模糊線性迴歸模型通常用來表示在模糊環境中的解釋變數與應變數之間的線性關係。過去有關模糊線性迴歸模型的研究顯示，以最小絕對距離為目標式的模型最為穩健，但仍存在著預測變數的不確定性增加和模型參數的正、負號需要預先設定的問題；其次，直覺模糊集合延伸模糊集合的概念且所提供的資訊更符合複雜的決策環境，但在目前文獻中考慮解釋變數、應變數及模型參數均為直覺模糊數的研究甚少。
為了建構直覺模糊線性迴歸模型，本研究首先提出了一個新的模糊運算子：模糊乘積核，透過模糊乘積核運算子建構的模糊線性迴歸模型改善了過去研究的缺點，減少了預測值的模糊性幅度且模型中的參數毋需預先設定其正、負號，且解釋變數為明確值時亦適用。接著，本研究提出以最小絕對距離為目標，解釋變數、應變數及模型參數均為直覺模糊數的直覺模糊線性迴歸模型，並分別建構考量隨機性與模糊性、使用標準模糊運算子、最弱範數運算子及模糊乘積核運算子等四個修正模型。這些模型均能改善過去模糊線性迴歸模型中的展幅擴大及參數符號問題；此外，不同模型的優劣關係則透過實例驗證予以分析及比較，提供未來研究改進與應用參考方向。

Fuzzy linear regression models (FLRMs) are typically formulated to characterize the relation between responses and explanatory variables in fuzzy environments. Based on a literature review of existing studies on FLRMs, an FLRM based on the least absolute deviation (LAD) is more robust than other approaches. However, some critical problems still exist, such as the uncertainty arising and the determination of the sign of the parameters of the FLRMs. In addition, observations described by intuitionistic fuzzy sets (IFSs) can contain more information than those described by fuzzy sets. However, there are only two approaches that have been proposed for developing intuitionistic fuzzy linear regression models (IFLRMs).
To establish an intuitionistic fuzzy linear regression model (IFLRM), in this study, the fuzzy product core (FPC) operator is first proposed for the purpose of formulating fuzzy linear regression models with fuzzy parameters using fuzzy observations with the fuzzy response and explanatory variables. Compared to existing approaches, the proposed approach improves the weaknesses of the relevant approaches. The proposed approach outperforms existing models in terms of distance and similarity measures even when crisp explanatory variables are used. Then, an IFLRM based on LAD is proposed that considers that the explanatory and response variables in the observation dataset, as well as the parameters of the model are triangular intuitionistic fuzzy numbers (TIFNs). Based on the LAD FLRM, some improved approaches are considered, such as randomness and fuzziness, as well as the use of the strongest T-norm, the weakest T-norm, and intuitionistic FPC (IFPC). These IFLRMs can avoid the wide spreads in the predicted TIFN responses, where the sign of the parameters is determined during the formulation process. Furthermore, some example illustrations and comparisons are discussed.

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