An approach to multiple attribute group decision making with interval intuitionistic trapezoidal fuzzy information.

Wei, Guiwu ; Zhao, Xiaofei ; Wang, Hongjun 等

1. Introduction

Atanassov (1986), Atanassov and Gargov (1989) introduced the concept of intuitionistic fuzzy set (IFS), which is a generalization of the concept of fuzzy set (Zadeh 1965). The intuitionistic fuzzy set has received more and more attention since its appearance (Hui et al. 2009; Lin et al. 2007; Liu 2007, 2009; Ye 2009a, b; Li 2008, 2010; Li et al. 2009; Wei 2008a, b, 2009, 2010a, b, c, 2011a, b, c, d, e, f, g; Wei et al. 2011b; Wei, Zhao 2011; Zhang, Liu 2010; Nowak 2011; Ulubeyli, Kazaz 2009). Xu and Yager (2006) developed some geometric aggregation operators with intuitionistic fuzzy information. Xu (2007a) further developed some arithmetic aggregation operators with intuitionistic fuzzy information. Wei (2008a) utilized the maximizing deviation method for intuitionistic fuzzy multiple attribute decision making with incomplete weight information. Wei (2010b) developed the GRA method for intuitionistic fuzzy multiple attribute decision making with incomplete weight information. Later, Atanassov and Gargov (1989), Atanassov (1994) further introduced the interval-valued intuitionistic fuzzy set (IVIFS), which is a generalization of the IFS. The fundamental characteristic of the IVIFS is that the values of its membership function and non-membership function are intervals rather than exact numbers. Xu (2007b) and Xu and Chen (2007) developed some aggregation operators with interval-valued intuitionistic fuzzy information. Xu (2008) and Wei (2009) proposed some aggregation functions for dynamic multiple attribute decision making in intuitionistic fuzzy setting or interval-valued intuitionistic fuzzy setting. Wei (2010a) developed some induced geometric aggregation operators with intuitionistic fuzzy information or interval-valued intuitionistic fuzzy information. Li (2010) proposed linear programming method for MADM with interval-valued intuitionistic fuzzy sets. Wei et al. (2011a) developed correlation coefficient for interval-valued intuitionistic fuzzy multiple attribute decision making with incomplete weight information. Shu et al. (2006) gave the definition and operational laws of intuitionistic triangular fuzzy number and proposed an algorithm of the intuitionistic fuzzy fault-tree analysis. Wang (2008) gave the definition of intuitionistic trapezoidal fuzzy number and interval intuitionistic trapezoidal fuzzy number. Wang and Zhang (2008) gave the definition of expected values of intuitionistic trapezoidal fuzzy number and proposed the programming method of multi-criteria decision-making based on intuitionistic trapezoidal fuzzy number with incomplete certain information. Wang and Zhang (2009) developed the Hamming distance of intuitionistic trapezoidal fuzzy numbers and intuitionistic trapezoidal fuzzy weighted arithmetic averaging (ITFWAA) operator, then proposed multi-criteria decision-making method with incomplete certain information based on intuitionistic trapezoidal fuzzy number.

Geometric means (Herrera et al. 2001; Xu, Da 2002; Wei 2010c; Wei et al. 2010a, b, c, d) is widely used as a tool to aggregate input data. Considering that, in the existing literature, the geometric mean is generally considered as a fusion technique of numerical data, interval data, intuitionistic fuzzy data and interval-valued intuitionistic fuzzy data, in the real-life situations, the input data sometimes cannot be obtained exactly, but interval intuitionistic trapezoidal fuzzy data can be given. Therefore, "how to aggregate interval intuitionistic trapezoidal fuzzy data by using the geometric mean?" is an interesting research topic and is worth paying attention to. The aim of this paper is to propose some new geometric aggregation operators including interval intuitionistic trapezoidal fuzzy ordered weighted geometric (IITFOWG) operator and interval intuitionistic trapezoidal fuzzy hybrid geometric (IITFHG) operator and studied some desirable properties of these operators. An IITFWG and IITFHG operators-based approach is developed to solve the MAGDM problems in which both the attribute weights and the expert weights takes the form of real numbers, attribute values takes the form of interval intuitionistic trapezoidal fuzzy numbers. Finally, an illustrative example is given to verify the developed approach.

2. Preliminaries

In the following, we shall introduce some basic concepts related to intuitionistic trapezoidal fuzzy numbers and interval intuitionistic trapezoidal fuzzy numbers.

Definition 1 (Wang 2008). Let [??] is an intuitionistic trapezoidal fuzzy number, its membership function is:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

its non-membership function is:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

where 0 [less than or equal to] [[mu].sub.[??]] [less than or equal to] 1; 0 [less than or equal to] [v.sub.[??]] [less than or equal to] 1 and [[mu].sub.[??]] + [v.sub.[??]] [less than or equal to] 1; a, b, c, d [member of] R.

Then [??] = <([a,b,c,d];[[mu].sub.[??]]),([[a.sub.1],b,c,[d.sub.1]];[V.sub.[??]]) is called an intuitionistic trapezoidal fuzzy number. For convenience, let [??] = ([a, b, c, d]; [[mu].sub.[??]], [v.sub.[??]]).

If [[??].sub.A] [subset] [0,l] and [[??].sub.A] [subset] [0,l] are interval numbers, and 0 [greater than or equal to] + sup([V.sub.A](x)) [greater than or equal to] 1, [for all] [chi] [member of] X, for convenience, let [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is called an interval intuitionistic trapezoidal fuzzy number (Wan 2011).

Definition 2 (Wan 2011). Let [[??].sub.1] = ([[a.sub.1],[b.sub.1],[c.sub.1],[d.sub.1]]; [[[[mu].bar].sub.2],[[bar.[mu]].sub.2]],[[[v.bar].sub.2],[[bar.v].sub.2]]) and [[??].sub.2] = ([[a.sub.2],[b.sub.2],[c.sub.2],[d.sub.2]];[[[[mu].bar].sub.2],[[bar.[mu]].sub.2]],[[[v.bar].sub.2],[[bar.v].sub.2]]) be two interval intuitionistic trapezoidal fuzzy number, and [lambda] [greater than or equal to] 0, then

1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Definition 3 (Wan 2011). Let [??] = ([a,b,c,d];[[[mu].bar],[bar.[mu]]],[[bar.v],[v.bar]]) be an interval intuitionistic trapezoidal fuzzy number, a score function S of an interval intuitionistic trapezoidal fuzzy number can be represented as follows:

S([??]) = [[a + b + c + d]/4] x [[mu].bar] - [[[v.bar] + [bar.[mu]] - [bar.v]]/2], S[??] [member of] [-1,1]. (3)

Definition 4 (Wan 2011). Let [??] = ([a,b,c,d];[[[mu.bar]],[bar.[mu]]],[[v.bar],[bar.v]]) be an interval intuitionistic trapezoidal fuzzy number, an accuracy function H of an interval intuitionistic trapezoidal fuzzy number can be represented as follows:

H([??]) = [[a + b + c + d]/4] x [[[[mu].bar] + [v.bar] + [bar.[mu]] + [bar.v]]/2], H([??]) [member of] [0,1] (4)

to evaluate the degree of accuracy of the interval intuitionistic trapezoidal fuzzy number [??], where H([??]) [member of] [0,1]. The larger the value of H([??]), the more the degree of accuracy of the interval intuitionistic trapezoidal fuzzy number [??].

As presented above, the score function S and the accuracy function H are, respectively, defined as the difference and the sum of the membership function [[??].sub.A](x) and the non-membership function [[??].sub.A] (x). Based on the score function S and the accuracy function H, in the following, Wan (2011) give an order relation between two interval intuitionistic trapezoidal fuzzy number, which is deined as follows:

Definition 5. Let [[??].sub.1] =([[a.sub.1], [b.sub.1], [c.sub.1], [d.sub.1]]; [[[[mu].bar].sub.1],[[bar.[mu]].sub.1]], [[[v.bar].sub.1],[[bar.v].sub.1]]) and [[??].sub.2] = ([[a.sub.2], [b.sub.2], [c.sub.2], [d.sub.2]]; [[[[mu].bar].sub.2],[[bar.[mu]].sub.2]], [[[v.bar].sub.2],[[bar.v].sub.2]]) be two interval intuitionistic trapezoidal fuzzy number, s ([[??].sub.1]) and s([[??].sub.2]) be the scores of [??] and [??], respectively, and let H([[??].sub.1]) and H ([[??].sub.2]) be the accuracy degrees of [??] and [??], respectively, then if S([??]) < S([??]), then [??] is smaller than [??], denoted by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], then [??] and [??] represent the same information, denoted by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. [??] is smaller than [??], denoted by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

3. Some geometric aggregation operators with interval intuitionistic trapezoidal fuzzy numbers

In the following, some geometric aggregation operators with interval intuitionistic trapezoidal fuzzy number are developed as follows:

Definition 6 (Wan 2011). Let [[??].sub.j](j = 1,2, ..., n) be a collection of interval intuitionistic trapezoidal fuzzy number, and let IITFWG: [Q.sup.n] [right arrow] Q, if

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

where [omega] = [([omega].sub.1], [omega].sub.2], ..., [omega].sub.n]).sup.T] be the weight vector of [[??].sub.j](j = 1, 2, ..., n), and [omega].sub.j] > 0, [n.summation over (j = 1)] [omega].sub.j] = 1, then IITFWG is called the interval intuitionistic trapezoidal fuzzy weighted geometric(IITFWG) operator.

Definition 7. Let [[??].sub.j] (j = 1, 2, ..., n) (j = 1, 2, ..., n) be a collection of interval intuitionistic trapezoidal fuzzy number. An interval intuitionistic trapezoidal fuzzy ordered weighted geometric (IITFOWG) operator of dimension n is a mapping IITFOWG: [Q.sup.n] [right arrow] Q, that has an associated vector w = ([w.sub.1], [w.sub.2], ..., [w.sub.n]) such that [w.sub.j] > 0 and [n.summation over (j = 1)] [w.sub.j] = 1. Furthermore,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

where ([sigma](1), [sigma](2), ..., [sigma](n)) is a permutation of (1, 2, ..., n), such that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] for all j = 2, ..., n.

The IITFOWG operator has the following properties.

Theorem 1. (Commutativity).

[IITFOWG.sub.w]([[??].sub.1], [[??].sub.2], ..., [[??].sub.n]) = [IITFOWG.sub.w]([[??].sup.*.sub.1], [[??].sup.*.sub.2], ..., [[??].sup.*.sub.n]).

where [[??].sup.*.sub.j] (j = 1, 2, ..., n) is any permutation of [[??].sub.j] (j = 1, 2, ..., n).

Theorem 2. (Idempotency) If [[??].sub.j] (j = 1, 2, ..., n) = [??] for all j, then [IITFOWG.sub.w] ([[??].sub.1], [[??].sub.2], ..., [[??].sub.n]) = [??].

From Definitions 6 and 7, we know that the IITFWG operator weights the interval intuitionistic trapezoidal fuzzy arguments while the IITFOWG operator weights the ordered positions of the interval intuitionistic trapezoidal fuzzy arguments instead of weighting the arguments themselves. Therefore, weights represent different aspects in both the IITFWG and IITFOWG operators. However, both the operators consider only one of them. To solve this drawback, in the following we shall propose an interval intuitionistic trapezoidal fuzzy hybrid geometric (IITFHG) operator.

Definition 8. An interval intuitionistic trapezoidal fuzzy hybrid geometric (IITFHG) operator of dimension n is a mapping IITFHG: [Q.sup.n] [right arrow] Q, that has an associated vector w = [([w.sub.1], [w.sub.2], ..., [w.sub.n]).sup.T] such that [w.sub.j] > 0 and [n.summation over (j = 1)] = 1. Furthermore,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

where [[??].sub.[omega](j)] is the jth largest of the weighted interval intuitionistic trapezoidal fuzzy numbers [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] be the weight vector of [[??].sub.j] (j = 1, 2, ..., n), and [[omega].sub.j] > 0, [n.summation over (j = 1)] [w.sub.j] = 1, and n is the balancing coefficient.

Theorem 3. The IITFWG operator is a special case of the IITFHG operator.

Proof. Let w = (1/n, 1/n, ..., 1/n), then

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Which completes the proof of Theorem 3.

Theorem 4. The IITFOWG operator is a special case of the IITFHG operator.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

This completes the proof of Theorem 4.

So we know that the IITFHG operator generalizes both the IITFWG and IITFOWG operators, and reflects the importance degrees of both the given arguments and their ordered positions.

4. An approach to multiple attribute group decision making with interval intuitionistic trapezoidal fuzzy information

In this section, we shall investigate the multiple attribute group decision making (MAGDM) problems based on the IITFWG and IITFHG operator in which both the attribute weights and the expert weights takes the form of real numbers, attribute values takes the form of interval intuitionistic trapezoidal fuzzy numbers.

Let A = {[A.sub.1], [A.sub.2], ..., [A.sub.m]} be a discrete set of alternatives, and G = {[G.sub.1], [G.sub.2], ..., [G.sub.n]} be the set of attributes, [omega] = ([[omega].sub.1], [[omega].sub.2], ..., [[omega].sub.n]) is the weighting vector of the attributes [G.sub.j] (j = 1, 2, ..., n), where [[omega].sub.j] [member of] [0,1], [n.summation over (j = 1)] = 1. Let D = {[D.sub.1],[D.sub.2], ..., [D.sub.t]} be the set of decision makers, v = ([v.sub.1], [v.sub.2], ..., [v.sub.n]) be the weighting vector of decision makers, with [v.sub.k] [member of] [0,1],[t.summation over (k = 1) [v.sub.k] = 1. Suppose that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the intuitionistic trapezoidal fuzzy decision matrix, where [[??].sup.(k).sub.ij] indicates the degree that the alternative [A.sub.i] satisies the attribute [G.sub.j] given by the decision maker [D.sub.k], [[??].sup.(k).sub.ij] indicates the degree that the alternative [A.sub.i] doesn't satisfy the attribute [G.sub.j], given by the decision maker [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

In the following, we apply the IITFWG and IITFHG operators to multiple attribute group decision making with interval intuitionistic trapezoidal fuzzy information. The method involves the following steps:

Step 1. Utilizing the decision information given in the interval intuitionistic trapezoidal fuzzy decision matrix [[??].sub.k], and the IITFWG operator

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

to derive the individual overall interval intuitionistic trapezoidal fuzzy numbers [[??].sup.k.sub.i] of the alternative [A.sub.i].

Step 2. Utilizing the IITFHG operator:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

to derive the collective overall interval intuitionistic trapezoidal fuzzy numbers [[??].sub.i](i = 1, 2, ..., m) of the alternative [A.sub.i], where v = ([v.sub.1], [v.sub.2], ..., [v.sub.n]) is the weighting vector of decision makers, with [v.sub.k] [member of] [0,l], [t.summation over (k = 1)] [v.sub.k] = 1; w = ([w.sub.1],[w.sub.2], ..., [w.sub.n]) is the associated weighting vector of the ITFHG operator, with [w.sub.j] [member of] [0,1], [n.summation over (j = 1)] [w.sub.j] = 1.

Step 3. Calculate the scores S([[??].sub.i]) (i = 1, 2, ..., m) of the collective overall interval intuitionistic trapezoidal fuzzy numbers [[??].sub.i] (i = 1, 2, ..., m) to rank all the alternatives [A.sub.i] (i = 1, 2, ..., m) and then to select the best one(s) (if there is no difference between two scores S (f) and S ([[??].sub.j]), then we need to calculate the accuracy degrees H ([[??].sub.i]) and H ([[??].sub.j]) of the overall interval intuitionistic trapezoidal fuzzy numbers [[??].sub.j] and [[??].sub.j], respectively, and then rank the alternatives [A.sub.i] and [A.sub.j] in accordance with the accuracy degrees

Step 4. Rank all the alternatives [A.sub.i] (i = 1, 2, ..., m) and select the best one(s) in accordance with S([[??].sub.i]) and H([[??].sub.i]) (i = 1, 2, ..., m).

Step 5. End.

5. Numerical example

Thus, in this section we shall present a numerical example to show potential evaluation of emerging technology commercialization with uncertain linguistic information in order to illustrate the method proposed in this paper. There is a panel with four possible emerging technology enterprises [A.sub.i] (i = 1, 2, 3, 4, 5) to select. The experts selects four attribute to evaluate the five possible emerging technology enterprises: (1) [G.sub.1] is the technical advancement; (2) [G.sub.2] is the potential market and market risk; (3) [G.sub.3] is the industrialization infrastructure, human resources and financial conditions; (4) [G.sub.4] is the employment creation and the development of science and technology. The five possible alternatives [A.sub.i] (i = 1, 2, ..., 5) are to be evaluated using the interval intuitionistic trapezoidal fuzzy numbers by the three decision makers (whose weighting vector v = [(0.35,0.40,0.25).sup.T])) under the above four attributes (whose weighting vector [omega] = [(0.2, 0.1, 0.3, 0.4).sup.T]), and three decision matrices are to be constricted as listed in the following matrices [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], respectively:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

we utilize the proposed procedure to get the most desirable alternative(s).

Step 1. Utilize the decision information given in the interval intuitionistic trapezoidal fuzzy decision matrix [[??].sub.k], and the IITFWG operator to derive the individual overall interval intuitionistic trapezoidal fuzzy values [[??].sup.(k).sub.i] of the alternative [A.sub.i].

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Step 2. Utilize the IITFHG operator to derive the collective overall interval intuitionistic trapezoidal fuzzy values [[??].sub.i](i = 1, 2, ..., m) of the alternative [A.sub.i] (Let w = [(0.20, 0.50, 0.30).sup.T]).

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Step 3. Calculate the scores S([[??].sub.i]) (i = 1, 2, ..., 5) of the overall interval intuitionistic trapezoidal fuzzy numbers [[??].sub.i](i = 1, 2, ..., 5)

S ([[??].sub.1]) = 0.0050, S([[??].sub.2]) = 0.2056,S ([[??].sub.3]) = 0.0719, S([[??].sub.4]) = 0.0887, S ([[??].sub.5]) = 0.1078.

Step 4. Rank all the alternatives [A.sub.i](i = 1, 2, 3, 4, 5) in accordance with the scores S([[??].sub.i]) (i = 1, 2, ..., 5) of the interval intuitionistic trapezoidal fuzzy numbers [r.sub.i](i = 1, 2, ..., 5): [A.sub.2] [??] [A.sub.5] [??] [A.sub.4] [??] [A.sub.3] [??] [A.sub.1], and thus the most desirable alternative is [A.sub.5].

6. Conclusion

In this paper, we investigate the multiple attribute group decision making (MAGDM) problems in which both the attribute weights and the expert weights take the form of real numbers, attribute values take the form of interval intuitionistic trapezoidal fuzzy numbers. Firstly, some operational laws of interval intuitionistic trapezoidal fuzzy numbers are introduced. Then, we have developed the interval intuitionistic trapezoidal fuzzy ordered weighted geometric (IITFOWG) operator and interval intuitionistic trapezoidal fuzzy hybrid geometric (IITFHG) operator. The IITFHG operator firstly weights the given arguments, and reorders the weighted arguments in descending order and weights these ordered arguments by the IITFHG weights, and finally aggregates all the weighted arguments into a collective one. Obviously, the IITFHG operator generalizes both the IITFWG and IITFOWG operators, and reflects the importance degrees of both the given argument and the ordered position of the argument. Furthermore, the IITFHG operator can relieve the influence of unfair arguments on the decision results by using the IITFHG weights to assign low weights to those "false" or "biased" ones. We have studied some desirable properties of these operators and applied the IITFWG and IITFHG operators to multiple attribute group decision making with interval intuitionistic trapezoidal fuzzy information. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness. In future research, our work will focus on the application of interval intuitionistic trapezoidal fuzzy multiple attribute group decision making in the fields such as investment, personnel examination, medical diagnosis, and military system efficiency evaluation.

DOI: 10.3846/20294913.2012.676995

Acknowledgment

The work was supported by the National Natural Science Foundation of China under Grant No. 61174149, Natural Science Foundation Project of CQ CSTC of the People's Republic of China (No. CSTC,2011BA0035), the Humanities and Social Sciences Foundation of Ministry of Education of the People's Republic of China under Grant No. 11XJC630011, the Project supported by the Research Foundation of Chongqing University of Arts and Sciences under Grant No. Y2011JG31, No. Y2009JG4 and the China Postdoctoral Science Foundation under Grant 20100480269. This research was also supported by the Science and Technology Research Foundation of Chongqing Education Commission under Grant No. KJ111214.

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Guiwu Wei (1), Xiaofei Zhao, Hongjun Wang

Institute of Decision Sciences, Chongqing University of Arts and Sciences, Chongqing 402160, P. R. China

E-mail: (1) weiguiwu@163.com (corresponding author)

Received 25 January 2011; accepted 19 March 2011

Guiwu WEI has a MSc and a PhD degree in applied mathematics from South West Petroleum University, Business Administration from school of Economics and Management at South West Jiaotong University, China, respectively. He is an Associate Professor in the Department of Economics and Management at Chongqing University of Arts and Sciences. He has published more than 90 papers in journals, books and conference proceedings including journals such as Expert Systems with Applications, Computers & Industrial Engineering, International Journal of Production Research, Applied Soft Computing, Knowledge and Information Systems, Knowledge-based Systems, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, International Journal of Computational Intelligence Systems and Information: An International Interdisciplinary Journal. He has published 1 book. He has participated in several scientific committees and serves as a reviewer in a wide range of journals including Expert Systems With Application, Computers & Industrial Engineering, International Journal of Information Technology and Decision Making, Knowledge-based Systems, Information Sciences, International Journal of Computational Intelligence Systems and European Journal of Operational Research. He is currently interested in Aggregation Operators, Decision Making and Computing with Words.

Xiaofei ZHAO is a lecturer in Department of Economics and Management, Chongqing University of Arts and Sciences. He received the B. E. and M. E. degree in applied mathematics from SouthWest Normal University, in management sciences and engineer from SouthWest Jiaotong University, China, respectively. He has worked for Department of Economics and Management, Chongqing University of Arts and Sciences, China as a lecturer since 2006. He has published more than 10 papers in journals including journals such as Knowledge and Information Systems, Knowledge-based Systems, International Journal of Computational Intelligence Systems and Information: An International Interdisciplinary Journal.

Hongjun WANG is a lecturer in Department of Economics and Management, Chongqing University of Arts and Sciences. He received the B. E. and M. E. degree in management sciences and engineer from SouthWest Petroleum University, China. She has worked for Department of Economics and Management, Chongqing University of Arts and Sciences, China as a lecturer since 2006. She has published more than 10 papers in journals including journals such as Knowledge and Information Systems, Knowledge-based Systems, International Journal of Computational Intelligence Systems and Information: An International Interdisciplinary Journal.