Fuzzy linguistic induced OWA Minkowski distance operator and its application in group decision making

The Minkowski distance is a distance measure that generalizes a wide range of other distances such as the Euclidean and the Hamming distance. In this paper, we develop a new decision making model using induced ordered weighted averaging operators and the Minkowski distance of the fuzzy linguistic variables. Then, the authors introduce a new aggregation operator called the fuzzy linguistic induced ordered weighted averaging Minkowski distance (FLIOWAMD) operator by defining a fuzzy linguistic variable distance. It is an induced generalized aggregation operator that utilizes induced OWA operator, Minkowski distance measures and uncertain information represented as fuzzy linguistic variables. Some of its main properties and particular cases are studied. And a further generalization that uses quasi-arithmetic means also is presented. A method based on the FLIOWAMD operator for decision making is presented. At last, we end the paper with a numerical example of the new method.

[1]  José M. Merigó,et al.  Induced aggregation operators in the Euclidean distance and its application in financial decision making , 2011, Expert Syst. Appl..

[2]  JOSE M. MERIGO,et al.  DECISION MAKING WITH THE INDUCED GENERALIZED ADEQUACY COEFFICIENT , 2011 .

[3]  F. Herrera,et al.  An intelligent news recommender agent for filtering and categorizing large volumes of text corpus , 2004 .

[4]  J. Merigó,et al.  The Induced Generalized OWA Operator , 2009, EUSFLAT Conf..

[5]  H. Rouhparvar,et al.  Fuzzy Distance Measure for Fuzzy Numbers , 2011 .

[6]  Enrique Herrera-Viedma,et al.  Evaluating the information quality of Web sites: A methodology based on fuzzy computing with words: Special Topic Section on Soft Approaches to Information Retrieval and Information Access on the Web , 2006 .

[7]  Zeshui Xu,et al.  Uncertain Multi-Attribute Decision Making: Methods and Applications , 2015 .

[8]  J. Merigó,et al.  A new aggregation method for strategic decision making and its application in assignment theory , 2011 .

[9]  Francisco Herrera,et al.  Aggregation operators for linguistic weighted information , 1997, IEEE Trans. Syst. Man Cybern. Part A.

[10]  Sidong Xian,et al.  Fuzzy Linguistic Induced Ordered Weighted Averaging Operator and Its Application , 2012, J. Appl. Math..

[11]  Enrique Herrera-Viedma,et al.  Evaluating the information quality of Web sites: A methodology based on fuzzy computing with words , 2006, J. Assoc. Inf. Sci. Technol..

[12]  Francisco Herrera,et al.  Direct approach processes in group decision making using linguistic OWA operators , 1996, Fuzzy Sets Syst..

[13]  Dimitar Filev,et al.  Induced ordered weighted averaging operators , 1999, IEEE Trans. Syst. Man Cybern. Part B.

[14]  Ch.-Ch Chou.  The canonical representation of multiplication operation on triangular fuzzy numbers , 2003 .

[15]  Chen Hua-you.  Induced Ordered Weighted Harmonic Averaging(IOWHA)Operator and Its Application to Combination Forecasting Method , 2004 .

[16]  Zeshui Xu.  Deviation measures of linguistic preference relations in group decision making , 2005 .

[17]  M. Chung,et al.  Identification of fuzzy relational model and its application to control , 1993 .

[18]  Ronald R. Yager,et al.  On ordered weighted averaging aggregation operators in multicriteria decision-making , 1988 .

[19]  Zeshui Xu.  A Note on Linguistic Hybrid Arithmetic Averaging Operator in Multiple Attribute Group Decision Making with Linguistic Information , 2006 .

[20]  J. Merigó,et al.  Fuzzy Generalized Hybrid Aggregation Operators and its Application in Fuzzy Decision Making , 2010 .

[21]  Shouzhen Zeng,et al.  Fuzzy Generalized Ordered Weighted Averaging Distance Operator and Its Application to Decision Making , 2012 .

[22]  János C. Fodor,et al.  Characterization of the ordered weighted averaging operators , 1995, IEEE Trans. Fuzzy Syst..

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

[24]  Z. S. Xu,et al.  Eowa And Eowg Operators For Aggregating Linguistic Labels Based On Linguistic Preference Relations , 2004, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[25]  H. B. Mitchell,et al.  A Modified OWA Operator and its Use in Lossless DPCM Image Compression , 1997, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[26]  Zeshui Xu,et al.  An overview of methods for determining OWA weights , 2005, Int. J. Intell. Syst..

[27]  Zeshui Xu.  Hybrid Weighted Distance Measures and Their Application to Pattern Recognition , 2008, IDEAL.

[28]  Zeshui Xu,et al.  Alternative form of Dempster's rule for binary variables: Research Articles , 2005 .

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

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

[31]  R. Yager,et al.  Operations for granular computing: mixing words and numbers , 1998, 1998 IEEE International Conference on Fuzzy Systems Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36228).

[32]  Ronald R. Yager,et al.  Norms Induced from OWA Operators , 2010, IEEE Transactions on Fuzzy Systems.

[33]  José M. Merigó,et al.  DECISION MAKING WITH DISTANCE MEASURES AND INDUCED AGGREGATION OPERATORS , 2008 .

[34]  A. Kaufmann,et al.  Introduction to fuzzy arithmetic : theory and applications , 1986 .

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

[36]  Sidong Xian,et al.  Fuzzy Linguistic Induced Euclidean OWA Distance Operator and its Application in Group Linguistic Decision Making , 2014, Int. J. Intell. Syst..

[37]  Madan M. Gupta,et al.  Fuzzy mathematical models in engineering and management science , 1988 .

[38]  José M. Merigó,et al.  New decision-making techniques and their application in the selection of financial products , 2010, Inf. Sci..

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

[40]  Su Weihua.  LINGUISTIC INDUCED GENERALIZED AGGREGATION DISTANCE OPERATORS AND THEIR APPLICATION TO DECISION MAKING , 2012 .

[41]  Ching-Lai Hwang,et al.  Fuzzy Multiple Attribute Decision Making - Methods and Applications , 1992, Lecture Notes in Economics and Mathematical Systems.

[42]  Ronald R. Yager,et al.  Induced aggregation operators , 2003, Fuzzy Sets Syst..

[43]  Ronald R. Yager,et al.  Centered OWA Operators , 2007, Soft Comput..

[44]  José M. Merigó,et al.  A New Minkowski Distance Based on Induced Aggregation Operators , 2011, Int. J. Comput. Intell. Syst..

[45]  Zeshui Xu,et al.  Induced uncertain linguistic OWA operators applied to group decision making , 2006, Inf. Fusion.

[46]  Z. S. Xu,et al.  An overview of operators for aggregating information , 2003, Int. J. Intell. Syst..