A multi-stage decision-making process for multiple attributes analysis under an interval-valued fuzzy environment

This paper presents a multi-stage decision-making process for multiple attributes analysis under an interval-valued fuzzy environment. The proposed method does not demand weights of conflicting attributes through the decision-making process under uncertainty. The performance ratings of potential alternatives with respect to selected conflicting attributes are first described by linguistic terms and then are represented as interval-valued triangular fuzzy numbers. Second, an outranking matrix is proposed to denote the frequency with which one potential alternative dominates all the other alternatives according to each selected attribute. Consequently, the outranking matrix is triangularized in order to provide an implicit preordering or provisional order of potential alternatives under uncertainty. Finally, the tentative order of alternatives undergoes different operations of the screening and balancing that requires sequential application of a balancing principle to the advantages–disadvantages table. It hybridizes the conflicting attributes with the pair-wise comparisons of the potential alternatives for the multiple attributes analysis. Furthermore, an application example is used for the decision-making in a selection problem to illustrate the feasibility and applicability of proposed method in an interval-valued fuzzy environment.

[1]  Ray W. Cooksey,et al.  Judgment analysis : theory, methods, and applications , 1996 .

[2]  Deng-Feng Li,et al.  Multiattribute decision making models and methods using intuitionistic fuzzy sets , 2005, J. Comput. Syst. Sci..

[3]  Gwo-Hshiung Tzeng,et al.  Extended VIKOR method in comparison with outranking methods , 2007, Eur. J. Oper. Res..

[4]  Richard Bellman,et al.  Decision-making in fuzzy environment , 2012 .

[5]  Raimo P. Hämäläinen,et al.  Decision Support by Interval SMART/SWING - Incorporating Imprecision in the SMART and SWING Methods , 2005, Decis. Sci..

[6]  Paul V. Preckel,et al.  Multiattribute Assessment of Alternative Cropping Systems , 1995 .

[7]  B. Vahdani,et al.  Selecting suppliers using a new fuzzy multiple criteria decision model: the fuzzy balancing and ranking method , 2010 .

[8]  P. Sevastianov,et al.  MCDM in a fuzzy setting: Investment projects assessment application , 2006 .

[9]  Przemyslaw Grzegorzewski,et al.  Distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric , 2004, Fuzzy Sets Syst..

[10]  Tony Prato,et al.  Selecting farming systems using a new multiple criteria decision model: the balancing and ranking method , 2002 .

[11]  Tony Prato,et al.  SELECTION AND SUSTAINABILITY OF LAND AND WATER RESOURCE MANAGEMENT SYSTEMS 1 , 1999 .

[12]  Jacek Żak,et al.  The methodology of multiple-criteria decision making in the optimization of an urban transportation system: case study of Poznań City in Poland , 1999 .

[13]  R. W. Saaty,et al.  The analytic hierarchy process—what it is and how it is used , 1987 .

[14]  Jerry M. Mendel,et al.  Operations on type-2 fuzzy sets , 2001, Fuzzy Sets Syst..

[15]  Chen-Tung Chen,et al.  A fuzzy approach for supplier evaluation and selection in supply chain management , 2006 .

[16]  Salvatore Greco,et al.  Rough set approach to multiple criteria classification with imprecise evaluations and assignments , 2009, Eur. J. Oper. Res..

[17]  Ivor Grattan-Guinness,et al.  Fuzzy Membership Mapped onto Intervals and Many-Valued Quantities , 1976, Math. Log. Q..

[18]  R. L. Keeney,et al.  Decisions with Multiple Objectives: Preferences and Value Trade-Offs , 1977, IEEE Transactions on Systems, Man, and Cybernetics.

[19]  M. Gorzałczany.  A method for inference in approximate reasoning based on interval-valued fuzzy sets , 1987 .

[20]  Nils Brunsson.  My own book review : The Irrational Organization , 2014 .

[21]  José L. Verdegay,et al.  Linguistic decision‐making models , 1992, Int. J. Intell. Syst..

[22]  I. Turksen.  Interval valued fuzzy sets based on normal forms , 1986 .

[23]  Chen-Tung Chen,et al.  Extensions of the TOPSIS for group decision-making under fuzzy environment , 2000, Fuzzy Sets Syst..

[24]  Dug Hun Hong,et al.  Some algebraic properties and a distance measure for interval-valued fuzzy numbers , 2002, Inf. Sci..

[25]  Francisco Herrera,et al.  Linguistic decision analysis: steps for solving decision problems under linguistic information , 2000, Fuzzy Sets Syst..

[26]  H. Hornich.  Vom Einmaleins zum Integral , 1935 .

[27]  Aregai Tecle,et al.  Conflict analysis in multi-resource forest management with multiple decision-makers. , 1995 .

[28]  Humberto Bustince Sola.  Conjuntos intuicionistas e intervalo-valorados difusos: propiedades y construccion. Relaciones intuicionistas y estructuras , 1994 .

[29]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[30]  I. Burhan Türksen,et al.  Interval valued strict preference with Zadeh triples , 1996, Fuzzy Sets Syst..

[31]  Chris Cornelis,et al.  Advances and challenges in interval-valued fuzzy logic , 2006, Fuzzy Sets Syst..

[32]  Zachary F. Lansdowne,et al.  Outranking methods for multicriterion decision making: Arrow’s and Raynaud’s conjecture , 1996 .

[33]  W. Bandler,et al.  Fuzzy Interval Inference Utilizing the Checklist Paradigm and BK-Relational Products , 1996 .

[34]  Francisco Herrera,et al.  A model of consensus in group decision making under linguistic assessments , 1996, Fuzzy Sets Syst..

[35]  Lotfi A. Zadeh,et al.  The Concepts of a Linguistic Variable and its Application to Approximate Reasoning , 1975 .

[36]  J. Buckley,et al.  Fuzzy hierarchical analysis , 1999, FUZZ-IEEE'99. 1999 IEEE International Fuzzy Systems. Conference Proceedings (Cat. No.99CH36315).

[37]  Josef Gruber,et al.  Econometric Decision Models , 1983 .

[38]  Habib Chabchoub,et al.  PROMETHEE-MD-2T method for project selection , 2009, Eur. J. Oper. Res..

[39]  Edmundas Kazimieras Zavadskas,et al.  Multicriteria selection of project managers by applying grey criteria , 2008 .

[40]  Ming-Miin Yu,et al.  Decision Making Based On Statistical Data, Signed Distance And Compositional Rule Of Inference , 2004, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[41]  Ferenc Szidarovszky,et al.  Multi-attribute decision making: dominance with respect to an importance order of the attributes , 1993 .

[42]  Xiaoping Li,et al.  The applications of interval-valued fuzzy numbers and interval-distribution numbers , 1998, Fuzzy Sets Syst..

[43]  Jürgen Bartnick.  Optimal triangulation of a matrix and a measure of interdependence for a linear econometric equation system , 1991 .

[44]  Evangelos Triantaphyllou,et al.  Multi-criteria Decision Making Methods: A Comparative Study , 2000 .

[45]  R. B. Kearfott,et al.  Applications of interval computations , 1996 .