Gaming and Disruptive Innovation Strategy - Toyota Motor Corp.
Journal of Intelligent & Fuzzy Systems 32 (2017) 4357–4365 DOI:10.3233/JIFS-16731 IOS Press
4357
An approach to evaluating the knowledge innovation ability of new ventures based on knowledge management with fuzzy number intuitionistic fuzzy information
Wei Fan∗ Graduate School, Chang Chun University of Science and Technology, Chang Chun, China
Abstract. Currently, most new ventures are knowledge-based enterprises; moreover, knowledge innovation constitutes the major activities of the enterprises’ production and knowledge management. Therefore, it is of great significance to be able to properly analyze and evaluate a new venture’s knowledge innovation ability. In this paper, we investigate the multiple attribute decision making problems with fuzzy number intuitionistic fuzzy information. Then, we develop the fuzzy number intuitionistic fuzzy Hamacher power weighted geometric (FNIFHPWG) operator. Then, we apply the FNIFHPWG operator to deal with multiple attribute decision making for evaluating the knowledge innovation ability of new ventures based on knowledge management under the fuzzy number intuitionistic fuzzy environments. Finally, an illustrative example for evaluating the knowledge innovation ability of new ventures based on knowledge management is given to verify the developed approach.
Keywords: Multiple attribute decision making, fuzzy number intuitionistic fuzzy sets, Hamacher aggregation operators, fuzzy number intuitionistic fuzzy Hamacher power weighted geometric (FNIFHPWG) operator, knowledge innovation ability, knowledge management
1. Introduction
Knowledge innovation refers to the processes of creating and possessing new knowledge, which occur during the creation, dissemination and application of knowledge in enterprises. Through knowledge inno- vation, an enterprise can develop its core competence by integrating explicit knowledge and tacit knowl- edge acquired in and out of the enterprise [1, 2]. Corporate knowledge innovation is an indispensable link between knowledge area and economic area, which combines the two areas into an organic whole
∗Corresponding author. Wei Fan, Graduate School, Chang Chun University of Science and Technology, Chang Chun, China. Tel./Fax: +86 13843176394; E-mail: 934289107@qq.com.
through knowledge creation and application [3, 4]. Thus, knowledge innovation is a significant compo- nent of business management and essential to the sur- vival and sustainable development of an enterprise. Besides, scientific and effective innovation manage- ment is a prerequisite for knowledge innovation to be systemic and comprehensive so that it can turn into a corporate advantage and increase corporate value.
New ventures are major contributors to eco- nomic progress [5]. At present, most of them are knowledge-based enterprises; in this way, knowledge innovation and knowledge management figure promi- nently therein. Organizational knowledge already possessed, that is, knowledge assets or intellectual capital, forms the basis of a new venture’s knowledge
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4358 W. Fan / An approach to evaluating the knowledge innovation ability
innovation, which refers to the knowledge an enter- prise has possessed or controlled that is not physical or tangible yet contributes greatly to corporate pro- duction and services and continuously generates economic gains. Knowledge assets are a special type of resources indispensible to a new venture [6], which are mainly composed of human capital, technolog- ical assets, market assets and infrastructure assets. Knowledge innovation is a systemic project involving the whole texture of a new venture, requiring the par- ticipation and cooperation of each department, such as HR, technical, marketing and management depart- ments. The writer of this paper deems that either knowledge creation or knowledge acquisition should base themselves on the new venture’s ability to dis- cover, to accumulate, to absorb, to understand, to grasp and to apply knowledge, which constitutes the new venture’s knowledge innovation ability [7].
Although the new ventures’ knowledge innovation is very important, but few studies have been done and the existing evaluation methods are incomplete [8]. In this paper, we investigate the multiple attribute decision making problems with fuzzy number intu- itionistic fuzzy information. Then, we develop the fuzzy number intuitionistic fuzzy Hamacher power weighted geometric (FNIFHPWG) operator. Then, we apply the FNIFHPWG operator to deal with mul- tiple attribute decision making for evaluating the knowledge innovation ability of new ventures based on knowledge management under the fuzzy number intuitionistic fuzzy environments. Finally, an illustra- tive example for evaluating the knowledge innovation ability of new ventures based on knowledge manage- ment is given to verify the developed approach.
2. Preliminaries
Liu and Yuan [9] introduced the concept of fuzzy number intuitionistic fuzzy set(FNIFS) which funda- mental characteristic of the FNIFS is that the values of its membership function and non-membership func- tion are triangular fuzzy numbers rather than exact numbers.
Definition 1. [9] Given a fixed set X = {x1, x2, · · · , xn}, An FNIFS Ã over X is an object having the form:
à = {⟨
xi, t̃A (xi) , f̃A (xi) ⟩ |xi ∈ X
} (1)
where t̃A(xi) ⊂ [0, 1] and f̃A(xi) ⊂ [0, 1] are tri- angular fuzzy numbers, and t̃A(xi) = (a(xi), b(xi),
c(xi)), X → [0, 1], f̃A(x) = (l(xi), m(xi), p(xi)), X → [0, 1], 0 ≤ c(xi) + p(xi) ≤ 1, ∀ x ∈ X.
For convenience, let t̃A(xi) = (a(xi), b(xi), c(xi)), f̃A(x) = (l(xi), m(xi), p(xi)), so ã(xi) = 〈(a (xi) , b (xi) , c (xi)) , (l (xi) , m (xi) , p (xi))〉 and we call ã(xi) an fuzzy number intuitionistic fuzzy value (FNIFV).
Definition 2. [10] Let ã (xi) = 〈(a (xi) , b (xi) , c (xi)), (l (xi) , m (xi) , p (xi))〉 be a collection of FNIFEs, a score function S of a FNIFV ã(xi) can be represented as follows:
S (ã (xi)) = a (xi) + 2b (xi) + c (xi)
4
− l (xi) + 2m (xi) + p (xi) 4
(2)
Definition 3. [10] Let ã (xi) = 〈(a (xi) , b (xi) , c (xi)), (l (xi) , m (xi) , p (xi))〉 be a collection of FNIFEs, an accuracy function H of a FNIFV ã (xi) can be represented as follows:
H (ã (xi))
= (a (xi) + 2b (xi) + c (xi)) + (l (xi) + 2m (xi) + p (xi)) 4
,
H (ã (xi)) ∈ [0, 1] . (3)
to evaluate the degree of accuracy of the FNIFV ã (xi) = 〈(a (xi) , b (xi) , c (xi)) , (l (xi) , m (xi) , p (xi))〉, where H (ã (xi)) ∈ [0, 1]. The larger the value of H (ã (xi)), the more the degree of accuracy of the FNIFV ã (xi) is.
In recent years, more and more scholars inves- tigated the multiple attribute decision making problems with fuzzy number intuitionistic fuzzy information [11–18].
3. FNIFHWG operator
Bsed on the Hamacher operation [19–22], Wang et al. [18] proposed the fuzzy number intuitionistic fuzzy Hamacher weighted geometric (FNIFHWG) operator as follows:
Definition 4. Let ã ( xj
) = 〈(a
( xj
) , b
( xj
) , c
( xj
) ),(
l ( xj
) , m
( xj
) , p
( xj
))⟩ be a collection of FNIFEs,
then we define the fuzzy number intuitionistic fuzzy Hamacher weighted geometric (FNIFHWG) operator as follows:
W. Fan / An approach to evaluating the knowledge innovation ability 4359
FNIFHWG (ã (x1) , ã (x2) , · · · , ã (xn)) = n⊗
j=1 ( ã
( xj
))ωj
= ⟨⎛⎜⎜⎜⎝
γ n∏
j=1 a
( xj
)ωj n∏
j=1
( 1 + (γ − 1)
( 1 − a
( xj
)))ωj + (γ − 1) n∏ j=1
a ( xj
)ωj ,
γ n∏
j=1 b
( xj
)ωj n∏
j=1
( 1 + (γ − 1)
( 1 − b
( xj
)))ωj + (γ − 1) n∏ j=1
b ( xj
)ωj ,
γ n∏
j=1 c ( xj
)ωj n∏
j=1
( 1 + (γ − 1)
( 1 − c
( xj
)))ωj + (γ − 1) n∏ j=1
c ( xj
)ωj ⎞ ⎟⎟⎟⎠ ,
⎛ ⎜⎜⎜⎝
n∏ j=1
( 1 + (γ − 1) l
( xj
))ωj − n∏ j=1
( 1 − l
( xj
))ωj n∏
j=1
( 1 + (γ − 1) l
( xj
))ωj + (γ − 1) n∏ j=1
( 1 − l
( xj
))ωj , n∏
j=1
( 1 + (γ − 1) m
( xj
))ωj − n∏ j=1
( 1 − m
( xj
))ωj n∏
j=1
( 1 + (γ − 1) m
( xj
))ωj + (γ − 1) n∏ j=1
( 1 − m
( xj
))ωj , n∏
j=1
( 1 + (γ − 1) p
( xj
))ωj − n∏ j=1
( 1 − p
( xj
))ωj n∏
j=1
( 1 + (γ − 1) p
( xj
))ωj + (γ − 1) n∏ j=1
( 1 − p
( xj
))ωj ⎞ ⎟⎟⎟⎠
⟩ (4)
where ω = (ω1, ω2, · · · , ωn)T be the weight vector of ã(xj ) (j = 1, 2, · · · , n), and ωj > 0,∑n
j=1 ωj = 1. Yager [23] developed a nonlinear weighted aver-
age aggregation operator called power geometric (PG) operator based on the PA operator [24–31] and geometric mean [32–42], which can be defined as follows:
PG (a1, a2, · · · , an) = n∏
i=1 (ai)
(1+T (ai)) /
n∑ i=1
(1+T (ai))
(5)
where T (ai) = n∑
j=1 j /= i
Sup ( ai, aj
) , and Sup (a, b) is
the support for a from b, which satisfies the following three properties:
(1) Sup (a, b) ∈ [0, 1]; (2) Sup (a, b) = Sup (b, a); (3) Sup (a, b) ≥ Sup (x, y), if |a − b| < |x − y|. In this Section, we shall investigate the PG operator
under fuzzy number intuitionistic fuzzy environ- ments and propose the fuzzy number intuitionistic fuzzy Hamacher power weighted geometric (FNIFH- PWG) operator as follows.
Definition 5. Let ã ( xj
) = 〈(a
( xj
) , b
( xj
) , c
( xj
) ),(
l ( xj
) , m
( xj
) , p
( xj
))⟩ be a collection of FNIFEs,
ω = (ω1, ω2, · · · , ωn)T be the weighting vector of FNIFEs α̃j (j = 1, 2, · · · , n) and ωj ∈ [0, 1],∑n
j=1 ωj = 1, then we define the fuzzy number intu- itionistic fuzzy Hamacher power weighted geometric (FNIFHPWG) as follows:
4360 W. Fan / An approach to evaluating the knowledge innovation ability
FNIFHPWG (ã (x1) , ã (x2) , · · · , ã (xn))
= n
⊕ j=1
( ãj
)ωj (1+T (ãj )) /
n∑ j=1
ωj (1+T (ãj ))
= ⟨
⎛ ⎜⎜⎜⎜⎜⎜⎝
γ n∏
j=1 a ( xj
)ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j ))
n∏ j=1
( 1 + (γ − 1)
( 1 − a
( xj
)))ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j )) + (γ − 1)
n∏ j=1
a ( xj
)ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j ))
,
γ n∏
j=1 b ( xj
)ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j ))
n∏ j=1
( 1 + (γ − 1)
( 1 − b
( xj
)))ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j )) + (γ − 1)
n∏ j=1
b ( xj
)ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j ))
,
γ n∏
j=1 c ( xj
)ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j ))
n∏ j=1
( 1 + (γ − 1)
( 1 − c
( xj
)))ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j )) + (γ − 1)
n∏ j=1
c ( xj
)ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j ))
⎞ ⎟⎟⎟⎟⎟⎟⎠
,
⎛ ⎜⎜⎜⎜⎜⎜⎝
n∏ j=1
( 1 + (γ − 1) l
( xj
))ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j )) −
n∏ j=1
( 1 − l
( xj
))ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j ))
n∏ j=1
( 1 + (γ − 1) l
( xj
))ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j )) + (γ − 1)
n∏ j=1
( 1 − l
( xj
))ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j ))
,
n∏ j=1
( 1 + (γ − 1) m
( xj
))ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j )) −
n∏ j=1
( 1 − m
( xj
))ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j ))
n∏ j=1
( 1 + (γ − 1) m
( xj
))ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j )) + (γ − 1)
n∏ j=1
( 1 − m
( xj
))ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j ))
,
n∏ j=1
( 1 + (γ − 1) p
( xj
))ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j )) −
n∏ j=1
( 1 − p
( xj
))ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j ))
n∏ j=1
( 1 + (γ − 1) p
( xj
))ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j )) + (γ − 1)
n∏ j=1
( 1 − p
( xj
))ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j ))
⎞ ⎟⎟⎟⎟⎟⎟⎠
⟩
(6)
W. Fan / An approach to evaluating the knowledge innovation ability 4361
where
T ( α̃j
) =
n∑ i=1 i /= j
ωiSup ( α̃j, α̃i
) (7)
and Sup ( α̃j, α̃i
) is the support for α̃j from α̃i, with
the conditions:
1) Sup ( α̃i, α̃j
) ∈ [0, 1];
2) Sup ( α̃i, α̃j
) = Sup
( α̃i, α̃j
) ;
3) Sup ( α̃i, α̃j
) ≥ Sup (α̃s, α̃t ), if d
( αi, αj
) ≥
d (αs, αt ), where d is a distance measure.
It can be easily proved that the FNIFHPWG oper- ator has the following properties.
Theorem 1. (Monotonicity) Let α̃j (j = 1, 2, · · · , n) and α̃′j (j = 1, 2, · · · , n) be two collection of FNIFEs, ω = (ω1, ω2, · · · , ωn)T be the weighting vector of picture fuzzy numbers α̃j (j = 1, 2, · · · , n) and ωj ∈ [0, 1],
∑n j=1 ωj = 1, if α̃j ≤ α̃′j , for all j,
then
FNIFHPWG (α̃1, α̃2, · · · , α̃n) ≤ FNIFHPWG
( α̃
′ 1, α̃
′ 2, · · · , α̃′n
) (8)
Theorem 2. (Boundedness) Let α̃j (j = 1, 2, · · · , n) be a collection of FNIFEs, ω = (ω1, ω2, · · · , ωn)T be the weighting vector of FNIFEs α̃j (j = 1, 2, · · · , n), and let
α̃ − = min
j α̃j, α̃
+ = max j
α̃j
Then
α̃ − ≤ FNIFHPWG (α̃1, α̃2, · · · , α̃n) ≤ α̃+ (9)
Theorem 3. (Idempotency) Let α̃j (j = 1, 2, · · · , n) be a collection of FNIFEs, ω = (ω1, ω2, · · · , ωn)T be the weighting vector of FNIFEs α̃j (j = 1, 2, · · · , n) and ωj ∈ [0, 1],
∑n j=1 ωj = 1.
If all α̃j (j = 1, 2, · · · , n) are equal, i.e. α̃j = α̃ for all j, then
FNIFHPWG (α̃1, α̃2, · · · , α̃n) = α̃ (10)
4. An approach to evaluating the knowledge innovation ability of new ventures based on knowledge management with fuzzy number intuitionistic fuzzy information
Let A = {A1, A2, · · · , Am} be a discrete set of alternatives, and G = {G1, G2, · · · , Gn} be the set of attributes, ω = (ω1, ω2, · · · , ωn) is the weight- ing vector of the attribute Gj (j = 1, 2, · · · , n), where ωj ∈ [0, 1],
∑n j=1 ωj = 1. Suppose that R̃ =(
r̃ij ) m×n =
⟨( aij, bij, cij
) , ( lij, mij, pij
)⟩ m×n is the
fuzzy number intuitionistic fuzzy decision matrix, i = 1, 2, · · · , m, j = 1, 2, · · · , n.
Then, we apply the FNIFHPWG operator to MADM problems for evaluating the knowledge inno- vation ability of new ventures based on knowledge management with fuzzy number intuitionistic fuzzy information.
Step 1. Utilize the information given in matrix R̃, and the FNIFHPWG operator.
r̃i = FNIFHPWGω (r̃i1, r̃i2, · · · , r̃in) = n⊕
j=1
( r̃ij
)ωj (1+T (ãj )) /
n∑ j=1
ωj (1+T (ãj ))
= ⟨
⎛ ⎜⎜⎜⎜⎜⎜⎜⎝
γ n∏
j=1
( aij
)ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j ))
n∏ j=1
( 1 + (γ − 1)
( 1 − aij
))ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j )) + (γ − 1)
n∏ j=1
( aij
)ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j )) ,
γ n∏
j=1
( bij
)ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j ))
n∏ j=1
( 1 + (γ − 1)
( 1 −
( bij
)))ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j )) + (γ − 1)
n∏ j=1
( bij
)ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j )) ,
4362 W. Fan / An approach to evaluating the knowledge innovation ability
γ n∏
j=1
( cij
)ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j ))
n∏ j=1
( 1 + (γ − 1)
( 1 − cij
))ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j )) + (γ − 1)
n∏ j=1
( cij
)ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j ))
⎞ ⎟⎟⎟⎟⎟⎟⎟⎠
,
⎛ ⎜⎜⎜⎜⎜⎜⎜⎝
n∏ j=1
( 1 + (γ − 1)
( lij
))ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j )) −
n∏ j=1
( 1 −
( lij
))ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j ))
n∏ j=1
( 1 + (γ − 1)
( lij
))ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j )) + (γ − 1)
n∏ j=1
( 1 −
( lij
))ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j )) ,
n∏ j=1
( 1 + (γ − 1)
( mij
))ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j )) −
n∏ j=1
( 1 −
( mij
))ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j ))
n∏ j=1
( 1 + (γ − 1)
( mij
))ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j )) + (γ − 1)
n∏ j=1
( 1 −
( mij
))ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j )) ,
n∏ j=1
( 1 + (γ − 1)
( pij
))ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j )) −
n∏ j=1
( 1 −
( pij
))ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j ))
n∏ j=1
( 1 + (γ − 1)
( pij
))ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j )) + (γ − 1)
n∏ j=1
( 1 −
( pij
))ωj (1+T (h̃j )) /
n∑ j=1
ωj (1+T (h̃j ))
⎞ ⎟⎟⎟⎟⎟⎟⎟⎠
⟩
(11)
to derive the overall preference values r̃i (i = 1, 2, · · · , m) of the alternative Ai.
Step 2. Calculate the scores S (r̃i) (i = 1, 2, · · · , m) of the overall preference values r̃i (i = 1, 2, · · · , m) to rank all the alternatives Ai (i = 1, 2, · · · , m) and then to select the best one(s)
Step 3. Rank all the alternatives Ai (i = 1, 2, · · · , m) and select the best one(s) in accordance with S (r̃i) and H (r̃i) (i = 1, 2, · · · , m).
5. Numerical example
As a source of competitive advantage, new ven- tures’ knowledge innovation ability plays a key role in the business operating process based on knowledge management. Since china’ new ventures are low in knowledge innovation control, it is of great signifi- cance to improve their knowledge innovation ability,
therefore how to correctly evaluate the knowledge innovation ability are new topics. Suppose a group of experts plan to evaluate the knowledge innova- tion ability based on knowledge management. There are five possible enterprises Ai (i = 1, 2, 3, 4, 5) to select. The expert group selects four attributes to evaluate the five enterprises: ① G1 is knowledge capturing ability; ② G2 is knowledge internal- izing ability; ③ G3 is knowledge externalizing ability; ④ G4 is the ability of knowledge competi- tion and cooperation. The five possible enterprises Ai (i = 1, 2, 3, 4, 5) are to be evaluated by the deci- sion maker by using the fuzzy number intuitionistic fuzzy information under the four attributes men- tioned above, as listed in the following matrix.The five possible enterprises Ai (i = 1, 2, · · · , 5) are to be evaluated using the fuzzy number intuitionistic fuzzy values by the decision maker under the above four attributes, and construct, respectively, the deci- sion matrices as listed in the following matrices R̃ =
( r̃ij
) 5×4 as follows:
W. Fan / An approach to evaluating the knowledge innovation ability 4363
R̃ =
⎡ ⎢⎢⎢⎢⎢⎢⎣
〈(0.5, 0.6, 0.7) , (0.1, 0.2, 0.3)〉 〈(0.4, 0.5, 0.6) , (0.2, 0.3, 0.4)〉 〈(0.3, 0.4, 0.5) , (0.1, 0.2, 0.3)〉 〈(0.2, 0.3, 0.4) , (0.3, 0.4, 0.5)〉 〈(0.5, 0.6, 0.7) , (0.1, 0.2, 0.3)〉 〈(0.2, 0.3, 0.4) , (0.4, 0.5, 0.6)〉 〈(0.4, 0.5, 0.6) , (0.2, 0.3, 0.4)〉 〈(0.3, 0.4, 0.5) , (0.2, 0.3, 0.4)〉 〈(0.4, 0.5, 0.6) , (0.1, 0.2, 0.3)〉 〈(0.2, 0.3, 0.4) , (0.3, 0.4, 0.5)〉
〈(0.2, 0.3, 0.4) , (0.3, 0.4, 0.5)〉 〈(0.5, 0.6, 0.7) , (0.1, 0.2, 0.3)〉 〈(0.4, 0.5, 0.6) , (0.1, 0.2, 0.3)〉 〈(0.4, 0.5, 0.6) , (0.1, 0.2, 0.3)〉 〈(0.1, 0.2, 0.3) , (0.3, 0.4, 0.5)〉 〈(0.3, 0.4, 0.5) , (0.3, 0.4, 0.5)〉 〈(0.4, 0.5, 0.6) , (0.1, 0.2, 0.3)〉 〈(0.5, 0.6, 0.7) , (0.1, 0.2, 0.3)〉 〈(0.5, 0.6, 0.7) , (0.1, 0.2, 0.3)〉 〈(0.4, 0.5, 0.6) , (0.1, 0.2, 0.3)〉
⎤ ⎥⎥⎥⎥⎥⎥⎦
In the following, we apply the FNIFHPWG opera- tor to MADM problems for evaluating the knowledge innovation ability of new ventures based on knowl- edge management with fuzzy number intuitionistic fuzzy information.
Step 1. We utilize the information given in matrix R̃, and the FNIFHPWG operator to obtain the values r̃i of the enterprises Ai (i = 1, 2, · · · , 5). r̃1 = 〈(0.345, 0.446, 0.521) , (0.265, 0.323, 0.378)〉 r̃2 = 〈(0.238, 0.343, 0.479) , (0.356, 0.488, 0.590)〉 r̃3 = 〈(0.232, 0.298, 0.377) , (0.489, 0.521, 0.645)〉 r̃4 = 〈(0.398, 0.478, 0.592) , (0.289, 0.383, 0.408)〉 r̃5 = 〈(0.376, 0.492, 0.563) , (0.323, 0.383, 0.476)〉
Step 2. Calculate the scores S (r̃i) (i = 1, 2, · · · , 5) of the values r̃i (i = 1, 2, · · · , 5). S (r̃1) = 0.178, S (r̃2) = −0.101, S (r̃3) = −0.237 S (r̃4) = 0.254, S (r̃5) = 0.107 Step 3. Rank all the enterprises Ai (i = 1, 2, 3, 4, 5) in accordance with the scores S (r̃i) (i = 1, 2, · · · , 5): A4 � A1 � A5 � A3 � A2, and thus the most desirable enterprises is A4.
6. Conclusion
Knowledge innovation is the essential part of knowledge-based new ventures’ management opera- tion. Only when the knowledge innovation ability of a new venture can be properly evaluated can the enter- prise establish a rational incentive system so as to motivate employees to get actively involved in knowl- edge innovation and help raise the overall innovation
level of the enterprise. In this paper, we investi- gate the multiple attribute decision making problems with fuzzy number intuitionistic fuzzy information. Then, we develop the fuzzy number intuitionistic fuzzy Hamacher power weighted geometric (FNIFH- PWG) operator. Then, we apply the FNIFHPWG operator to deal with multiple attribute decision mak- ing for evaluating the knowledge innovation ability of new ventures based on knowledge management under the fuzzy number intuitionistic fuzzy environ- ments. Finally, an illustrative example for evaluating the knowledge innovation ability of new ventures based on knowledge management is given to ver- ify the developed approach. In our future studies, we shall extend our proposed operators and approaches to other application domains [43–54].
References
[1] I. Nonaka, The knowledge-creating company, Harvard Business Review 85 (2007), 7–8.
[2] P. Carrillo and P. Chinowsky, Exploiting knowledge man- agement: The engineering and construction perspective, Journal of Management in Engineering 22 (2006), 2–10.
[3] B. Petersen, T. Pedersen and M.A. Lyles, Closing knowl- edge gaps in foreign markets, Journal of International Business Studies 39 (2008), 1097–1113.
[4] J.C. Spender, Making knowledge the basis of a dynamic theory of the firm, Strategic Management Journal 17 (1996), 45–62.
[5] M. Kenney, Schumpeterian innovation and entrepreneurs in capitalism: A case study of the U.S. biotechnology industry, Research Policy 15 (1986), 21–31.
[6] S.G. Winter, Knowledge and Competence as Strategic Assets, Ballinger, 1987.
[7] A. Javernick-Will and R.E. Levitt, Mobilizing institutional knowledge for international projects, Journal of Construc- tion Engineering and Management 136 (2010), 430–441.
[8] A. Javernick-Will and W.R. Scott, Who needs to know what? Institutional knowledge and international projects, Journal
4364 W. Fan / An approach to evaluating the knowledge innovation ability
of Construction Engineering and Management 136 (2010), 546–557.
[9] F. Liu and X.H. Yuan, Fuzzy number intuitionistic fuzzy set, Fuzzy Systems and Mathematics 21(1) (2007), 88–91.
[10] X.F. Wang, Fuzzy number intuitionistic fuzzy arithmetic aggregation operators, International Journal of Fuzzy Sys- tems 10(2) (2008), 104–111.
[11] X.F. Wang, Fuzzy number intuitionistic fuzzy geometric aggregation operators and their application to decision mak- ing, Control and Decision 23(6) (2008), 607–612.
[12] R. Lin, X.F. Zhao and G.W. Wei, Fuzzy number intuitionistic fuzzy prioritized operators and their application to multiple attribute decision making, Journal of Intelligent and Fuzzy Systems 24 (2013), 879–888.
[13] S.-P. Wan, F. Wang, L.-L. Lin and J.-Y. Dong, Some new generalized aggregation operators for triangular intuitionis- tic fuzzy numbers and application to multi-attribute group decision making, Computers & Industrial Engineering 93 (2016), 286–301.
[14] J.-Y. Dong and S.-P. Wan, A new method for prioritized multi-criteria group decision making with triangular intu- itionistic fuzzy numbers, Journal of Intelligent and Fuzzy Systems 30(3) (2016), 1719–1733.
[15] J. Dong and S. Wan, A new method for multi-attribute group decision making with triangular intuitionistic fuzzy numbers, Kybernetes 45(1) (2016), 158–180.
[16] G.W. Wei, Approaches to interval intuitionistic trapezoidal fuzzy multiple attribute decision making with incomplete weight information, International Journal of Fuzzy Systems 17(3) (2015), 484–489.
[17] S. Zhou and W. Chang, Approach to multiple attribute deci- sion making based on the Hamacher operation with fuzzy number intuitionistic fuzzy information and their applica- tion, Journal of Intelligent and Fuzzy Systems 27(3) (2014), 1087–1094.
[18] Y. Wang, X. Peng and J. Bian, Study on the security of infor- mation system authentication scheme based on the fuzzy number intuitionistic fuzzy information, Journal of Intelli- gent and Fuzzy Systems 28(5) (2015), 2225–2232.
[19] H. Hamachar, Uber logische verknunpfungenn unssharfer Aussagen undderen Zugenhorige Bewertungsfunktione, in: Trappl, Klir, Riccardi(Eds.), Progress in Cybernatics and Systems Research, vol. 3, Hemisphere, Washington DC, 1978, pp. 276–288.
[20] S. Roychowdhury and B.H. Wang, On generalized Hamacher families of triangular operators, International Journal of Approximate Reasoning 19 (1998), 419–439.
[21] L. Zhou, X. Zhao and G. Wei, Hesitant fuzzy hamacher aggregation operators and their application to multiple attribute decision making, Journal of Intelligent and Fuzzy Systems 26(6) (2014), 2689–2699.
[22] P. Liu, Some hamacher aggregation operators based on the interval-valued intuitionistic fuzzy numbers and their appli- cation to group decision making, IEEE Trans Fuzzy Systems 22(1) (2014), 83–97.
[23] Z. Xu and R.R. Yager, Power-geometric operators and their use in group decision making, IEEE Transactions on Fuzzy Systems 18(1) (2010), 94–105.
[24] R.R. Yager, The power average operator, IEEE Transactions on Systems, Man, and Cybernetics-Part A 31(6) (2001), 724–731.
[25] G. Wei, Some linguistic power aggregating operators and their application to multiple attribute group decision mak- ing, Journal of Intelligent and Fuzzy Systems 25 (2013), 695–707.
[26] L.-G. Ran and G. Wei, Uncertain prioritized operators and their application to multiple attribute group decision mak- ing, Technological and Economic Development of Economy 21(1) (2015), 118–139.
[27] Z. Zhang, Hesitant fuzzy power aggregation operators and their application to multiple attribute group decision mak- ing, Inf Sci 234 (2013), 150–181.
[28] Y. He, Z. He, G. Wang and H. Chen, Hesitant fuzzy power bonferroni means and their application to multiple attribute decision making, IEEE Trans Fuzzy Systems 23(5) (2015), 1655–1668.
[29] L. Wang, Q. Shen and L. Zhu, Dual hesitant fuzzy power aggregation operators based on Archimedean t-conorm and t-norm and their application to multiple attribute group deci- sion making, Appl Soft Comput 38 (2016), 23–50.
[30] G. Wei, X. Zhao and R. Lin, Some hesitant interval-valued fuzzy aggregation operators and their applications to mul- tiple attribute decision making, Knowledge-Based Systems 46 (2013), 43–53.
[31] Y.J. Xu and H.M. Wang, Approaches based on 2-tuple lin- guistic power aggregation operators for multiple attribute group decision making under linguistic environment, Applied Soft Computing Journal 11(5) (2011), 3988–3997.
[32] L. Rui, G. Wei, H. Wang and X. Zhao, Choquet integrals of weighted triangular fuzzy linguistic information and their applications to multiple attribute decision making, Jour- nal of Business Economics and Management 15(5) (2014), 795–809.
[33] R.R. Yager and D.P. Filev, Induced ordered weighted aver- aging operators, IEEE Transactions on Systems, Man, and Cybernetics- Part B 29 (1999), 141–150.
[34] Z.S. Xu and Q.L. Da, An overview of operators for aggregat- ing information, International Journal of Intelligent System 18 (2003), 953–969.
[35] R. Lin, X. Zhao, H. Wang and G. Wei, Hesitant fuzzy linguistic aggregation operators and their application to multiple attribute decision making, Journal of Intelligent and Fuzzy Systems 27 (2014), 49–63.
[36] G. Wei and X. Zhao, Induced hesitant interval-valued fuzzy einstein aggregation operators and their application to mul- tiple attribute decision making, Journal of Intelligent and Fuzzy Systems 24 (2013), 789–803.
[37] N. Zhang, Method for aggregating correlated interval grey linguistic variables and its application to decision mak- ing, Technological and Economic Development of Economy 19(2) (2013), 189–202.
[38] G. Wei, An approach to multiple attribute group deci- sion making with interval intuitionistic trapezoidal fuzzy information, Technological and Economic Development of Economy 18(2) (2012), 317–330.
[39] P.D. Liu and F. Jin, The multi-attribute group decision mak- ing method based on the interval grey linguistic variables, African Journal of Business Management 4(17) (2010), 3708–3715.
[40] P.D. Liu and X. Zhang, The multi-attribute group decision making method based on the interval grey linguistic vari- ables weighted geometric aggregation operator, Control and Decision 26(5) (2011), 743–747.
[41] F. Jin, P.D. Liu and X. Zhang, The multi attribute group deci- sion making method based on the interval grey linguistic variables weighted harmonic aggregation operators, Tech- nological and Economic Development of Economy 19(3) (2013), 409–430.
[42] G.W. Wei, A method for multiple attribute group decision making based on the ET-WG and ET-OWG operators with
W. Fan / An approach to evaluating the knowledge innovation ability 4365
2-tuple linguistic information, Expert Systems with Appli- cations 37(12)(2010), 7895–7900.
[43] F. Herrera and E. Herrera-Viedma, Linguistic decision anal- ysis: Steps for solving decision problems under linguistic information, Fuzzy Sets and Systems 115 (2000), 67–82.
[44] F. Herrera, E. Herrera-Viedma and L. Martı́nez, A fusion approach for managing multi-granularity linguistic term sets in decision making, Fuzzy Sets and Systems 114 (2000), 43–58.
[45] M. Delgado, F. Herrera, E. Herrera-Viedma, M.J. Martin- Bautista, L. Martı́nez and M.A. Vila, A communication model based on the 2-tuple fuzzy linguistic representation for a distributed intelligent agent system on internet, Soft Computing 6 (2002), 320–328.
[46] O. Cordón, F. Herrera and I. Zwir, Linguistic modeling by hierarchical systems of linguistic rules, IEEE Transactions on Fuzzy Systems 10 (2002), 2–20.
[47] G.W. Wei, J.M. Wang and J. Chen, Potential optimality and robust optimality in multiattribute decision analysis with incomplete information: A comparative study, Deci- sion Support Systems 55(3) (2013), 679–684.
[48] Y. Ouyang and W. Pedrycz, A new model for intuitionistic fuzzy multi-attributes decision making, European Journal of Operational Research 249(2) (2016), 677–682.
[49] Z.S. Xu and R.R. Yager, Intuitionistic fuzzy bonferroni means, IEEE Transactions on Systems Man and Cybernetics Part B-Cybernetics 41 (2011), 568–578.
[50] G.W. Wei, GRA method for multiple attribute decision making with incomplete weight information in intuition- istic fuzzy setting, Knowledge-Based Systems 23 (2010), 243–247.
[51] G.W. Wei, Gray relational analysis method for intuitionistic fuzzy multiple attribute decision making, Expert Systems with Applications 38 (2011), 11671–11677.
[52] D.F. Li, Mathematical-programming approach to matrix games with payoffs represented by atanassov’s interval- valued intuitionistic fuzzy sets, Ieee Transactions on Fuzzy Systems 18 (2010), 1112–1128.
[53] D.F. Li, TOPSIS-Based nonlinear-programming methodol- ogy for multiattribute decision making with interval-valued intuitionistic fuzzy sets, IEEE Transactions on Fuzzy Sys- tems 18 (2010), 299–311.
[54] D.F. Li, Closeness coefficient based nonlinear pro- gramming method for interval-valued intuitionistic fuzzy multiattribute decision making with incomplete prefer- ence information, Applied Soft Computing 11 (2011), 3402–3418.
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