Multi-criteria decision-making method based on interval-valued intuitionistic fuzzy sets

Nayagam, V. Lakshmana Gomathi; Muralikrishnan, S.; Sivaraman, Geetha

doi:10.1016/j.eswa.2010.07.055

Cited by 232 publications

(49 citation statements)

References 23 publications

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“…Algorithm 2 [38]: [17], Qi et al [19], and Wang et al [33] pointed out that Algorithm 2 sometimes could not tell the difference between two A-IVIFVs. Based on the geometrical meaning of A-IVIFVs, Qi et al [19] put forward an approach for ranking A-IVIFVs, which is simply denoted by…”

Section: B Ranking Methods For Atanassov's Interval-valued Intuitionmentioning

confidence: 99%

Amount of Information and Attitudinal-Based Method for Ranking Atanassov's Intuitionistic Fuzzy Values

Guo

2014

IEEE Trans. Fuzzy Syst.

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The ranking of Atanassov's intuitionistic fuzzy values (A-IFVs) is nontrivial because there is no natural linear order among them, as opposed to fuzzy sets. In this paper, we tackle this difficult problem and develop a new novel technique for ranking A-IFVs based on amount of information using the geometrical representation of Atanassov's intuitionistic fuzzy sets (A-IFSs), with the aim of overcoming some drawbacks and ambiguities in existing methods and to build a new ranking model in the A-IFS context from the viewpoint of amount of information. We prove that the order on nonempty A-IFVs induced by our function is admissible in the A-IFS context. Thus, our developed method provides a total order that extends the usual partial order between A-IFVs. Moreover, we discuss the role that a decision maker's attitude can play in decision making under uncertainty. This allows us to introduce the idea of attitudinal-based extension of our developed technique, which is much more useful and flexible in real-world applications. By this, we also provide a new idea and explanation to evaluate two special A-IFVs: the completely known opposition (0,1,0) and the completely unknown information (0,0,1). Finally, an effort is made to extend the applicability of the developed methods by considering the situation in which Atanassov's interval-valued intuitionistic fuzzy sets are involved. Experimental studies show the good performance of the developed methods in the A-IF and A-IVIF situations, respectively.Index Terms-Atanassov's intuitionistic fuzzy sets (A-IFSs), attitudinal character, decision making, ranking.

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Section: B Ranking Methods For Atanassov's Interval-valued Intuitionmentioning

confidence: 99%

Amount of Information and Attitudinal-Based Method for Ranking Atanassov's Intuitionistic Fuzzy Values

Guo

2014

IEEE Trans. Fuzzy Syst.

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“…(3) A ranking with multiples: 3 Λ with the property that the difference between weights of attributes in the sets 5 T and 5 J , is greater than or equal to that of attributes in the sets 5 K and 5 L .…”

Section: Description For Madm Problems Using Tifns With Incomplete Wementioning

confidence: 99%

“…Both IFS and IVIFS have widely been applied to the multi-attribute decision making (MADM) and multi-attribute group decision making (MAGDM). [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] Fuzzy numbers are a special case of fuzzy sets. As a generalization of fuzzy numbers (Dubois and Prade 23 ), an intuitionistic fuzzy number (IFN) seems to suitably describe an ill-known quantity (Li 24 ).…”

Section: Introductionmentioning

confidence: 99%

Multi-Attribute Decision Making Method Based on Possibility Variance Coefficient of Triangular Intuitionistic Fuzzy Numbers

Wan

2013

Int. J. Unc. Fuzz. Knowl. Based Syst.

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Triangular intuitionistic fuzzy numbers (TIFNs) are a special case of intuitionistic fuzzy sets. The purpose of this paper is to develop a new decision making method based on possibility variance coefficient to solve the multi-attribute decision making (MADM) problems, in which the attribute values are in the form of TIFNs and the weight preference information is incomplete. The possibility mean, variance and standard deviation for a TIFN are introduced as well as the possibility variance coefficient. Hereby, a new method to rank TIFNs is given on the basis of the possibility variance coefficients. The bi-objective mathematical programming, which minimizes the possibility variance coefficients of membership and non-membership functions for alternative's overall attribute values, is constructed. Using the max-min method, two non-linear fractional programming models are transformed into the linear programming models through the Charnes and Cooper transformation. Thus, the Pareto optimal solution to the bi-objective mathematical programming can be derived by solving the single-objective programming model. The ranking order of alternatives is obtained according to the minimum possibility variance coefficients. A personal selection example is given to verify the developed method and to demonstrate its feasibility and effectiveness. The analysis of comparison with other method is also conducted.

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“…Li (2010c) proposed a mathematical-programming methodology of matrix games with payoffs represented by IVIFSs. Nayagam et al (2011) introduced a new accuracy function and proposed an MCDA method based on IVIFSs. Chen and Yang (2011) established optimization models to determine the criterion weights under incomplete information and developed group decision-making methods for IVIFS settings.…”

Section: Introductionmentioning

confidence: 99%

An Inclusion Comparison Approach for Multiple Criteria Decision Analysis Based on Interval-Valued Intuitionistic Fuzzy Sets

Chen

2015

Technological and Economic Development of Economy

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The theory of interval-valued intuitionistic fuzzy sets provides an intuitive and feasible way of addressing uncertain and ambiguous properties. Many useful models and methods have been developed for multiple criteria decision analysis within the interval-valued intuitionistic fuzzy environment. In contrast to the elaborate existing methods, this paper establishes a simple and effective method for managing the sophisticated data expressed by interval-valued intuitionistic fuzzy sets. An inclusion comparison possibility defined on interval-valued intuitionistic fuzzy sets is proposed, and some important properties are investigated. Then, an inclusion-based index that considers positive and negative ideals is offered. Considering the maximal comprehensive inclusion-based indices, this paper constructs a linear programming model (for consistent information) and an integrated, nonlinear programming model (for inconsistent information) to estimate the criterion weights and the optimal ranking order of the alternatives under an incomplete preference structure. The feasibility of the proposed method is illustrated by a practical example of selecting a suitable bridge construction method, and a comparative analysis with other relevant methods is conducted to validate the effectiveness and applicability of the proposed methodology.Keywords: interval-valued intuitionistic fuzzy set, multiple criteria decision analysis, inclusion comparison possibility, inclusion-based index, incomplete preference structure.JEL Classification: C44, D81, R42.

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Multi-criteria decision-making method based on interval-valued intuitionistic fuzzy sets

Cited by 232 publications

References 23 publications

Amount of Information and Attitudinal-Based Method for Ranking Atanassov's Intuitionistic Fuzzy Values

Amount of Information and Attitudinal-Based Method for Ranking Atanassov's Intuitionistic Fuzzy Values

Multi-Attribute Decision Making Method Based on Possibility Variance Coefficient of Triangular Intuitionistic Fuzzy Numbers

An Inclusion Comparison Approach for Multiple Criteria Decision Analysis Based on Interval-Valued Intuitionistic Fuzzy Sets

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