Abstract:

Based on the properties and advantages of t-spherical fuzzy sets (T-SFSs) and probability hesitant fuzzy sets (PHFSs), First, the concept of t-spherical probability hesitant fuzzy sets (T-SPFSs) is proposed, which can more accurately express the fuzziness and uncertainty of data. Then, the algorithm and properties of T-SPFSs are given. T-spherical probabilistic hesitant fuzzy weighted averaging (T-SPHFWA) operator and t-spherical probabilistic hesitant fuzzy weighted geometric (T-SPHFWG) operator are proposed and their properties are studied, including idempotency, commutativity, boundedness, and monotonicity. Finally, for solving the multi-attribute decision-making problem where the decision information is t-spherical probability hesitation fuzzy number (T-SPHFN), a multi-attribute decision-making model is constructed based on T-SPHFWA operator and T-SPHFWG operator. A green entrepreneurship project performance evaluation is to illustrate the feasibility and rationality of the proposed approaches method.

Key words: T-spherical probabilistic hesitant fuzzy sets (T-SPHFSs), T-spherical probabilistic hesitant fuzzy weighted averaging (T-SPHFWA) operator, T-spherical probabilistic hesitant fuzzy weighted geometric (T-SPHFWG) operator, green entrepreneurship project performance evaluation

摘要：

基于T-球面模糊集（T-Spherical Fuzzy Sets，T-SFSs）和概率犹豫模糊集（Probabilistic Hesitant Fuzzy Sets，PHFSs）的性质，首先融合两者优点提出T-球面概率犹豫模糊集（T-Spherical Probabilistic Hesitant Fuzzy Sets，T-SPHFSs）概念，其能更准确地表达数据的模糊性和不确定性；然后，给出T-SPHFSs的运算法则和性质，提出T-球面概率犹豫模糊加权平均（T-Spherical Probabilistic Hesitant Fuzzy Weighted Averaging，T-SPHFWA）算子和T-球面概率犹豫模糊加权几何（T-Spherical Probabilistic Hesitant Fuzzy Weighted Geometric，T-SPHFWG）算子，并研究它们的幂等性、置换不变性，有界性和单调性等性质；最后，针对决策信息为T-球面概率犹豫模糊数的多属性决策问题，基于T-SPHFWA算子和T-SPHFWG算子构建多属性决策模型，通过绿色创业企业绩效评估算例证明决策方法的有效性与可行性。

关键词: T-球面概率犹豫模糊集, T-球面概率犹豫模糊加权平均算子, T-球面概率犹豫模糊加权几何算子, 绿色创业企业绩效评估