Some Interval-Valued Pythagorean Fuzzy Einstein Weighted Averaging Aggregation Operators and Their Application to Group Decision Making
-
Khaista Rahman
,
Saleem Abdullah
Abstract
In this paper, we introduce the notion of Einstein aggregation operators, such as the interval-valued Pythagorean fuzzy Einstein weighted averaging aggregation operator and the interval-valued Pythagorean fuzzy Einstein ordered weighted averaging aggregation operator. We also discuss some desirable properties, such as idempotency, boundedness, commutativity, and monotonicity. The main advantage of using the proposed operators is that these operators give a more complete view of the problem to the decision makers. These operators provide more accurate and precise results as compared the existing method. Finally, we apply these operators to deal with multiple-attribute group decision making under interval-valued Pythagorean fuzzy information. For this, we construct an algorithm for multiple-attribute group decision making. Lastly, we also construct a numerical example for multiple-attribute group decision making.
1 Introduction
Atanassov [1] introduced the concept of intuitionistic fuzzy sets (IFSs) characterized by a membership function and a non-membership function. It is more suitable for dealing with fuzziness and uncertainty than the ordinary fuzzy set developed by Zadeh [33] characterized by membership function. In 1986, many scholars [2], [3], [4], [5], [6], [22] have done works in the field of IFS and its applications. Particularly, information aggregation is a very crucial research area in IFS theory that has been receiving more and more focus. Xu [23] developed some basic arithmetic aggregation operators, including intuitionistic fuzzy weighted averaging (IFWA) aggregation operator, intuitionistic fuzzy ordered weighted averaging (IFOWA) aggregation operator, and intuitionistic fuzzy hybrid averaging (IFHA) aggregation operator, and applied them to group decision making. Xu and Yager [26] defined some basic geometric aggregation operators, such as intuitionistic fuzzy weighted geometric (IFWG) aggregation operator, intuitionistic fuzzy ordered weighted geometric (IFOWG) aggregation operator, and intuitionistic fuzzy hybrid geometric (IFHG) aggregation operator. In Refs. [24], [25], Chen and Xu familiarized a series of a new types of aggregation operators, such as interval-valued IFWA (IIFWA) aggregation operator, interval-valued IFOWA (IIFOWA) aggregation operator, interval-valued IFHA (IIFHA) aggregation operator, interval-valued IFWG (IIFWG) aggregation operator, interval-valued IFOWG (IIFOWG) aggregation operator, and interval-valued IFHG (IIFHG) aggregation operator. In Refs. [20], [21], Wang and Liu introduced the concept of intuitionistic fuzzy Einstein weighted geometric (IFEWG) aggregation operator, intuitionistic fuzzy Einstein ordered weighted geometric (IFEOWG) aggregation operator, intuitionistic fuzzy Einstein weighted averaging (IFEWA) aggregation operator, and intuitionistic fuzzy Einstein ordered weighted averaging (IFEOWA) aggregation operator, and applied them to group decision making. In Refs. [29], [30], [31], [32], Yu also worked in the field of IFS theory and introduced many aggregation operators and applied them to group decision making. However, there are many cases where the decision maker may provide the degree of membership and non-membership of a particular attribute in such a way that their sum is greater than one. Therefore, Yager [27] introduced the concept of another set called Pythagorean fuzzy set. The Pythagorean fuzzy set is a more powerful tool for solving uncertain problems. Like intuitionistic fuzzy aggregation operators, Pythagorean fuzzy aggregation operators have also become an interesting and important area for research, after the advent of the Pythagorean fuzzy set theory. In Ref. [28], Yager and Abbasov introduced the notion of two new Pythagorean fuzzy aggregation operators, such as Pythagorean fuzzy weighted averaging (PFWA) aggregation operator and Pythagorean fuzzy ordered weighted averaging (PFOWA) operator. In Refs. [12], [13], [14], [16], [17], Rahman et al. introduced the concept of Pythagorean fuzzy hybrid averaging (PFHA) aggregation operator, Pythagorean fuzzy weighted geometric (PFWG) aggregation operator, Pythagorean fuzzy ordered weighted geometric (PFOWG) operator, Pythagorean fuzzy hybrid geometric (PFHG) aggregation operator, and Pythagorean fuzzy Einstein weighted geometric (PFEWG) operator, and applied them to group decision making. In Refs. [7], [8], Garg introduced the notion of Pythagorean fuzzy Einstein weighted averaging (PFEWA) aggregation operator, Pythagorean fuzzy Einstein ordered weighted averaging (PFEOWA) operator, generalized PFEWA (GPFEWA) aggregation operator, generalized PFEOWA (GPFEOWA) aggregation operator, PFWG aggregation operator, PFOWG aggregation operator, PFEWG aggregation operator, Pythagorean fuzzy Einstein ordered weighted geometric (PFEOWG) aggregation operator, GPFEOWA aggregation operator, and generalized PFEOWG (GPFEOWG) aggregation operator, and applied them to group decision making. In Ref. [11], Peng and Yang introduced the notion of interval-valued PFWA (IVPFWA) aggregation operator and interval-valued PFWG (IVPFWG) aggregation operator. In Refs. [15], [18], Rahman et al. introduced the concept of interval-valued PFOWA (IVPFOWA) aggregation operator, interval-valued PFHA (IVPFHWA) aggregation operator, interval-valued PFOWG (IVPFOWG) aggregation operator, and interval-valued Pythagorean fuzzy hybrid weighted geometric operator, and applied them to group decision making. In Refs. [9], [10], [19], [34], many scholars worked in Pythagorean fuzzy set theory and aggregation operators.
Thus, keeping the advantages of these operators, in this paper, we introduce the notion of interval-valued PFEWA (IVPFEWA) aggregation operator and interval-valued PFEOWA (IVPFEOWA) aggregation operator. By comparison with the existing method, it is decided that the method developed in this paper is a good complement to the existing method.
The remainder of this paper is structured as follows. In Section 2, we give some basic definitions and results, which will be used in later sections. In Section 3, we introduce some Einstein operations for interval-valued Pythagorean fuzzy values. In Section 4, we introduce the notion of IVPFEWA and IVPFEOWA aggregation operators. In Section 5, we apply these operators to deal with multiple-attribute group decision-making (MAGDM) problems with Pythagorean fuzzy information. In Section 6, we develop a numerical example. In Section 7, we present our conclusion.
2 Preliminaries
Definition 1 ([11]): Let K be a fixed set, then an IVPFS can be defined as
where
As
and
If
then it is called the interval-valued Pythagorean fuzzy index of k to I, where
Definition 2 ([11]). Let λ=([uλ, vλ ], [xλ, yλ ]) be an IVPFN, then the score function and accuracy function of λ can be defined as
and
If λ1 and λλ2 are two IVPFNs, then
If S(λ1)<S(λ2), then λ1<λ2.
If S(λ1)=S(λ2), then we have the following three conditions:
If H(λ1)=H(λ2), then λ1=λ2.
If H(λ1)<H(λ2), then λ1<λ2.
If H(λ1)>H(λ2), then λ1>λ2.
Definition 3 ([11]): Let
where w=(w1, w2, …, wn)T is the weighted vector of λj with wj∈[0, 1] and
Definition 4 ([18]): Let
where w=(w1, w2, …, wn)T is the weighted vector of λj with wj∈[0, 1] and
Definition 5 ([18]): An IVPFHA operator of dimension n is a mapping IVPFHA: Θn → Θ, which has an associated vector w=(w1, w2, …, wn)T, such that wj∈[0, 1] and
where
3 Some Einstein Operations of Interval-Valued Pythagorean Fuzzy Sets
Definition 6: Let λ=([u, v], [x, y]), λ1=([u1, v1], [x1, y1]), and λ2=([u2, v2], [x2, y2]) be three IVPFNs and δ>0, then some Einstein operations for λ, λ1, λ2 can be defined as follows:
4 Some Interval-Valued Pythagorean Fuzzy Einstein Averaging Aggregation Operators
In this section, we introduce two interval-valued Einstein aggregation operators, namely the IVPFEWA and IVPFEOWA operators. We also discuss some desirable properties of these proposed operators, such as idempotency, boundedness, commutativity, and monotonicity. These operators provide more accurate and precise results as compared to the existing method.
4.1 IVPFEWA Aggregation Operator
Definition 7. Let λj=([uj, vj], [xj, yj]) (j=1, 2, 3, …, n) be the collection of IVPFVs, then an IVPFEWA operator of dimension n is a mapping IVPFEWAw: Θn→Θ, and
where w=(w1, w2, w3, …, wn)T is the weighted vector of λj such that wj∈[0, 1] and
Theorem 1. Let
where w=(w1, w2, w3, …, wn)T is the weighted vector of λj (j=1, 2, 3, …, n) such that wj∈[0, 1] (j=1, 2, 3, …, n) and
Proof. We can prove this theorem by mathematical induction. First we show that Eq. (22) holds for n=1.
Taking the left-hand side,
Taking the right-hand side,
From Eqs. (23) and (24), we have Eq. (22) holds for n=1. Now we show that Eq. (22) holds for n=k. That is
If Eq. (25) holds for n=k, then we show that Eq. (25) holds for n=k+1.
Let
Now putting these values in Eq. (26), we have
Again putting the values of (t1w2)2+(t2w1)2, (t2w2)2+(t1w1)2, (p1a2)2+(a1p2)2, (p2a2)2+(p1a1)2, r1b1,
Hence, Eq. (22) holds for n=k+1. Thus, Eq. (22) holds for all n.□
Lemma 1 ([16]). Let λj>0, wj>0 (j=1, 2, …, n) and
where the equality holds if and only if λ1=λ2= … =λn.
Theorem 2. Let
Proof. Straightforward.□
Example 1. Let
and let w=(0.1, 0.2, 0.3, 0.4)T be the weighted vector of λj (j=1, 2, 3, 4), then we have
Now
Theorem 3. Commutativity: Let λj and
Proof. As we know that
and
as
Theorem 4. Idempotency: If λj=λ for all j (j=1, 2, 3, …, n), where λ=([u, v], [x, y]), then
Proof. As λj=λ for all j, then we have
This completes the proof.□
Theorem 5. Boundedness: Let
for all wj and also
Proof. Let
Now by the score function, we have
as from Eqs. (38) and (39), we have
Thus, Eq. (34) always holds.□
Theorem 6. Monotonicity: If
Proof. As we know that
and
as
4.2 IVPFEOWA Aggregation Operator
Definition 8: Let λj (j=1, 2, 3, …, n) be a collection of IVPFVs, then an IVPFEOWA operator of dimension n is a mapping IVPFEOWAw: Θn→Θ, and
where (σ(1), σ(2), …, σ(n)) is a permutation of (1, 2, …, n) such that σ(j)≤σ(j–1) for all j, and w=(w1, w2, …, wn)T is the weighted vector of λσ(j) (j=1, 2, …, n) such that wj∈[0, 1] and
Theorem 7. Let
where (σ(1), σ(2), …, σ(n)) is a permutation of (1, 2, …, n) such that σ(j)≤σ(j−1) for all j, and w=(w1, w2, …wn)T is the weighted vector of λσ(j) (j=1, 2, …n) such that wj∈[0, 1] (j=1, 2, …, n) and
Proof. Proof is similar to Theorem 1.□
Theorem 8. Let
Proof. Straightforward.□
Theorem 9. Commutativity: If
Proof. Proof is similar to Theorem 3.□
Theorem 10. Idempotency: If λj=λ for all j (j=1, 2, 3, …, n), where λ=([u, v], [x, y]), then
Proof. Proof is similar to Theorem 4.□
Theorem 11. Boundedness: Let
for all wj and
Proof. Proof is similar to Theorem 5.□
Theorem 12. Monotonicity: If
Proof. Proof is similar to Theorem 6.□
5 An Approach to the MAGDM Problem Based on Interval-Valued Pythagorean Fuzzy Information
Algorithm 1. Let X={X1, X2, X3, …, Xm} be a finite set of m alternatives, and C={C1, C2, C3, …, Cn} be a finite set of attributes. Suppose the grade of the alternatives Xi (i=1, 2, …, m) on attributes Cj (j=1, 2, …, n) given by decision makers are IVPFNs. Let D={D1, D2, D3, …, Dk} be the set of k decision makers, and let w=(w1, w2, …, wn)T be the weighted vector of the attributes Cj (j=1, 2, …, n), such that wj∈[0, 1] and
Step 1: In this step, we construct the interval-valued Pythagorean fuzzy decision-making matrices,
Step 2: If the criteria have two types, such as benefit criteria and cost criteria, then the interval-valued Pythagorean fuzzy decision matrices,
and
Step 3: In this step, we apply the IVPFEWA operator to aggregate all the individual normalized interval-valued Pythagorean fuzzy decision matrices,
Step 4: In this step, we apply the IVPFEWA operator to aggregate all preference values.
Step 5: In this step, we calculate the score functions. If there is no difference between two or more than two scores, then we must find out the accuracy degrees of the collective overall preference values.
Step 6: Arrange the scores of all alternatives in descending order and select that alternative having the highest score function.
6 Illustrative Example
Suppose a company wants to invest money in the following best options: X1, car company; X2, food company; and X3, computer company. There are three experts Ds (s=1, 2, 3) from a group to act as decision makers, whose weight vector is ω=(0.2, 0.3, 0.5)T. There are many factors that must be considered when selecting the most suitable company; however, here, we have to consider only the following four criteria, whose weighted vector is w=(0.1, 0.2, 0.3, 0.4)T:
C1: risk analysis,
C2: growth analysis,
C3: social political impact analysis,
C4: environmental analysis,
where C1 and C3, are cost-type criteria and C2 and C4 are benefit-type criteria, i.e. the attributes have two types of criteria. Thus, we must change the cost-type criteria into the benefit-type criteria.
Interval-Valued Pythagorean Fuzzy Decision Matrix of D1.
| X1 | X2 | X3 | |
|---|---|---|---|
| C1 | ([0.5, 0.8], [0.3, 0.4]) | ([0.6, 0.7], [0.3, 0.6]) | ([0.3, 0.7], [0.3, 0.5]) |
| C2 | ([0.3, 0.5], [0.6, 0.7]) | ([0.3, 0.7], [0.2, 0.6]) | ([0.3, 0.6], [0.4, 0.7]) |
| C3 | ([0.5, 0.7], [0.3, 0.7]) | ([0.5, 0.6], [0.3, 0.7]) | ([0.2, 0.6], [0.3, 0.7]) |
| C4 | ([0.3, 0.6], [0.6, 0.7]) | ([0.6, 0.5], [0.2, 0.7]) | ([0.3, 0.4], [0.5, 0.6]) |
Interval-Valued Pythagorean Fuzzy Decision Matrix of D2.
| X1 | X2 | X3 | |
|---|---|---|---|
| C1 | ([0.5, 0.6], [0.3, 0.5]) | ([0.5, 0.7], [0.3, 0.6]) | ([0.2, 0.8], [0.3, 0.4]) |
| C2 | ([0.3, 0.4], [0.6, 0.8]) | ([0.3, 0.8], [0.2, 0.6]) | ([0.3, 0.6], [0.3, 0.7]) |
| C3 | ([0.4, 0.5], [0.3, 0.8]) | ([0.5, 0.7], [0.3, 0.6]) | ([0.2, 0.6], [0.3, 0.8]) |
| C4 | ([0.3, 0.6], [0.5, 0.7]) | ([0.3, 0.4], [0.2, 0.8]) | ([0.3, 0.5], [0.5, 0.7]) |
Interval-Valued Pythagorean Fuzzy Decision Matrix of D3.
| X1 | X2 | X3 | |
|---|---|---|---|
| C1 | ([0.3, 0.8], [0.5, 0.6]) | ([0.3, 0.5], [0.5, 0.7]) | ([0.2, 0.4], [0.5, 0.7]) |
| C2 | ([0.5, 0.7], [0.3, 0.4]) | ([0.4, 0.6], [0.5, 0.8]) | ([0.5, 0.7], [0.2, 0.5]) |
| C3 | ([0.3, 0.6], [0.4, 0.6]) | ([0.3, 0.5], [0.5, 0.6]) | ([0.2, 0.8], [0.4, 0.6]) |
| C4 | ([0.5, 0.7], [0.3, 0.4]) | ([0.5, 0.7], [0.2, 0.4]) | ([0.5, 0.6], [0.3, 0.5]) |
Normalized Pythagorean Fuzzy Decision Matrix R1.
| X1 | X2 | X3 | |
|---|---|---|---|
| C1 | ([0.3, 0.4], [0.5, 0.8]) | ([0.3, 0.6], [0.6, 0.7]) | ([0.3, 0.5], [0.3, 0.7]) |
| C2 | ([0.3, 0.5], [0.6, 0.7]) | ([0.3, 0.7], [0.2, 0.6]) | ([0.3, 0.6], [0.4, 0.7]) |
| C3 | ([0.3, 0.7], [0.5, 0.7]) | ([0.3, 0.7], [0.5, 0.6]) | ([0.3, 0.7], [0.2, 0.6]) |
| C4 | ([0.3, 0.6], [0.6, 0.7]) | ([0.6, 0.5], [0.2, 0.7]) | ([0.3, 0.4], [0.5, 0.6]) |
Normalized Pythagorean Fuzzy Decision Matrix R2.
| X1 | X2 | X3 | |
|---|---|---|---|
| C1 | ([0.3, 0.5], [0.5, 0.6]) | ([0.3, 0.6], [0.5, 0.7]) | ([0.3, 0.4], [0.2, 0.8]) |
| C2 | ([0.3, 0.4], [0.6, 0.8]) | ([0.3, 0.8], [0.2, 0.6]) | ([0.3, 0.6], [0.3, 0.7]) |
| C3 | ([0.3, 0.8], [0.4, 0.5]) | ([0.3, 0.6], [0.5, 0.7]) | ([0.3, 0.8], [0.2, 0.6]) |
| C4 | ([0.3, 0.6], [0.5, 0.7]) | ([0.3, 0.4], [0.2, 0.8]) | ([0.3, 0.5], [0.5, 0.7]) |
Normalized Pythagorean Fuzzy Decision Matrix R3.
| X1 | X2 | X3 | |
|---|---|---|---|
| C1 | ([0.5, 0.6], [0.3, 0.8]) | ([0.5, 0.7], [0.3, 0.5]) | ([0.5, 0.7], [0.2, 0.4]) |
| C2 | ([0.5, 0.7], [0.3, 0.4]) | ([0.4, 0.6], [0.5, 0.8]) | ([0.5, 0.7], [0.2, 0.5]) |
| C3 | ([0.4, 0.6], [0.3, 0.6]) | ([0.5, 0.6], [0.3, 0.5]) | ([0.4, 0.6], [0.2, 0.8]) |
| C4 | ([0.5, 0.7], [0.3, 0.4]) | ([0.5, 0.7], [0.2, 0.4]) | ([0.5, 0.6], [0.3, 0.5]) |
Collective Interval-Valued Pythagorean Fuzzy Decision Matrix R.
| X1 | X2 | X3 | |
|---|---|---|---|
| C1 | ([0.413, 0.537], [0.389, 0.738]) | ([0.413, 0.653], [0.405, 0.595]) | ([0.413, 0.593], [0.216, 0.562]) |
| C2 | ([0.413, 0.593], [0.429, 0.563]) | ([0.352, 0.692], [0.320, 0.697]) | ([0.413, 0.653], [0.259, 0.595]) |
| C3 | ([0.352, 0.692], [0.363, 0.587]) | ([0.413, 0.622], [0.389, 0.576]) | ([0.352, 0.693], [0.200, 0.697]) |
| C4 | ([0.413, 0.653], [0.405, 0.536]) | ([0.475, 0.593], [0.200, 0.563]) | ([0.413, 0.538], [0.389, 0.576]) |
Pythagorean Fuzzy Ordered Decision Matrix R1.
| X1 | X2 | X3 | |
|---|---|---|---|
| C1 | ([0.3, 0.7], [0.5, 0.7]) | ([0.3, 0.7], [0.2, 0.6]) | ([0.3, 0.7], [0.2, 0.6]) |
| C2 | ([0.3, 0.6], [0.6, 0.7]) | ([0.6, 0.5], [0.2, 0.7]) | ([0.3, 0.6], [0.4, 0.7]) |
| C3 | ([0.3, 0.5], [0.6, 0.7]) | ([0.3, 0.7], [0.5, 0.6]) | ([0.3, 0.5], [0.3, 0.7]) |
| C4 | ([0.3, 0.4], [0.5, 0.8]) | ([0.3, 0.6], [0.6, 0.7]) | ([0.3, 0.4], [0.5, 0.6]) |
Pythagorean Fuzzy Ordered Decision Matrix R2.
| X1 | X2 | X3 | |
|---|---|---|---|
| C1 | ([0.3, 0.8], [0.4, 0.5]) | ([0.3, 0.8], [0.2, 0.6]) | ([0.3, 0.8], [0.2, 0.6]) |
| C2 | ([0.3, 0.5], [0.5, 0.6]) | ([0.3, 0.6], [0.5, 0.7]) | ([0.3, 0.6], [0.3, 0.7]) |
| C3 | ([0.3, 0.6], [0.5, 0.7]) | ([0.3, 0.6], [0.5, 0.7]) | ([0.3, 0.5], [0.5, 0.7]) |
| C4 | ([0.3, 0.4], [0.6, 0.8]) | ([0.3, 0.4], [0.2, 0.8]) | ([0.3, 0.4], [0.2, 0.8]) |
Pythagorean Fuzzy Ordered Decision Matrix R3.
| X1 | X2 | X3 | |
|---|---|---|---|
| C1 | ([0.5, 0.7], [0.3, 0.4]) | ([0.5, 0.7], [0.2, 0.4]) | ([0.5, 0.7], [0.2, 0.4]) |
| C2 | ([0.5, 0.7], [0.3, 0.4]) | ([0.5, 0.7], [0.3, 0.5]) | ([0.5, 0.7], [0.2, 0.5]) |
| C3 | ([0.4, 0.6], [0.3, 0.6]) | ([0.5, 0.6], [0.3, 0.5]) | ([0.5, 0.6], [0.3, 0.5]) |
| C4 | ([0.5, 0.6], [0.3, 0.8]) | ([0.4, 0.6], [0.5, 0.8]) | ([0.4, 0.6], [0.2, 0.8]) |
Collective Pythagorean Fuzzy Ordered Decision Matrix R.
| X1 | X2 | X3 | |
|---|---|---|---|
| C1 | ([0.413, 0.734], [0.363, 0.481]) | ([0.413, 0.734], [0.200, 0.495]) | ([0.413, 0.734], [0.200, 0.492]) |
| C2 | ([0.413, 0.630], [0.404, 0.509]) | ([0.476, 0.638], [0.323, 0.595]) | ([0.413, 0.653], [0.259, 0.595]) |
| C3 | ([0.352, 0.582], [0.404, 0.649]) | ([0.413, 0.622], [0.389, 0.576]) | ([0.413, 0.553], [0.351, 0.595]) |
| C4 | ([0.413, 0.512], [0.412, 0.800]) | ([0.352, 0.550], [0.399, 0.779]) | ([0.352, 0.512], [0.241, 0.758]) |
Step 2: In this step, we normalize the decision matrices.
Step 3: In this step, we apply the IVPFEWA operator to aggregate all the individual normalized interval-valued Pythagorean fuzzy decision matrices,
Step 4: In this step, we apply the IVPFEWA aggregation operator to aggregate all preference values:
Step 5: In this step, we calculate the score functions:
Step 6: Arrange the scores of all alternatives in descending order and select that alternative having the highest score function. Hence, X3>X2>X1. Thus, the best alternative is X3.
For the IVPFEOWA aggregation operator:
Step 1: In this step, we construct the interval-valued Pythagorean fuzzy ordered decision matrices.
Step 2: In this step, we apply the IVPFEOWA operator to aggregate all the individual interval-valued Pythagorean fuzzy ordered decision matrices,
Step 3: In this step, we apply the IVPFEOWA aggregation operator to aggregate all preference values:
Step 4: In this step, we calculate the score functions:
Step 5: Arrange the scores of all alternatives in descending order and select that alternative having the highest score function. Hence, X3>X2>X1. Thus, the best alternative is X3.
7 Conclusion
In this paper, we have developed the notions of the IVPFEWA operator, IVPFEOWA operator, and interval-valued Pythagorean fuzzy Einstein hybrid weighted averaging operator. We have also discussed some of their desirable properties, such as idempotency, boundedness, commutativity, and monotonicity. Finally, we have applied these operators to deal with the MAGDM problem under interval-valued Pythagorean fuzzy information. For this, we constructed an algorithm for the MAGDM problem. Lastly, we also developed a numerical example for MAGDM.
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Articles in the same Issue
- An Optimized K-Harmonic Means Algorithm Combined with Modified Particle Swarm Optimization and Cuckoo Search Algorithm
- Texture Feature Extraction Using Intuitionistic Fuzzy Local Binary Pattern
- Leaf Disease Segmentation From Agricultural Images via Hybridization of Active Contour Model and OFA
- Deadline Constrained Task Scheduling Method Using a Combination of Center-Based Genetic Algorithm and Group Search Optimization
- Efficient Classification of DDoS Attacks Using an Ensemble Feature Selection Algorithm
- Distributed Multi-agent Bidding-Based Approach for the Collaborative Mapping of Unknown Indoor Environments by a Homogeneous Mobile Robot Team
- An Efficient Technique for Three-Dimensional Image Visualization Through Two-Dimensional Images for Medical Data
- Combined Multi-Agent Method to Control Inter-Department Common Events Collision for University Courses Timetabling
- An Improved Particle Swarm Optimization Algorithm for Global Multidimensional Optimization
- A Kernel Probabilistic Model for Semi-supervised Co-clustering Ensemble
- Pythagorean Hesitant Fuzzy Information Aggregation and Their Application to Multi-Attribute Group Decision-Making Problems
- Using an Efficient Optimal Classifier for Soil Classification in Spatial Data Mining Over Big Data
- A Bayesian Multiresolution Approach for Noise Removal in Medical Magnetic Resonance Images
- Gbest-Guided Artificial Bee Colony Optimization Algorithm-Based Optimal Incorporation of Shunt Capacitors in Distribution Networks under Load Growth
- Graded Soft Expert Set as a Generalization of Hesitant Fuzzy Set
- Universal Liver Extraction Algorithm: An Improved Chan–Vese Model
- Software Effort Estimation Using Modified Fuzzy C Means Clustering and Hybrid ABC-MCS Optimization in Neural Network
- Handwritten Indic Script Recognition Based on the Dempster–Shafer Theory of Evidence
- An Integrated Intuitionistic Fuzzy AHP and TOPSIS Approach to Evaluation of Outsource Manufacturers
- Automatically Assess Day Similarity Using Visual Lifelogs
- A Novel Bio-Inspired Algorithm Based on Social Spiders for Improving Performance and Efficiency of Data Clustering
- Discriminative Training Using Noise Robust Integrated Features and Refined HMM Modeling
- Self-Adaptive Mussels Wandering Optimization Algorithm with Application for Artificial Neural Network Training
- A Framework for Image Alignment of TerraSAR-X Images Using Fractional Derivatives and View Synthesis Approach
- Intelligent Systems for Structural Damage Assessment
- Some Interval-Valued Pythagorean Fuzzy Einstein Weighted Averaging Aggregation Operators and Their Application to Group Decision Making
- Fuzzy Adaptive Genetic Algorithm for Improving the Solution of Industrial Optimization Problems
- Approach to Multiple Attribute Group Decision Making Based on Hesitant Fuzzy Linguistic Aggregation Operators
- Cubic Ordered Weighted Distance Operator and Application in Group Decision-Making
- Fault Signal Recognition in Power Distribution System using Deep Belief Network
- Selector: PSO as Model Selector for Dual-Stage Diabetes Network
- Oppositional Gravitational Search Algorithm and Artificial Neural Network-based Classification of Kidney Images
- Improving Image Search through MKFCM Clustering Strategy-Based Re-ranking Measure
- Sparse Decomposition Technique for Segmentation and Compression of Compound Images
- Automatic Genetic Fuzzy c-Means
- Harmony Search Algorithm for Patient Admission Scheduling Problem
- Speech Signal Compression Algorithm Based on the JPEG Technique
- i-Vector-Based Speaker Verification on Limited Data Using Fusion Techniques
- Prediction of User Future Request Utilizing the Combination of Both ANN and FCM in Web Page Recommendation
- Presentation of ACT/R-RBF Hybrid Architecture to Develop Decision Making in Continuous and Non-continuous Data
- An Overview of Segmentation Algorithms for the Analysis of Anomalies on Medical Images
- Blind Restoration Algorithm Using Residual Measures for Motion-Blurred Noisy Images
- Extreme Learning Machine for Credit Risk Analysis
- A Genetic Algorithm Approach for Group Recommender System Based on Partial Rankings
- Improvements in Spoken Query System to Access the Agricultural Commodity Prices and Weather Information in Kannada Language/Dialects
- A One-Pass Approach for Slope and Slant Estimation of Tri-Script Handwritten Words
- Secure Communication through MultiAgent System-Based Diabetes Diagnosing and Classification
- Development of a Two-Stage Segmentation-Based Word Searching Method for Handwritten Document Images
- Pythagorean Fuzzy Einstein Hybrid Averaging Aggregation Operator and its Application to Multiple-Attribute Group Decision Making
- Ensembles of Text and Time-Series Models for Automatic Generation of Financial Trading Signals from Social Media Content
- A Flame Detection Method Based on Novel Gradient Features
- Modeling and Optimization of a Liquid Flow Process using an Artificial Neural Network-Based Flower Pollination Algorithm
- Spectral Graph-based Features for Recognition of Handwritten Characters: A Case Study on Handwritten Devanagari Numerals
- A Grey Wolf Optimizer for Text Document Clustering
- Classification of Masses in Digital Mammograms Using the Genetic Ensemble Method
- A Hybrid Grey Wolf Optimiser Algorithm for Solving Time Series Classification Problems
- Gray Method for Multiple Attribute Decision Making with Incomplete Weight Information under the Pythagorean Fuzzy Setting
- Multi-Agent System Based on the Extreme Learning Machine and Fuzzy Control for Intelligent Energy Management in Microgrid
- Deep CNN Combined With Relevance Feedback for Trademark Image Retrieval
- Cognitively Motivated Query Abstraction Model Based on Associative Root-Pattern Networks
- Improved Adaptive Neuro-Fuzzy Inference System Using Gray Wolf Optimization: A Case Study in Predicting Biochar Yield
- Predict Forex Trend via Convolutional Neural Networks
- Optimizing Integrated Features for Hindi Automatic Speech Recognition System
- A Novel Weakest t-norm based Fuzzy Fault Tree Analysis Through Qualitative Data Processing and Its Application in System Reliability Evaluation
- FCNB: Fuzzy Correlative Naive Bayes Classifier with MapReduce Framework for Big Data Classification
- A Modified Jaya Algorithm for Mixed-Variable Optimization Problems
- An Improved Robust Fuzzy Algorithm for Unsupervised Learning
- Hybridizing the Cuckoo Search Algorithm with Different Mutation Operators for Numerical Optimization Problems
- An Efficient Lossless ROI Image Compression Using Wavelet-Based Modified Region Growing Algorithm
- Predicting Automatic Trigger Speed for Vehicle-Activated Signs
- Group Recommender Systems – An Evolutionary Approach Based on Multi-expert System for Consensus
- Enriching Documents by Linking Salient Entities and Lexical-Semantic Expansion
- A New Feature Selection Method for Sentiment Analysis in Short Text
- Optimizing Software Modularity with Minimum Possible Variations
- Optimizing the Self-Organizing Team Size Using a Genetic Algorithm in Agile Practices
- Aspect-Oriented Sentiment Analysis: A Topic Modeling-Powered Approach
- Feature Pair Index Graph for Clustering
- Tangramob: An Agent-Based Simulation Framework for Validating Urban Smart Mobility Solutions
- A New Algorithm Based on Magic Square and a Novel Chaotic System for Image Encryption
- Video Steganography Using Knight Tour Algorithm and LSB Method for Encrypted Data
- Clay-Based Brick Porosity Estimation Using Image Processing Techniques
- AGCS Technique to Improve the Performance of Neural Networks
- A Color Image Encryption Technique Based on Bit-Level Permutation and Alternate Logistic Maps
- A Hybrid of Deep CNN and Bidirectional LSTM for Automatic Speech Recognition
- Database Creation and Dialect-Wise Comparative Analysis of Prosodic Features for Punjabi Language
- Trapezoidal Linguistic Cubic Fuzzy TOPSIS Method and Application in a Group Decision Making Program
- Histopathological Image Segmentation Using Modified Kernel-Based Fuzzy C-Means and Edge Bridge and Fill Technique
- Proximal Support Vector Machine-Based Hybrid Approach for Edge Detection in Noisy Images
- Early Detection of Parkinson’s Disease by Using SPECT Imaging and Biomarkers
- Image Compression Based on Block SVD Power Method
- Noise Reduction Using Modified Wiener Filter in Digital Hearing Aid for Speech Signal Enhancement
- Secure Fingerprint Authentication Using Deep Learning and Minutiae Verification
- The Use of Natural Language Processing Approach for Converting Pseudo Code to C# Code
- Non-word Attributes’ Efficiency in Text Mining Authorship Prediction
- Design and Evaluation of Outlier Detection Based on Semantic Condensed Nearest Neighbor
- An Efficient Quality Inspection of Food Products Using Neural Network Classification
- Opposition Intensity-Based Cuckoo Search Algorithm for Data Privacy Preservation
- M-HMOGA: A New Multi-Objective Feature Selection Algorithm for Handwritten Numeral Classification
- Analogy-Based Approaches to Improve Software Project Effort Estimation Accuracy
- Linear Regression Supporting Vector Machine and Hybrid LOG Filter-Based Image Restoration
- Fractional Fuzzy Clustering and Particle Whale Optimization-Based MapReduce Framework for Big Data Clustering
- Implementation of Improved Ship-Iceberg Classifier Using Deep Learning
- Hybrid Approach for Face Recognition from a Single Sample per Person by Combining VLC and GOM
- Polarity Analysis of Customer Reviews Based on Part-of-Speech Subcategory
- A 4D Trajectory Prediction Model Based on the BP Neural Network
- A Blind Medical Image Watermarking for Secure E-Healthcare Application Using Crypto-Watermarking System
- Discriminating Healthy Wheat Grains from Grains Infected with Fusarium graminearum Using Texture Characteristics of Image-Processing Technique, Discriminant Analysis, and Support Vector Machine Methods
- License Plate Recognition in Urban Road Based on Vehicle Tracking and Result Integration
- Binary Genetic Swarm Optimization: A Combination of GA and PSO for Feature Selection
- Enhanced Twitter Sentiment Analysis Using Hybrid Approach and by Accounting Local Contextual Semantic
- Cloud Security: LKM and Optimal Fuzzy System for Intrusion Detection in Cloud Environment
- Power Average Operators of Trapezoidal Cubic Fuzzy Numbers and Application to Multi-attribute Group Decision Making
Articles in the same Issue
- An Optimized K-Harmonic Means Algorithm Combined with Modified Particle Swarm Optimization and Cuckoo Search Algorithm
- Texture Feature Extraction Using Intuitionistic Fuzzy Local Binary Pattern
- Leaf Disease Segmentation From Agricultural Images via Hybridization of Active Contour Model and OFA
- Deadline Constrained Task Scheduling Method Using a Combination of Center-Based Genetic Algorithm and Group Search Optimization
- Efficient Classification of DDoS Attacks Using an Ensemble Feature Selection Algorithm
- Distributed Multi-agent Bidding-Based Approach for the Collaborative Mapping of Unknown Indoor Environments by a Homogeneous Mobile Robot Team
- An Efficient Technique for Three-Dimensional Image Visualization Through Two-Dimensional Images for Medical Data
- Combined Multi-Agent Method to Control Inter-Department Common Events Collision for University Courses Timetabling
- An Improved Particle Swarm Optimization Algorithm for Global Multidimensional Optimization
- A Kernel Probabilistic Model for Semi-supervised Co-clustering Ensemble
- Pythagorean Hesitant Fuzzy Information Aggregation and Their Application to Multi-Attribute Group Decision-Making Problems
- Using an Efficient Optimal Classifier for Soil Classification in Spatial Data Mining Over Big Data
- A Bayesian Multiresolution Approach for Noise Removal in Medical Magnetic Resonance Images
- Gbest-Guided Artificial Bee Colony Optimization Algorithm-Based Optimal Incorporation of Shunt Capacitors in Distribution Networks under Load Growth
- Graded Soft Expert Set as a Generalization of Hesitant Fuzzy Set
- Universal Liver Extraction Algorithm: An Improved Chan–Vese Model
- Software Effort Estimation Using Modified Fuzzy C Means Clustering and Hybrid ABC-MCS Optimization in Neural Network
- Handwritten Indic Script Recognition Based on the Dempster–Shafer Theory of Evidence
- An Integrated Intuitionistic Fuzzy AHP and TOPSIS Approach to Evaluation of Outsource Manufacturers
- Automatically Assess Day Similarity Using Visual Lifelogs
- A Novel Bio-Inspired Algorithm Based on Social Spiders for Improving Performance and Efficiency of Data Clustering
- Discriminative Training Using Noise Robust Integrated Features and Refined HMM Modeling
- Self-Adaptive Mussels Wandering Optimization Algorithm with Application for Artificial Neural Network Training
- A Framework for Image Alignment of TerraSAR-X Images Using Fractional Derivatives and View Synthesis Approach
- Intelligent Systems for Structural Damage Assessment
- Some Interval-Valued Pythagorean Fuzzy Einstein Weighted Averaging Aggregation Operators and Their Application to Group Decision Making
- Fuzzy Adaptive Genetic Algorithm for Improving the Solution of Industrial Optimization Problems
- Approach to Multiple Attribute Group Decision Making Based on Hesitant Fuzzy Linguistic Aggregation Operators
- Cubic Ordered Weighted Distance Operator and Application in Group Decision-Making
- Fault Signal Recognition in Power Distribution System using Deep Belief Network
- Selector: PSO as Model Selector for Dual-Stage Diabetes Network
- Oppositional Gravitational Search Algorithm and Artificial Neural Network-based Classification of Kidney Images
- Improving Image Search through MKFCM Clustering Strategy-Based Re-ranking Measure
- Sparse Decomposition Technique for Segmentation and Compression of Compound Images
- Automatic Genetic Fuzzy c-Means
- Harmony Search Algorithm for Patient Admission Scheduling Problem
- Speech Signal Compression Algorithm Based on the JPEG Technique
- i-Vector-Based Speaker Verification on Limited Data Using Fusion Techniques
- Prediction of User Future Request Utilizing the Combination of Both ANN and FCM in Web Page Recommendation
- Presentation of ACT/R-RBF Hybrid Architecture to Develop Decision Making in Continuous and Non-continuous Data
- An Overview of Segmentation Algorithms for the Analysis of Anomalies on Medical Images
- Blind Restoration Algorithm Using Residual Measures for Motion-Blurred Noisy Images
- Extreme Learning Machine for Credit Risk Analysis
- A Genetic Algorithm Approach for Group Recommender System Based on Partial Rankings
- Improvements in Spoken Query System to Access the Agricultural Commodity Prices and Weather Information in Kannada Language/Dialects
- A One-Pass Approach for Slope and Slant Estimation of Tri-Script Handwritten Words
- Secure Communication through MultiAgent System-Based Diabetes Diagnosing and Classification
- Development of a Two-Stage Segmentation-Based Word Searching Method for Handwritten Document Images
- Pythagorean Fuzzy Einstein Hybrid Averaging Aggregation Operator and its Application to Multiple-Attribute Group Decision Making
- Ensembles of Text and Time-Series Models for Automatic Generation of Financial Trading Signals from Social Media Content
- A Flame Detection Method Based on Novel Gradient Features
- Modeling and Optimization of a Liquid Flow Process using an Artificial Neural Network-Based Flower Pollination Algorithm
- Spectral Graph-based Features for Recognition of Handwritten Characters: A Case Study on Handwritten Devanagari Numerals
- A Grey Wolf Optimizer for Text Document Clustering
- Classification of Masses in Digital Mammograms Using the Genetic Ensemble Method
- A Hybrid Grey Wolf Optimiser Algorithm for Solving Time Series Classification Problems
- Gray Method for Multiple Attribute Decision Making with Incomplete Weight Information under the Pythagorean Fuzzy Setting
- Multi-Agent System Based on the Extreme Learning Machine and Fuzzy Control for Intelligent Energy Management in Microgrid
- Deep CNN Combined With Relevance Feedback for Trademark Image Retrieval
- Cognitively Motivated Query Abstraction Model Based on Associative Root-Pattern Networks
- Improved Adaptive Neuro-Fuzzy Inference System Using Gray Wolf Optimization: A Case Study in Predicting Biochar Yield
- Predict Forex Trend via Convolutional Neural Networks
- Optimizing Integrated Features for Hindi Automatic Speech Recognition System
- A Novel Weakest t-norm based Fuzzy Fault Tree Analysis Through Qualitative Data Processing and Its Application in System Reliability Evaluation
- FCNB: Fuzzy Correlative Naive Bayes Classifier with MapReduce Framework for Big Data Classification
- A Modified Jaya Algorithm for Mixed-Variable Optimization Problems
- An Improved Robust Fuzzy Algorithm for Unsupervised Learning
- Hybridizing the Cuckoo Search Algorithm with Different Mutation Operators for Numerical Optimization Problems
- An Efficient Lossless ROI Image Compression Using Wavelet-Based Modified Region Growing Algorithm
- Predicting Automatic Trigger Speed for Vehicle-Activated Signs
- Group Recommender Systems – An Evolutionary Approach Based on Multi-expert System for Consensus
- Enriching Documents by Linking Salient Entities and Lexical-Semantic Expansion
- A New Feature Selection Method for Sentiment Analysis in Short Text
- Optimizing Software Modularity with Minimum Possible Variations
- Optimizing the Self-Organizing Team Size Using a Genetic Algorithm in Agile Practices
- Aspect-Oriented Sentiment Analysis: A Topic Modeling-Powered Approach
- Feature Pair Index Graph for Clustering
- Tangramob: An Agent-Based Simulation Framework for Validating Urban Smart Mobility Solutions
- A New Algorithm Based on Magic Square and a Novel Chaotic System for Image Encryption
- Video Steganography Using Knight Tour Algorithm and LSB Method for Encrypted Data
- Clay-Based Brick Porosity Estimation Using Image Processing Techniques
- AGCS Technique to Improve the Performance of Neural Networks
- A Color Image Encryption Technique Based on Bit-Level Permutation and Alternate Logistic Maps
- A Hybrid of Deep CNN and Bidirectional LSTM for Automatic Speech Recognition
- Database Creation and Dialect-Wise Comparative Analysis of Prosodic Features for Punjabi Language
- Trapezoidal Linguistic Cubic Fuzzy TOPSIS Method and Application in a Group Decision Making Program
- Histopathological Image Segmentation Using Modified Kernel-Based Fuzzy C-Means and Edge Bridge and Fill Technique
- Proximal Support Vector Machine-Based Hybrid Approach for Edge Detection in Noisy Images
- Early Detection of Parkinson’s Disease by Using SPECT Imaging and Biomarkers
- Image Compression Based on Block SVD Power Method
- Noise Reduction Using Modified Wiener Filter in Digital Hearing Aid for Speech Signal Enhancement
- Secure Fingerprint Authentication Using Deep Learning and Minutiae Verification
- The Use of Natural Language Processing Approach for Converting Pseudo Code to C# Code
- Non-word Attributes’ Efficiency in Text Mining Authorship Prediction
- Design and Evaluation of Outlier Detection Based on Semantic Condensed Nearest Neighbor
- An Efficient Quality Inspection of Food Products Using Neural Network Classification
- Opposition Intensity-Based Cuckoo Search Algorithm for Data Privacy Preservation
- M-HMOGA: A New Multi-Objective Feature Selection Algorithm for Handwritten Numeral Classification
- Analogy-Based Approaches to Improve Software Project Effort Estimation Accuracy
- Linear Regression Supporting Vector Machine and Hybrid LOG Filter-Based Image Restoration
- Fractional Fuzzy Clustering and Particle Whale Optimization-Based MapReduce Framework for Big Data Clustering
- Implementation of Improved Ship-Iceberg Classifier Using Deep Learning
- Hybrid Approach for Face Recognition from a Single Sample per Person by Combining VLC and GOM
- Polarity Analysis of Customer Reviews Based on Part-of-Speech Subcategory
- A 4D Trajectory Prediction Model Based on the BP Neural Network
- A Blind Medical Image Watermarking for Secure E-Healthcare Application Using Crypto-Watermarking System
- Discriminating Healthy Wheat Grains from Grains Infected with Fusarium graminearum Using Texture Characteristics of Image-Processing Technique, Discriminant Analysis, and Support Vector Machine Methods
- License Plate Recognition in Urban Road Based on Vehicle Tracking and Result Integration
- Binary Genetic Swarm Optimization: A Combination of GA and PSO for Feature Selection
- Enhanced Twitter Sentiment Analysis Using Hybrid Approach and by Accounting Local Contextual Semantic
- Cloud Security: LKM and Optimal Fuzzy System for Intrusion Detection in Cloud Environment
- Power Average Operators of Trapezoidal Cubic Fuzzy Numbers and Application to Multi-attribute Group Decision Making
