-criteria decision making”, IEEE Trans.Systems, Man Cybernet. v 18, pp.183–190.
Yager, R.R., (1993), “Families of OWA operators”, Fuzzy Sets and Systems, v 59, pp.125–148.
Yager, R.R., (1994a), “On weighted median aggregation”, International Journal of Uncertainty, Fuzziness and Knowledge-based Systems, v 2, pp. 101– 113.
Yager, R.R., (1994b), “Aggregation operators and fuzzy systems modeling”, Fuzzy Sets and Systems, v 67, pp. 129–145.
Yager, R.R., (1996), “Quantifier guided aggregation using OWA operators’. International Journal of Intelligent Systems, v 11, pp. 49-73.
Zadeh, L.A., (1983), “A computational approach to fuzzy quantifiers in natural languages”. Computing and Mathematics with Applications, v 9, pp.149-184.
Zadrozny, S., (1997), “An approach to the consensus reaching support in fuzzy environment consensus under fuzziness”, Kluwer, Norwell, MA.