Power average operators of linguistic intuitionistic fuzzy numbers and their application to multiple-attribute decision making

2017 ◽  
Vol 32 (1) ◽  
pp. 1029-1043 ◽  
Author(s):  
Peide Liu ◽  
Xiyou Qin
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Multiple Attribute Decision Making ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute

PROJECTION MODELS FOR INTUITIONISTIC FUZZY MULTIPLE ATTRIBUTE DECISION MAKING

2010 ◽  
Vol 09 (02) ◽  
pp. 267-280 ◽  
Author(s):  
ZESHUI XU ◽  
HUI HU
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Ideal Point ◽  
Multiple Attribute Decision Making ◽  
Included Angle ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
Fuzzy Ideal ◽  
Interval Valued

The aim of this paper is to investigate the intuitionistic fuzzy multiple attribute decision-making problems where the attribute values are expressed in intuitionistic fuzzy numbers or interval-valued intuitionistic fuzzy numbers. We introduce some notions, such as intuitionistic fuzzy ideal point, interval-valued intuitionistic fuzzy ideal point, the modules of intuitionistic fuzzy numbers, and interval-valued intuitionistic fuzzy numbers. We also introduce the cosine of the included angle between the attribute value vectors of each alternative and the intuitionistic fuzzy ideal point, and the cosine of the included angle between the attribute value vectors of each alternative and the interval-valued intuitionistic fuzzy ideal point. Then we establish two projection models to measure the similarity degrees between each alternative and the intuitionistic fuzzy ideal point, and between each alternative and the interval-valued intuitionistic fuzzy ideal point. Based on the projection models, we can rank the given alternatives and then select the most desirable one. Finally, we illustrate the developed projection models with a numerical example.

scholarly journals Decision-Maker’s Risk Preference Based Intuitionistic Fuzzy Multiattribute Decision-Making and Its Application in Robot Enterprises Investment

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Liandong Zhou ◽  
Qifeng Wang
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Weight Vector ◽  
Multiple Attribute Decision Making ◽  
Decision Makers ◽  
Research Papers ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
Fuzzy Weight

At present, the utilization of hesitation information of intuitionistic fuzzy numbers is insufficient in many methods which were proposed to solve the intuitionistic fuzzy multiple attribute decision-making problems. And also there exist some flaws in the intuitionistic fuzzy weight vector constructions in many research papers. In order to solve these insufficiencies, this paper defined three construction equations of weight vectors based on the risk preferences of decision-makers. Then we developed an intuitionistic fuzzy dependent hybrid weighted operator (IFDHW) and proposed an intuitionistic fuzzy multiattribute decision-making method. Finally, the effectiveness of this method is verified by a robot manufacturing investment example.

SOME CONTINUOUS AGGREGATION OPERATORS WITH INTERVAL-VALUED INTUITIONISTIC FUZZY INFORMATION AND THEIR APPLICATION TO DECISION MAKING

2012 ◽  
Vol 20 (02) ◽  
pp. 185-209 ◽  
Author(s):  
JIAN LIN ◽  
QIANG ZHANG
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Fuzzy Information ◽  
Numerical Examples ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
Interval Valued

In this paper, some new operators for aggregating interval-valued intuitionistic fuzzy information are proposed to deal with multiple attribute decision making problems. Firstly, the C-IFOWA operator and C-IFOWG operator are developed to aggregate all the values in the interval-valued intuitionistic fuzzy numbers. Some of their desirable properties are also studied. Secondly, in order to aggregate a set of interval-valued intuitionistic fuzzy numbers, some new aggregation operators are proposed based on the C-IFOWA operator and C-IFOWG operator. Thirdly, two methods for multiple attribute decision making, in which the attribute values are given in the forms of interval-valued intuitionistic fuzzy numbers are presented. Finally, two numerical examples are provided to illustrate the practicality and validity of the proposed methods.

SOME GEOMETRIC AGGREGATION FUNCTIONS AND THEIR APPLICATION TO DYNAMIC MULTIPLE ATTRIBUTE DECISION MAKING IN THE INTUITIONISTIC FUZZY SETTING

2009 ◽  
Vol 17 (02) ◽  
pp. 179-196 ◽  
Author(s):  
G. W. WEI
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Membership Function ◽  
Fuzzy Set ◽  
Fuzzy Numbers ◽  
Fuzzy Variable ◽  
Multiple Attribute Decision Making ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute

The intuitionistic fuzzy set (IFS) characterized by a membership function and a non-membership function, was introduced by [K. Atanassov, "Intuitionistic fuzzy sets", Fuzzy Sets and Systems20 (1986) 87–96] as a generalization of Zadeh' fuzzy set [L. A. Zadeh, "Fuzzy sets", Information and Control8 (1965) 338–356] to deal with fuzziness and uncertainty. In this paper, the dynamic multiple attribute decision making (DMADM) problems with intuitionistic fuzzy information are investigated. The notions of intuitionistic fuzzy variable and uncertain intuitionistic fuzzy variable are defined, and two new aggregation operators called dynamic intuitionistic fuzzy weighted geometric (DIFWG) operator and uncertain dynamic intuitionistic fuzzy weighted geometric (UDIFWG) operator are proposed. Moreover, a procedure based on the DIFWG and IFWG operators is developed to solve the dynamic intuitionistic fuzzy multiple attribute decision making problems where all the decision information about attribute values takes the form of intuitionistic fuzzy numbers collected at different periods, and a procedure based on the UDIFWG and IIWG operators is developed for uncertain dynamic intuitionistic fuzzy multiple attribute decision making problems under interval uncertainty in which all the decision information about attribute values takes the form of interval-valued intuitionistic fuzzy numbers collected at different periods. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

IFWA and IFWGM Methods for MADM under Atanassov's Intuitionistic Fuzzy Environment

2015 ◽  
Vol 23 (02) ◽  
pp. 263-284 ◽  
Author(s):  
Yejun Xu ◽  
Huimin Wang
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Geometric Mean ◽  
Weighted Average ◽  
Multiple Attribute Decision Making ◽  
Fuzzy Decision Making ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Multiple Attribute

In this paper, we first give the formula of possibility degree to rank the Atanassov's intuitionistic fuzzy numbers. Two methods called Atanassov's intuitionistic fuzzy weighted average (IFWA) and Atanassov's intuitionistic fuzzy weighted geometric mean (IFWGM) are developed to solve the multiple attribute decision making problems under Atanassov's intuitionistic fuzzy environment, in which the performance ratings of alternatives and relative importance of attributes are expressed with Atanassov's intuitionistic fuzzy sets. The IFWA and IFWGM methods, respectively, are treated as an auxiliary pair of fractional programming models and two linear programming (LP) solution procedures are proposed simultaneously by using Charnes and Cooper transformation. Furthermore, two algorithms which are based on the IFWA and IFWGM models, respectively, are developed to solve Atanassov's intuitionistic fuzzy decision making problems where attribute values and weights of attributes are all in Atanassov's intuitionistic fuzzy numbers. The order relationship between IFWA and IFWGM are investigated. Finally, a numerical example is illustrated to show the feasibility and effectiveness of the proposed methods.

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