A Ranking Method of Triangular Intuitionistic Fuzzy Numbers and Application to Decision Making
International Journal of Computational Intelligence SystemsPublished 1 October 2010Open access
Deng Feng Li, Jiang Nan, Mao Jun Zhang
Citations134
SJR quartileQ2
SJR score0.59
SNIP0.83
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
TL;DR
A value and ambiguity based ranking method is developed and applied to solve multiattribute decision making problems in which the ratings of alternatives on attributes are expressed using TIFNs.
Abstract
Ranking of triangular intuitionistic fuzzy numbers (TIFNs) is an important problem, which is solved by the value and ambiguity based ranking method developed in this paper. Firstly, the concept of TIFNs is introduced. Arithmetic operations and cut sets over TIFNs are investigated. Then, the values and ambiguities of the membership degree and the non-membership degree for TIFNs are defined as well as the value-index and ambiguity-index. Finally, a value and ambiguity based ranking method is developed and applied to solve multiattribute decision making problems in which the ratings of alternatives on attributes are expressed using TIFNs. A numerical example is examined to demonstrate the implementation process and applicability of the method proposed in this paper. Furthermore, comparison analysis of the proposed method is conducted to show its advantages over other similar methods.
Keywords
Decision SciencesMathematicsEngineering
Fuzzy Sets and SystemsIntuitionistic fuzzy sets
16,153 Citations1986Krassimir Atanassov
Various properties are proved, which are connected to the operations and relations over sets, and with modal and topological operators, defined over the set of IFS's.
Medical Entomology and ZoologyMultiple Attribute Decision Making: Methods and Applications
8,268 Citations1981Shu-Jen J. Chen, C. L. Hwang +2 more
Mathematics in Science and Engineering/Mathematics in science and engineeringFuzzy Sets and Systems - Theory and Applications
6,430 Citations1980Didier Dubois, Henri Prade
Studies in fuzziness and soft computingIntuitionistic Fuzzy Sets
1,927 Citations1999Krassimir Atanassov
Lecture notes in economics and mathematical systemsFuzzy Multiple Attribute Decision Making
1,844 Citations1992Shu‐Jen Chen, Ching-Lai Hwang
Expert Systems with ApplicationsEXPERT SYSTEMS WITH APPLICATIONS
1,660 Citations2004Short Communication, Been-chian Chien A +3 more
Fuzzy Sets and SystemsReasonable properties for the ordering of fuzzy quantities (II)
665 Citations2001Xuzhu Wang, Etienne E. Kerre
Computers & Mathematics with ApplicationsRanking fuzzy numbers with an area between the centroid point and original point
510 Citations2002Ta‐Chung Chu, Chung-Tsen Tsao
This work proposes ranking fuzzy numbers with the area between the centroid point and original point to overcome shortcomings in the coefficient of variation (CV index).
Fuzzy Sets and SystemsReasonable properties for the ordering of fuzzy quantities (I)
481 Citations2001Xuzhu Wang, Etienne E. Kerre
Computers & Mathematics with ApplicationsA new approach for ranking of trapezoidal fuzzy numbers
442 Citations2008S. Abbasbandy, Tayebeh Hajjari
This paper introduces a new approach for ranking of trapezoidal fuzzy numbers based on the left and the right spreads at some @a-levels of Trapezoid fuzzy numbers.
Microelectronics ReliabilityUsing intuitionistic fuzzy sets for fault-tree analysis on printed circuit board assembly
408 Citations2006Ming‐Hung Shu, Ching‐Hsue Cheng +1 more
An algorithm of the intuitionistic fuzzy fault-tree analysis is proposed in this paper to calculate fault interval of system components and to find the most critical system component for the managerial decision-making based on some basic definitions.
Fuzzy Sets and SystemsOn a canonical representation of fuzzy numbers
347 Citations1998Miguel Delgado, M.A. Vila +1 more
This paper proposes two parameters, value and ambiguity, for fuzzy number representation and uses them to obtain canonical representations and to deal with fuzzy numbers in decision-making problems.
Information SciencesRanking of fuzzy numbers by sign distance
317 Citations2005S. Abbasbandy, B. Asady
A modification of the distance based approach called the sign distance is proposed, which is both efficient to evaluate and able to overcome the shortcomings of the previous techniques.
Computers & GeosciencesComputers and Mathematics with Applications
200 Citations1976Douglas M. Hawkins
The differential transform method (DTM) for solving a class of the system of two-dimensional linear and nonlinear Volterra integro-differential equations of the second kind is developed.
Information SciencesLinear programming method for multiattribute group decision making using IF sets
178 Citations2010Deng‐Feng Li, Guohong Chen +1 more
In this methodology, IF sets are constructed to capture fuzziness in decision information and decision making process, and the group consistency and inconsistency indices are defined on the basis of pairwise comparison preference relations on alternatives given by the decision makers.
Applied Soft ComputingFractional programming methodology for multi-attribute group decision-making using IFS
176 Citations2008Deng‐Feng Li, Yongchun Wang +2 more
A new methodology for solving multi-attribute group decision-making problems using IFS, in which multiple attributes are explicitly considered, is developed.
Expert Systems with ApplicationsLinear programming method for MADM with interval-valued intuitionistic fuzzy sets
170 Citations2010Deng‐Feng Li
A methodology for solving MADM problems with both ratings of alternatives on attributes and weights being expressed with IVIF sets is developed, where a weighted absolute distance between IF sets is defined using weights of IF sets.
Information SciencesFuzzy linear programming technique for multiattribute group decision making in fuzzy environments
161 Citations2003Deng‐Feng Li
A linear programming technique for multidimensional analysis of preferences in multiattribute group decision making under fuzzy environments by constructing a linear programming decision model based on the distance of each alternative to a fuzzy positive ideal solution which is unknown.
International Journal of Uncertainty Fuzziness and Knowledge-Based SystemsRANKING-INTUITIONISTIC FUZZY NUMBERS
156 Citations2004H. B. Mitchell
This paper considers the problem of rank-based fuzzy sets, a generalization of ordinary fuzzy sets which are characterized by a membership function and a non-membership function.
Fuzzy Sets and SystemsA new approach for defuzzification
151 Citations2000Ming Ma, Abraham Kandel +1 more
A new approach on defuzzification using the metric (distance) between two fuzzy numbers is introduced and an application of this new approach is investigated.
Kongzhi yu jueceMulti-criteria decision-making method with incomplete certain information based on intuitionistic fuzzy number
121 Citations2009Zhong Zhang
A method of multi-criteria decision-making with incomplete certain information based on intuitionistic trapezoidal fuzzy number is proposed, and the optimized nonlinear programming based on Hamming distance between integrated intuitionisitc trapezoid fuzzy number of each alternative and ideal-solution and non-ideal solution is constructed.
International Journal of Computational Intelligence SystemsA Lexicographic Method for Matrix Games with Payoffs of Triangular Intuitionistic Fuzzy Numbers
101 Citations2010Jiangxia Nan, Deng‐Feng Li +1 more
A lexicographic methodology is developed to determine the solutions of matrix games with payoffs of TIFNs for both Players through solving a pair of bi-objective linear programming models derived from two new auxiliary intuitionistic fuzzy programming models.
Microelectronics ReliabilityA note on “using intuitionistic fuzzy sets for fault-tree analysis on printed circuit board assembly”
94 Citations2008Deng‐Feng Li
The aim of this note is to point out and correct some errors in the definition of the four arithmetic operations for triangle intuitionistic fuzzy numbers introduced by Shu et al.
International Journal of Approximate ReasoningThe nearest trapezoidal form of a generalized left right fuzzy number
91 Citations2006S. Abbasbandy, Majid Amirfakhrian
A pseudo-metric on the set of fuzzy numbers and the Hausdorff metric are described, which can approximate an arbitrary generalized left right fuzzy number with a trapezoidal one.
Ranking of intuitionistic fuzzy numbers
91 Citations2008V. Lakshmana Gomathi Nayagam, G. Venkateshwari +1 more
A new method of intuitionistic fuzzy scoring to intuitionist fuzzy numbers that generalizes Chen and Hwangpsilas scoring method for ranking of intuitionism fuzzy numbers has been introduced and studied.
International Journal of Computational Intelligence SystemsAn Alternative Ranking Approach and Its Usage in Multi-Criteria Decision-Making
56 Citations2009Cengiz Kahraman, A. Çağrı Tolga
The proposed method has some advantages with respect to the other methods in both graphical representations and calculations and applicability to multi-criteria decision-making methods, i.e. fuzzy scoring, fuzzy AHP and fuzzy TOPSIS methods, is shown in the paper.
International Journal of Computational Intelligence SystemsA Linguistic-Valued Weighted Aggregation Operator to Multiple Attribute Group Decision Making with Quantative and Qualitative Information
35 Citations2008Xiaobing Li, Da Ruan +2 more
International Journal of Computational Intelligence SystemsImproved Fuzzy Art Method for Initializing K-means
10 Citations2010Sevinç İlhan Omurca, N. Jeremi Duru +1 more
International Journal of Computational Intelligence SystemsClustering feature vectors with mixed numerical and categorical attributes
9 Citations2008Roelof K. Brouwer
This paper describes a method for finding a fuzzy membership matrix in case of numerical and categorical features using fuzzy c-means and shows the method to be very effective in comparison with other methods.
International Journal of Computational Intelligence SystemsClustering feature vectors with mixed numerical and categorical attributes
9 Citations2008R.K. Brouwer