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Selecting products through text reviews: An MCDM method incorporating personalized heuristic judgments in the prospect theory


Online reviews have become an increasingly popular information source in consumer’s decision making process. To help consumers make informed decisions, how to select products through online reviews is a valuable research topic. This work deals with a personized product selection problem with review sentiments under probabilistic linguistic circumstances. To this end, we propose a multi-criteria decision making (MCDM) method incorporating personalized heuristic judgments in the prospect theory (PT). We focus on the role of personalized heuristic judgments on review helpfulness in the final decision outcomes. We demonstrate the consistency between the three common heuristic judgments (with respect to review valence, sentiment extremity, and aspiration levels) and the three behavioral principles of the PT. Then, the products are ranked with the probabilistic linguistic term set (PLTS) input, based on the proposed adjustable PT framework, in which the coefficients of negativity bias are derived from the consumer’s heuristic judgments. Finally, a real case on and two simulation experiments are given to illustrate the validity of the proposed method.

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  1. The open source software, Stanford Core NLP, can be found in

  2. Note that \(e_{j}\) should first be normalized and ordered. To avoid confusion, the processed aspiration is still denoted as \(e_{j}\).

  3. In the PT, risk aversion actually is a principle that there is risk aversion for gains and risk seeking for losses (Tversky and Kahneman 1992), and can be derived from the idea that a certain loss is particularly undesirable (loss aversion) and hence encourages risk taking (Rozin and Royzman 2001).



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This work was supported by the National Natural Science Foundation of China (Grant Nos. 71701037, 71971051), and Youth Top-notch Talent Support Program of Hebei province (No. BJ2020211).

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Correspondence to Huchang Liao.

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The proof of Proposition 1

(1) The derivative \(f^{\prime}\left( {{\text{AI}}} \right) = \left( {1 - \frac{{{\text{AI}}}}{2}} \right)^{\eta } + \left( {1 + \frac{{{\text{AI}}}}{2}} \right)^{\eta } - {2} \times \left( {\frac{{\text{AI + 1}}}{2}} \right)^{\eta } > 0\) for any \({\text{AI}} \in (0,\;1)\) and \(\eta \ge 1\). So \(f({\text{AI}})\) is monotonically increasing with respect to the level of \({\text{AI}}\). \(\min f({\text{AI}}) = f(0) = - \frac{2}{\eta + 1}\left[ {2 \times \left( \frac{1}{2} \right)^{\eta + 1} - \frac{1}{{2^{\eta } }} + 1^{\eta + 1} - 1^{\eta + 1} } \right] = 0\), hence we have \(U(0,X) = U(0,Y)\) and \(U({\text{AI}},Y) > U({\text{AI}},X)\) for any \({\text{AI}} \in (0,\;1)\). The results mean that when \({\text{AI}} \in (0,\;1)\), a greater expected utility is brought by fixed income than that by uncertain returns. Thus, we prove that the decision-maker is risk averse when \({\text{AI}} \in (0,\;1)\), and risk neutral when \({\text{AI}} = 0\).

(2) The proof of loss neutral for \({\text{AI}} = 0\) can be directly derived because \(U(y) + U( - y) - \left[ {U(x) + U( - x)} \right] = 0\) hold when \({\text{AI}} = 0\). For any \(x > y \ge 0\), we have three possible cases. Consider the case \(x > y > {\text{AI}}\), there is \(U(y) + U( - y) - \left[ {U(x) + U( - x)} \right] = y\left[ {\left( {\frac{{y - {\text{AI}} + 1}}{2}} \right)^{\eta } - \left( {\frac{{{\text{AI}} + y + 1}}{2}} \right)^{\eta } } \right] - \left[ {x\left( {\frac{{x - {\text{AI}} + 1}}{2}} \right)^{\eta } - \left( {\frac{{{\text{AI}} + x + 1}}{2}} \right)^{\eta } } \right]\). If \(\eta = 1\),\(U(y) + U( - y) - \left[ {U(x) + U( - x)} \right] = - {\text{AI}}\left( {y - x} \right) > 0\). If \(\eta \ge 2\), according to the equation of difference of two nth powers, \(U(y) + U( - y) - \left[ {U(x) + U( - x)} \right] = - {\text{AI}}\left( {yG_{1} - xG_{2} } \right)\), where \(G_{1} = \left( {\frac{{y - {\text{AI}} + 1}}{2}} \right)^{\eta - 1} + \left( {\frac{{y - {\text{AI}} + 1}}{2}} \right)^{\eta - 2} \times \left( {\frac{{{\text{AI}} + y + 1}}{2}} \right) + \left( {\frac{{y - {\text{AI}} + 1}}{2}} \right)^{\eta - 3} \times \left( {\frac{{{\text{AI}} + y + 1}}{2}} \right)^{2} \cdots + \left( {\frac{{{\text{AI}} + y + 1}}{2}} \right)^{\eta - 1} > 0\) and \(G_{2} = \left( {\frac{{x - {\text{AI}} + 1}}{2}} \right)^{\eta - 1} + \left( {\frac{{x - {\text{AI}} + 1}}{2}} \right)^{\eta - 2} \times \left( {\frac{{{\text{AI}} + x + 1}}{2}} \right) + \left( {\frac{{x - {\text{AI}} + 1}}{2}} \right)^{\eta - 3} \times \left( {\frac{{{\text{AI}} + x + 1}}{2}} \right)^{2} \cdots + \left( {\frac{{{\text{AI}} + x + 1}}{2}} \right)^{\eta - 1} > 0\). Since \(x > y > {\text{AI}} > 0\), there is \(0 < G_{1} < G_{2}\), So, there is \(U(y) + U( - y) > U(x) + U( - x)\) for any \(x > y > {\text{AI}}\). The proofs for \(x > {\text{AI}} > y\) and \({\text{AI}} > x > y\) are similar. So, we prove the decision-maker is loss averse when \({\text{AI}} \in (0,\;1)\). □

The proof of Proposition 2

(1) We have proved that \(f({\text{AI}})\) is monotonically increasing as \({\text{AI}} \in (0,\;1)\) in the aforementioned proofs. The greater superiority possessed by the expected utility from fixed income is indicative of a greater degree of risk aversion. So, we prove that the degree of risk aversion increases with the increase of AI.

(2) We code the reward \(x\) as a gain or loss relative to the sentimental neutral point, for any \(x \in (0,1)\), the ratio of absolute utility value with respect to AI, denote by \(\lambda ({\text{AI}},x)\), is calculated as \(\lambda ({\text{AI}},x){ = }\left( {\frac{{{\text{AI}} + x + 1}}{{\left| {{\text{AI}} - x} \right| + 1}}} \right)^{\eta }\), where \(\lambda ({\text{AI}},x) > 1\) means loss aversion, and a greater \(\lambda\) indicates more loss sensitive. We have \(\lambda \left( {{\text{AI}}_{1} ,x} \right) - \lambda \left( {{\text{AI}}_{2} ,x} \right) = \left| {{\text{AI}}_{2} - x} \right|\left( {{\text{AI}}_{1} + x + 1} \right) - \left| {{\text{AI}}_{1} - x} \right|\left( {{\text{AI}}_{2} + x + 1} \right) + {\text{AI}}_{1} - {\text{AI}}_{2}\). Three possible position for \(x\) relative to \({\text{AI}}\) should be discussed separately. (i) For any \(x > {\text{AI}}_{2} > {\text{AI}}_{1}\), there is \(\lambda ({\text{AI}}_{1} ,x) - \lambda ({\text{AI}}_{2} ,x) = 2({\text{AI}}_{1} - {\text{AI}}_{2} )(x + 1) < 0\). (ii) For any \({\text{AI}}_{2} > {\text{AI}}_{1} > x\), there is \(\lambda \left( {{\text{AI}}_{1} ,x} \right) - \lambda \left( {{\text{AI}}_{2} ,x} \right) = 2x\left( {{\text{AI}}_{2} - {\text{AI}}_{1} } \right) > 0\). (iii) Consider the case \({\text{AI}}_{2} > x > {\text{AI}}_{1}\), the sign of \(\lambda ({\text{AI}}_{1} ,x) - \lambda ({\text{AI}}_{2} ,x) = 2\left[ { - x^{2} - x + {\text{AI}}_{1} (1 + {\text{AI}}_{2} )} \right]\) is not fixed. However, only the case for any \(x > {\text{AI}}_{2} > {\text{AI}}_{1}\) makes perfect sense, because the loss aversion coefficient is meaningful only when the gain and loss coexist. So, the result in Proposition 2.(2) holds. □

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Zhao, M., Shen, X., Liao, H. et al. Selecting products through text reviews: An MCDM method incorporating personalized heuristic judgments in the prospect theory. Fuzzy Optim Decis Making 21, 21–44 (2022).

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  • Product selection
  • Online reviews
  • Multi-criteria decision making
  • Prospect theory
  • Probabilistic linguistic term set
  • Negativity bias
  • Heuristic judgments