A Linguistic-Valued Approximate Reasoning Approach for Financial Decision Making

Xin Liu; Ying Wang; Xiaonan Li; Li Zou

doi:10.2991/ijcis.2017.10.1.21

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Volume 10, Issue 1, 2017, Pages 312 - 319

A Linguistic-Valued Approximate Reasoning Approach for Financial Decision Making

Authors

Xin Liu¹^,liuxin67812@163.com, Ying Wang², Xiaonan Li², Li Zou²^{, *}^,zoulicn@163.com

^*corresponding author

Corresponding Author

Li Zouzoulicn@163.com

Received 11 April 2016, Accepted 29 September 2016, Available Online 1 January 2017.

DOI: 10.2991/ijcis.2017.10.1.21 How to use a DOI?
Keywords: Linguistic Truth-Valued Lattice Implication Algebra; Approximate Reasoning; Decision Making; Linguistic-Valued Similarity
Abstract: In order to process the linguistic-valued information with uncertainty in the financial decision- making, the present work uses a lattice-valued logical algebra - lattice implication algebra to deal with both comparable and incomparable linguistic truth-values. A new personal financial decision auxiliary modeling framework based on the lattice-ordered linguistic truth-valued logic is proposed. The concepts of linguistic-valued similarity and linguistic valued degree assignment function are introduced, and then a linguistic-valued approximate reasoning approach for financial decision making is presented. A case study is then provided which illustrates that the proposed approach is more flexible and effective with handling the financial decision-making problem involved with linguistic-valued information with uncertainty.
Copyright: © 2017, the Authors. Published by Atlantis Press.
Open Access: This is an open access article under the CC BY-NC license (http://creativecommons.org/licences/by-nc/4.0/).

1. Introduction

In the representation and processing of uncertain information ¹, we often get cross some information represented with linguistic values in natural language. In this regard, the researchers put forward the theories about linguistic variables ^2–3. People often judge the truth-values of a fuzzy proposition with linguistic hedges rather than exactly true or false, such as very true, quite false, somewhat true, slightly false and so on. A linguistic hedge possesses an intuitive meaning which can be expressed by a semantic ordering relation, e.g. Approximately True<True, while Very True>True. These truth values are called linguistic truth-values ⁴.

The knowledge representation and processing are the basis of knowledge engineering and decision making. Many researchers have proposed some ideas and methods on knowledge representation. Elbedwehy et al. have proposed a semantic model (CKRMCC) based on cognitive aspects that enables cognitive computer to process the knowledge as the human mind and find a suitable representation of that knowledge ⁵. Bentahar et al. have proposed such a conceptual framework based on taxonomy of the most important argumentation models ⁶. Orriols-Puig and Casillas have studied two key aspects in Fuzzy-UCS: the ability of the system to learn models from data streams where concepts change over time and the behavior of different fuzzy representations ⁷. In intuitionistic fuzzy reasoning, Xu and Cai have provided a survey of the aggregation techniques of intuitionistic fuzzy information ⁸. Many approaches have been presented for representation and reasoning of uncertain knowledge in the last decade ^9–11. Ha et al. have presented a similarity measure to improve the evaluation method of weighted fuzzy production rules and the multilevel fuzzy reasoning ¹².

The conventional linguistic-valued handling methodology is based on fuzzy set theory, which generally converts the linguistic information into a membership function, after which the generated fuzzy set will be transformed back into a word or proposition using linguistic approximation ¹³. The process of converting each other is mainly based on the extension principle, is usually time consuming, computationally complex, and involving loss of information ¹⁴. It would be more natural and reasonable to represent and reason about linguistic information in its original form, i.e., through the symbolic way ¹⁵. Although most symbolic approaches have the advantages that without the loss of information and computational simplicity by avoiding use of membership function ^{14, 16}, it requires that the linguistic information is totally ordered and can be manipulated by indexes. This limits the application of symbolic linguistic approach to more general situations where partially ordered information often involved.

Partially ordered information is ubiquitous in our daily decision-making problems and more flexible than total orders to represent incomplete, uncertain and imprecise knowledge ¹⁷. Lattice, a special kind of partially ordered structure, has been shown to be an appropriate and efficient structure for representing ordinal qualitative information in the real world due to its additional operations and better properties ^18–19. Linguistic hedge algebra can be constructed as essentially a partially ordered structure according to the natural meanings of the represented linguistic terms, and generally a lattice. There have been some important works on lattice-ordered linguistic-valued based approach for decision making problems under uncertain environment ²⁰.

Furthermore, in order to establish approximate reasoning scheme with positive evidence and negative evidence, Zou and other scholars have established the linguistic truth-valued intuitionistic fuzzy lattice(LI_2n) which is based on the linguistic truth-valued lattice implication algebra(L_V(n×2))^21–23. Kahramanetc et al. have surveyed the status of fuzzy multi-criteria decision-making methods and classified these methods into two parts: fuzzy multi-attribute decision-making (MADM) and fuzzy multi-objective decision-making (MODM) ²⁴. Feki et al. have presented a new method for ranking physical features of consumer goods according to their relevancy to multiple evaluators’ perception at different levels and selecting the most important ones for quality characterization ²⁵.

In order to process the linguistic-valued information with uncertainty in the financial decision-making, the present work proposes the algorithms of the distance and the similarity between two linguistic values based on 2n-element linguistic truth-valued fuzzy lattice L_V(n×2), then a approximate reasoning method which can deal with both comparable and incomparable linguistic values is presented. A new personal financial decision modeling framework based on the lattice-ordered linguistic truth-valued logic is proposed. In order to grade the investors’ income and deposit, a linguistic-valued degree assignment function is discussed, and a linguistic-valued approximate reasoning approach for financial decision making is presented then. An example is provided to illustrate the flexibility and effectiveness of the proposed method for handling the financial decision-making problem involved with linguistic-valued information with uncertainty.

The rest of the paper is organized as follows: Section 2 outlines some preliminary concepts about the linguistic truth-valued algebra and their corresponding propositional logic system. Section 3 presents a kind of similarity based on 2n-element linguistic truth-valued fuzzy lattice and establishes a linguistic-valued approximated reasoning method. A knowledge representation scheme based on linguistic-valued credibility is discussed and a financial decision-making model is constructed in Section 4. The paper is then concluded in Section 5.

2. Linguistic Truth-valued Propositional Logic

2.1. Linguistic Truth-Valued lattice implication algebra

Definition 1.²³

Let (L, ∨, ∧, O, I) be a bounded lattice with universal boundaries O (the least element) and I (the greatest element) respectively, and “′” be an order–reversing involution. For any x, y, z∈L, if mapping →: L × L→L satisfies:

(1)
x → (y → z) = y → (x → z);
(2)
x → x= I;
(3)
x → y = y′ → x′;
(4)
x → y = y → x implies x = y;
(5)
(x → y) → y = (y → x) → x;
(6)
(x ∨ y) → z = (x → z)∨(y → z);
(7)
(x ∧ y) → z = (x → z) ∧(y → z).

Then (L, ∨, ∧, ′, →, O, I) is a lattice implication algebra (LIA for short).

Definition 2.²³

Let AD_n={h₀, h₁, …, h_n} be a set with n modifiers and h₀<h₁<…<h_n, MT={f, t} be a set of meta truth values, and f<t. Denote L_V(n×2)=AD_n×MT.

Define a mapping g: L_V(n×2)→L_n×L₂,

g((ci,mt))={(ai,b1),mt=f,(ai,b2),mt=t,

Then g is a bijection, denote its inverse mapping as g⁻¹. For any x, y∈L_V(n×2), define x∨y=g⁻¹(g(x)∨g(y)), x∧y=g⁻¹(g(x)∧g(y)), x′=g⁻¹((g(x))′), x→y=g⁻¹(g(x)→g(y)), then L_V(n×2)=(L_V(n×2), ∨, ∧, ′, →, (h_n, f), (h_n, t)) is called a linguistic truth-valued lattice implication algebra generated by AD_n and MT.

2.2. Six-element Linguistic Truth-Valued Propositional Logic

Definition 3.

Let H={h₁, h₂, h₃} and the basic truth value set C={t, f}, where t= true, f =false. Let V be a linguistic truth-valued set, every linguistic truth value v∈V is composed of a linguistic hedge operator and a basic word c, i.e. V=H×C where the linguistic hedge operator set H is linear and finite set. Denote V={(h₃, t), (h₂, t), (h₁, t), (h₁, f), (h₂, f), (h₃, f) }, L₆=(V,∨, ∧, →) , the operation “∨” and “∧” in the Hasse diagram of L₆ (Fig.1), (h_i, t)′=(h_i, f) and its operations “→”are defined as follows:

(1)
(h_i, t)→(h_j, f)=(h_max{1,i+j-3}, f) ;
(2)
(h_i, f)→(h_j, t)=(h_min{3,i+j}, t);
(3)
(h_i, t)→(h_j, t)=(h_min{3,3-i+j}, t);
(4)
(h_i, f)→(h_j, f)=(h_min{3,3-j+i},t).

So L₆= (V, ∨, ∧, ′, →)is a lattice implication algebra.

The formal language of the six-element linguistic truth-valued propositional logic is made up of the following symbols:

1.
Constant: a, b, c, … ;
2.
Propositional symbol: F, G, H, … ;
3.
Connective operator: ¬, ∨, ∧,→ , ↔,…;
4.
Others: (,).

Definition 4.

Let P be an atomic proposition, then h_iP is called an atomic proposition of 6LTVP, where h_i∈H.

Definition 5.

The formula in 6LTVP is defined as follows recursively:

(1)
6LTVP atom h_iP is a formula;
(2)
If A is a formula, then (h_iA), (¬ A) is the formula, h_i∈H;
(3)
If A and B are formulas, then (A∨B), (A∧B), (A→B) are formulas;
(4)
All the formulas are the symbolic strings which use (1) to (3) with finite times.

Definition 6.

(Assignment Function) A valuation of 6LTVP is a propositional algebra homomorphism, γ: 6LTVP→L₆.

3. Approximate reasoning method

3.1. Linguistic-Valued similarity based on L_2n

In this section, we introduce a kind of similarity based on 2n-element linguistic truth-valued fuzzy lattice L_V(n×2).

Definition 7.

In the L_V(n×2), for any A=(h_i, C_k), B=(h_j, C_l)∈L_V(n×2), the distance between two linguistic values is defined as follows:

(1)d(A,B)={|i−j|,Ck=Cl|i−(n−j+1)|,Ck≠Cl,where 0≤d≤n

Definition 8.

In the L_V(n×2), for any A=(h_i, C_k), B=(h_j, C_l)∈L_V(n×2), the similarity between two linguistic values is defined as follows:

(2)S(A,B)={(h|n−d|,t),Ck=Cl(h(d+1),f),Ck≠Cl

Theorem 1.

In the L_V(n×2), for any A=(h_i, C_k), B=(h_j, C_l)∈L_V(n×2), the following properties holds:

(1)
(h_n, f)≤S(A, B)≤(h_n, t);
(2)
if and only if A=B, (h_i, C_k)=(h_j, C_l) then S(A, B)=(h_n, t);
(3)
S(A, B)=S(B, A);
(4)
S(A, B)= (h_n, f) if and only if i=j and C_k≠C_l;
(5)
if A≤B≤C, then S (A, C) ≤ min{S (A, B), S (B, C)}.

Proof.

According to Definition 7 and Definition 8

(1)
When d=0, C_k=C_l, S (A, B) is the largest, denote by (h_n, t); when d=0, C_k≠C_l, S(A, B) is the smallest, denote by (h_n, f).
(2)
When A=B, there exists (h_i, C_k)= (h_j, C_l), then d(A, B)=|i-j|=0 and S(A, B)=(h_n, t). If S(A, B)=(h_n, t), then d(A, B)=|i-j|=0, C_k=C_l. Hence h_i=h_j, i.e. A=B.
(3)
We have d(A,B)={|i−j| ,Ck=Cl|i−(n−j+1)|,Ck≠Cl and d(B,A)={|j−i| ,Ck=Cl|j−(n−i+1)|,Ck≠Cl , then d(A, B)=d(B, A). Hence S(A, B)=S(B, A) is obtained.
(4)
For (h_n, t) is the maximum element, (h_n, f) is the minimum element in L_V(n×2), so the larger the distance, the smaller the similarity.
(5)
For any A=(h_i, C_l), B=(h_j, C_m), C=(h_k, C_n) ∈L_V(n×2).
- Case1: if A≤B≤C and C_l=C_m=C_n, then i≤j≤k, d(A, B)=|i-j|, d(A, C)=|i-k|, d(B, C)=|j-k|. Hence d(A, C)≥d(A, B), d(A, C)≥d(B, C). Because the similarity decreases when the distance increases, S(A, C)≤S(A, B), S(A, C)≤S(B, C). So S(A, C)≤min{S(A, B), S(B, C)}.
- Case2: if A=(h_i, t), B=(h_j, f), C=(h_k, f) and A>B>C, j<k, then d(A, B)=|i+j-n-1|, d(B, C)=|j-k|,d(A, C)=|i+k-n-1|. Hence S(A, B)=(h_{(|i+j-n-1|+1)}, f), S(B, C)=(h_|n-|j-k||, t), S(A, C)=(h_{(|i+k-n-1|+1)}, f). Because j<k, so |i+j-n-1|+1<|i+k-n-1|+1, S(A, B)=(h_{(|i+j-n-1|+1)}, f)>S(A, C)=(h_{(|i+k-n-1|+1)}, f). So S(A, C)≤min{S(A, B), S(B, C)}.
- Case3: if A=(h_i, t), B=(h_j, t), C=(h_k, f) and A>B>C, j<i, then d(A, B)=|i-j|, d(B, C)=|j+k-n-1|,d(A, C)=|i+k-n-1|. Hence S(A, B)=(h_|n-|i-j||, t), S(B, C)=(h_{(|j+k-n-1|+1)}, f), S(A, C)=(h_{(|i+k-n-1|+1)}, f). Because j<i, so |j+k-n-1|+1<|i+k-n-1|+1, S(B, C)=(h_{(|j+k-n-1|+1)}, f)>S(A, C)=(h_{(|i+k-n-1|+1)}, f). So S(A, C)≤min{S(A, B), S(B, C)}.

3.2. Approximate reasoning method based on L_V(n×2)

The approximated reasoning is simply summarized as the following steps: Firstly, we calculate the similarity between the facts and the antecedents of the rules. Then pattern matching is used to choose which rule will be activated. Secondly, by using the correction function based on the similarity measure, we construct the rule of inference phase correction after reasoning result is obtained.

Consider a simple rule, R: P→Q. The basic reasoning model is:

Rule: P→Q
Input: P*
Output: Q*

The algorithm of 2n-element linguistic-valued approximate reasoning is detailed as follows:

Step 1: Input all the rules R₁, R₂, …, R_m, and set i=1, j=1.
Step 2: Input the facts P* (i.e. the input part of the reasoning).
Step 3: Set the threshold τ_i=(h_n-i+1, t) for the rules activation.
Step 4: Calculate the similarity S(P_j, P*) between the facts P* and the antecedent P_j of the rule R_j.
Step 5: Compare S(P_j, P*) with τ_i. If S(P_j, P*)= τ, then the corresponding rule R_j will be activated and go to Step 6. If j<m, then set j=j+1 and go to Step 4. If i<3, then set i=i+1 and go to Step 3.
Step 6: Take S(Q_j, Q*)=S(P_j, P*), where Q_j is the after of the rule R_j. Then we can obtain the approximate reasoning results Q* through formula (1) and (2).
Step 7: Output the conclusion Q* and terminate the algorithm.
Note 1: It is worth mentioning that the selection of the threshold τ is closely related to the application field, so the system actual case study is required before operation. If there is an unsatisfactory result, one can choose different threshold values.

4. Linguistic-Valued Approximate Reasoning Model for Financial Decision Making

4.1. Knowledge representation model based on L₆

The knowledge representation method proposed in this paper is on the basis of propositional logic representation. We express the values of knowledge by linguistic values directly.

The following is an example of a simple financial investment decision making problem. The function of the auxiliary decision-making process is to help users decide whether save their money or invest in the stock market. Some investors may put their money on these two aspects. Individual investors’ investment scheme depends on their income and the bank deposit, according to the following principle:

(1)
if the investor has less deposit, then all of his income should be saved;
(2)
if the investor has much more deposit and income, then he could consider investing in stocks;
(3)
if the investor has more deposits and income, then he should invest most of the extra money to buy stocks and save the few;
(4)
if the investor has less deposit and his income is much more, then he should save most of the extra money and invest the few to buy stocks.

Note that if the investor is low-income or very little income, then he is regarded as has no extra money.

Here the capital letters represent the investors. The lowercase letters represent the functions. Taking the individual as the universe, requirements:

•
D represents investor has deposit;
•
I represents investor has income;
•
IS represents that the investor should invest in stocks;
•
IM represents that the investor should save money;
•
MS represents that the money for the stock is greater than the money saved in the bank;
•
MM represents that the money saved in the bank is greater than the money for the stock.

Assume that

1.
The value of investor’s much more deposits is: (h₃, t)D;
2.
The value of investor’s more deposits is: (h₂, t)D;
3.
The value of investor’s less deposits is: (h₁, t)D;
4.
The value of investor’s much more income is: (h₃, t)I ;
5.
The value of investor’s more income is: (h₂, t) I;
6.
The value of investor’s less income is: (h₁, t) I;

The different investment strategies are represented by a logical expression.”

•
Rule 1 can be expressed as (h₁, t)D→IM.
•
Rule 2 can be expressed as (h₃, t)D∧(h₃, t)I→IS.
•
Rule 3 can be expressed as (h₂, t)D∧(h₂, t) I→IS∧IM∧MS.
•
Rule 4 can be expressed as (h₁, t)D∧(h₃, t) I→IS∧IM∧MM.

4.2. Financial decision-making model

Considering the specific linguistic-valued data, if we want to help the investors to make rational investment, firstly, we need to grade his income and deposit, then according to the different degrees of income and deposit to provide him with different advices. The income and deposit of the investors can be divided into three degrees based on L₆. We denote the highest income and deposit as α_T and the lowest income and deposit as α_F in the whole data. The ε_T is the highest floating value and the ε_F is the lowest floating value. So naturally if an investor’s income is more than the difference between the highest income and the highest floating value, then his income is much more; if an investor’s income is less than the difference between the lowest income and the lowest floating value, then his income is less; otherwise his income is more. Similarly, we can get the degree of the investor’s deposit. The definition of the linguistic-valued hierarchical assignment function is as follows.

Definition 9

For any survey data set X, ∀x ∈ X , V_(x) is linguistic-valued hierarchical assignment function (Fig.2), expressed as

(3)V(x)={(h1,t),x≤αF+εF(h2,t),αF+εF<x<αT−εT(h3,t),x≥αT−εT

where α_T as the highest one and α_F as the lowest one in X. The ε_T is the highest floating value and the ε_F is the lowest floating value.

Example 1

In Table 1, as to the high income concept, Florida comprehensive data corresponding to the highest is 14400$, so α_T=14400$, 500$ for its elastic range ε_T; for the low-income concept, low comprehensive survey data of Colorado is 920$, so α_F=920, ε_F= 100 for its elastic range. Therefore, for the income:

(4)V(x)={(h1,t),x≤1020(h2,t),1020<x<13900(h3,t),x≥13900

area	High income ( ±$500)	Low income ( ±$100)	More deposit (ten thousand) ( ±$2)	Less deposit (ten thousand) ( ±$1)
Alaska	11000	1340	16.0	8.2
Florida	14400	2000	21.0	10.0
Colorado	5000	920	10.0	5.6
Alabama	7000	1100	12.4	6.8

Table1.

Income and savings survey

The same for deposit:

(5)V(x)={(h1,t),x≤6.6(h2,t),6.6<x<19(h3,t),x≥19

According to the above analysis, the financial investigation decision-making algorithm based on six-element linguistic-valued approximate reasoning approach is as follows.

Step 1: Input all the rules R₁, R₂, …, R_m, and set i=1, j=1.
Step 2: Calculate the linguistic-valued evaluation (h_k, t) of the user’s income and deposit through the linguistic-valued hierarchical assignment function.
Step 3: Set the threshold τ_i = (h_n-i+1, t) for the rules activation.
Step 4: Calculate the similarity S_x between (h_k, t) and the value of the antecedent (h_l, t) of the rule R_j.
Step 5: Compare S_x with τ. If S_x= τ_i, then the corresponding rule R_j will be activated and go to Step 6. If j<m, then set j=j+1 and go to Step 4. If i<3, then set i=i+1 and go to Step 3.
Step 6: Execute the rule R_j and output the conclusion.

4.3. Example Illustration

Example 2

Suppose there is one person lives in Alaska, a monthly salary is $5000, household deposits is $120000. He wants to know how to make investment programs. According to linguistic-valued hierarchical assignment function, the corresponding degree of the rules can be obtained as follows.

(1)
V_{(D (x) )}=V_{(D(12) )}=(h₂, t);
(2)
V_{( I(x) )}=V_{(I(5000) )}=(h₂, t);
(3)
V_{( D (12) ) )} ∧V_{(I(5000) )}=(h₂, t).

Firstly let τ₁=(h₃, t), for the distance d of the facts and the antecedent of the rules is 0, then the facts and the antecedent of the rules are extremely similar. According to Definition 7 and Definition 8,

(1)
Rule 1: (h₁, t) D→IM.

The matching degree of the precondition S₁=(h_|3-1|,t)< τ₁ because d₁=1, so the Rule 1 can’t be executed.
(2)
Rule 2: (h₃, t)D∧(h₃, t)I→IS.

The matching degree of the precondition S₂=(h_|3-1|,t)< τ₁ because d₂=1, so the Rule 2 can’t be executed.
(3)
Rule 3: (h₂,t)D∧(h₂,t)I→IS∧IM∧MS.

The matching degree of the antecedent S₃=(h_|3-0|,t)= τ₁ because d₃=0, so it is executed.
(4)
Rule 4: (h₁, t)D∧(h₃, t)I→IS∧IM∧MM.

The matching degree of the precondition S₄=(h_|3-1|,t)< τ₁ because d₄=1, so the Rule 4 can’t be executed.

In conclusion, the person can adopt Rule 3, i.e. he should use most of the extra money to buy stocks and save the few. If the threshold τ₁=(h₃, t) can’t activate any rules then let τ₂ = (h₂, t) or τ₃= (h₁, t) until one rule can be activated.

In general, we use linguistic truth-valued propositional logic to express human’s language information effectively. The financial decision making system based on approximate reasoning method in L₆ makes knowledge representation more comprehensive and the decision results are more effective with linguistic values.

5. Conclusions

This paper proposed an approximate reasoning approach based on linguistic truth-valued lattice implication algebra for financial decision-making problem with the linguistic information. Knowledge representation with linguistic values has a very wide range of application prospects. Based on the linguistic truth-valued propositional logic, we present an extended knowledge representation method and apply it to financial decision making. The proposed approach can deal with both comparable and incomparable linguistic-valued information under uncertain circumstances. Further work is to use the linguistic-valued approximate reasoning approach into the big data analytics. It is an important research that how to discover the rules and get a reasonable results with linguistic-valued data in some fields such as risk analysis, decision-making and so on.

Acknowledgements

This work is partially supported by National Natural Science Foundation of China (No. 61672127) and National Natural Science Foundation of Liaoning Province (Nos. 2015020059 and 201602464).

References

1.LA Zadeh, Toward a generalized theory of uncertainty (GTU)–an outline [J], Information Sciences, Vol. 172, 2005, pp. 1-40.

2.NC Ho, A topological completion of refined hedge algebras and a model of fuzziness of linguistic terms and hedges, Fuzzy Sets and Systems, Vol. 158, 2007, pp. 436-451.

3.NC Ho and NV Long, Fuzziness measure on complete hedge algebras and quantifying semantics of terms in linear hedge algebras, Fuzzy Sets and Systems, Vol. 158, 2007, pp. 452-471.

4.L Zou, D Ruan, Z Pei, and Y Xu, A linguistic truth-valued reasoning approach in decision making with incomparable information, Journal of Intelligent and Fuzzy Systems, Vol. 19, No. 4–5, 2008, pp. 335-343.

5.MN Elbedwehy, ME Ghoneim, AE Hassanien, and AT Azar, A computational knowledge representation model for cognitive computers, Neural Computing & Applicication, Vol. 25, 2014, pp. 1517-1534.

6.J Bentahar, B Moulin, and M Bélanger, A taxonomy of argumentation models used for knowledge representation, ArtifIntell Rev, Vol. 33, 2010, pp. 211-259.

7.A Orriols-Puig and J Casillas, Fuzzy knowledge representation study for incremental learning in data streams and classification problems, Soft Computing, Vol. 15, 2011, pp. 2389-2414.

8.Z Xu and X Cai, Recent advances in intuitionistic fuzzy information aggregation, Fuzzy Optimize Decision Making, Vol. 9, 2010, pp. 359-381.

9.Z Pei, Y Xu, D Ruan, and K Qin, Extracting complex linguistic data summaries from personnel database via simple linguistic aggregations, Information Sciences, Vol. 179, 2009, pp. 2325-2332.

10.L Zou, S Fang, and Y Xu, Resolution method of six-element linguistic truth-valued intuitionistic propositional logic [J], in Proc. 3rd International Conference on Intelligent System and Knowledge Engineering (2008), pp. 141-145.

11.XM Zhong, Y Xu, J Liu, D Ruan, and SW Chen, General form of α-resolution based on linguistic truth-valued lattice-valued logic [J], Soft Computing, Vol. 10, 2012, pp. 1767-1781.

12.M-H Ha, Y Li, and X-F Wang, Fuzzy knowledge representation and reasoning using a generalized fuzzy petri net and a similarity measure, Soft Computing, Vol. 11, 2007, pp. 323-327.

13.JM Mendel, Computing with words and its relationships with fuzzistics, Information Sciences, Vol. 177, No. 4, 2007, pp. 988-1006.

14.F Herrera and L Martínez, The 2-tuple linguistic computational model: advantages of its linguistic description, accuracy and consistency, International Journal of Uncertainty, Fuzziness and Knowledge-based Systems, Vol. 9, 2001, pp. 33-48.

15.Y Xu, J Liu, L Martínez, and D Ruan, Some views on information fusion and logic based approaches in decision making under uncertainty, Journal of Universal Computer Science, Vol. 16, No. 1, 2010, pp. 3-21.

16.L Martínez and F Herrera, An overview on the 2-tuple linguistic model for computing with words in decision making: extensions, applications and challenges, Information Sciences, Vol. 207, 2012, pp. 1-18.

17.B Malakooti, Ranking and screening multiple criteria alternatives with partial information and use of ordinal and cardinal strength of preferences, IEEE Transactions on Systems, Man, and Cybernetics—Part A, Vol. 30, No. 3, 2000, pp. 355-368.

18.G Birkhoff, Lattice Theory, 3rd ed, American Mathematical Society, Providence, RL, 1967.

19.VG Kaburlasos and GX Ritter, Computational Intelligence Based on Lattice Theory, Springer, Heidelberg, 2007.

20.Z Pei, D Ruan, J Liu, and Y Xu, Atlantis Press/World Scientific, Paris/Singapore, in Linguistic Values Based Intelligent Information Processing: Theory, Methods, and Applications (December, 2009).

21.L Zou, Z Pei, X Liu, and Y Xu, Semantics of linguistic truth-valued intuitionistic fuzzy proposition calculus, International Journal of Innovative Computing, Information and Control, Vol. 5, No. 12, 2009, pp. 4745-4752.

22.L Zou, X Liu, Z Wu, and Y Xu, A uniform approach of linguistic truth values in sensor evaluation, International Journal of Fuzzy Optimization and Decision Making, Vol. 7, No. 4, 2008, pp. 387-397.

23.L Zou, D Ruan, Z Pei, and Y Xu, A linguistic-valued lattice implication algebra approach for risk analysis, Journal of Multi-Valued Logic and Soft Computing, Vol. 17, No. 4, 2011, pp. 293-303.

24.C Kahramana, SC Onara, and B Oztaysia, Fuzzy Multicriteria Decision-Making: A Literature Review [J], International Journal of Computational Intelligence Systems, Vol. 8, No. 4, 2015, pp. 637-666.

25.Fekia, X Fengb, A Ghithc, L Koehlb, F Msahlia, and F Saklid, Selecting Multiple Evaluator’s Perception-Oriented Relevant Physical Features of Consumer Goods by Using Fuzzy Data Sensitivity and OWA Operators[J], International Journal of Computational Intelligence Systems, Vol. 9, No. 2, 2016, pp. 213-226.

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Journal: International Journal of Computational Intelligence Systems
Volume-Issue: 10 - 1
Pages: 312 - 319
Publication Date: 2017/01/01
ISSN (Online): 1875-6883
ISSN (Print): 1875-6891
DOI: 10.2991/ijcis.2017.10.1.21 How to use a DOI?
Open Access: This is an open access article under the CC BY-NC license (http://creativecommons.org/licences/by-nc/4.0/).

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TY  - JOUR
AU  - Xin Liu
AU  - Ying Wang
AU  - Xiaonan Li
AU  - Li Zou
PY  - 2017
DA  - 2017/01/01
TI  - A Linguistic-Valued Approximate Reasoning Approach for Financial Decision Making
JO  - International Journal of Computational Intelligence Systems
SP  - 312
EP  - 319
VL  - 10
IS  - 1
SN  - 1875-6883
UR  - https://doi.org/10.2991/ijcis.2017.10.1.21
DO  - 10.2991/ijcis.2017.10.1.21
ID  - Liu2017
ER  -

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International Journal of Computational Intelligence Systems

A Linguistic-Valued Approximate Reasoning Approach for Financial Decision Making

1. Introduction

2. Linguistic Truth-valued Propositional Logic

2.1. Linguistic Truth-Valued lattice implication algebra

Definition 1.23

Definition 2.23

2.2. Six-element Linguistic Truth-Valued Propositional Logic

Definition 3.

Definition 4.

Definition 5.

Definition 6.

3. Approximate reasoning method

3.1. Linguistic-Valued similarity based on L2n

Definition 7.

Definition 8.

Theorem 1.

Proof.

3.2. Approximate reasoning method based on LV(n×2)

4. Linguistic-Valued Approximate Reasoning Model for Financial Decision Making

4.1. Knowledge representation model based on L6

4.2. Financial decision-making model

Definition 9

Example 1

4.3. Example Illustration

Example 2

5. Conclusions

Acknowledgements

References

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Definition 1.²³

Definition 2.²³

3.1. Linguistic-Valued similarity based on L_2n

3.2. Approximate reasoning method based on L_V(n×2)

4.1. Knowledge representation model based on L₆