Hierarchical semi-numeric method for pairwise fuzzy group decision making

Gradual improvements to a single-level semi-numeric method, i.e., linguistic labels preference representation by fuzzy sets computation for pairwise fuzzy group decision making are summarized. The method is extended to solve multiple criteria hierarchical structure pairwise fuzzy group decision-making problems. The problems are hierarchically structured into focus, criteria, and alternatives. Decision makers express their evaluations of criteria and alternatives based on each criterion by using linguistic labels. The labels are converted into and processed in triangular fuzzy numbers (TFNs). Evaluations of criteria yield relative criteria weights. Evaluations of the alternatives, based on each criterion, yield a degree of preference for each alternative or a degree of satisfaction for each preference value. By using a neat ordered weighted average (OWA) or a fuzzy weighted average operator, solutions obtained based on each criterion are aggregated into final solutions. The hierarchical semi-numeric method is suitable for solving a larger and more complex pairwise fuzzy group decision-making problem. The proposed method has been verified and applied to solve some real cases and is compared to Saaty's (1996) analytic hierarchy process (AHP) method.

[1]  Mao-Jiun J. Wang,et al.  A fuzzy multi-criteria decision-making method for facility site selection , 1991 .

[2]  R. Yager,et al.  PARAMETERIZED AND-UKE AND OR-LIKE OWA OPERATORS , 1994 .

[3]  Pao-Long Chang,et al.  A fuzzy multi-criteria decision making method for technology transfer strategy selection in biotechnology , 1994 .

[4]  Ronald R. Yager,et al.  Non-numeric multi-criteria multi-person decision making , 1993 .

[5]  T. Saaty.  Axiomatic foundation of the analytic hierarchy process , 1986 .

[6]  Itsuo Hatono,et al.  Non-numeric preference relations and their satisfaction degrees for pairwise fuzzy group-decision making , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[7]  J. Kacprzyk,et al.  Group decision making and consensus under fuzzy preferences and fuzzy majority , 1992 .

[8]  Valerie Belton,et al.  On a short-coming of Saaty's method of analytic hierarchies , 1983 .

[9]  J. Bezdek,et al.  Fuzzy relation spaces for group decision theory: An application , 1979 .

[10]  José L. Verdegay,et al.  A model for linguistic partial information in decision‐making problems , 1994, Int. J. Intell. Syst..

[11]  Itsuo Hatono,et al.  Linguistic labels for expressing fuzzy preference relations in fuzzy group decision making , 1998, IEEE Trans. Syst. Man Cybern. Part B.

[12]  Ronald R. Yager,et al.  On ordered weighted averaging aggregation operators in multicriteria decisionmaking , 1988, IEEE Trans. Syst. Man Cybern..

[13]  Thomas L. Saaty,et al.  Decision making with dependence and feedback : the analytic network process : the organization and prioritization of complexity , 1996 .

[14]  Slawomir Zadrozny,et al.  An interactive multi-user decision support system for consensus reaching processes using fuzzy logic with linguistic quantifiers , 1988, Decis. Support Syst..

[15]  R. Yager.  Families of OWA operators , 1993 .

[16]  Gloria Bordogna,et al.  A linguistic modeling of consensus in group decision making based on OWA operators , 1997, IEEE Trans. Syst. Man Cybern. Part A.

[17]  Lotfi A. Zadeh,et al.  The concept of a linguistic variable and its application to approximate reasoning-III , 1975, Inf. Sci..

[18]  T. Saaty,et al.  The Analytic Hierarchy Process , 1985 .

[19]  F. Lootsma.  SCALE SENSITIVITY IN THE MULTIPLICATIVE AHP AND SMART , 1993 .

[20]  Itsuo Hatono,et al.  Non-Numeric Method for Pairwise Fuzzy Group-Decision Analysis , 1997, J. Intell. Fuzzy Syst..

[21]  Roland T. Rust.  Selecting network television advertising schedules , 1985 .

[22]  田村 坦之,et al.  階層化意思決定法(AHP)の記述的モデルの提案と選好順位逆転現象の整合的解釈 , 1998 .

[23]  J. Kacprzyk.  Group decision making with a fuzzy linguistic majority , 1986 .

[24]  H. Nurmi.  Approaches to collective decision making with fuzzy preference relations , 1981 .

[25]  P. Iz.  Application of fuzzy arithmetic in group decision and negotiations involving multicriteria and conflicting priorities , 1994, 1994 Proceedings of the Twenty-Seventh Hawaii International Conference on System Sciences.

[26]  H. J. Skala.  Arrow’s Impossibility Theorem: Some New Aspects , 1978 .