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Öğe Conjunctive and disjunctive combination rules in random permutation set theory: A layer-2 belief structure perspective(Elsevier, 2024) Zhou, Qianli; Cui, Ye; Pedrycz, Witold; Deng, YongIn uncertainty reasoning, conjunctive and disjunctive combination rules are the core tools for information updates. As an extension of evidential reasoning, random permutation set reasoning models uncertain information based on ordered focal sets. Existing combination rules in random permutation set theory, orthogonal sums, do not satisfy the commutativity of one of the original distributions and overly obey its order information. In this paper, the random permutation set theory is interpreted as an refined extension of Dempster-Shafer theory, and a layer-2 belief structure is proposed to describe the permutation event space. Compared with the traditional belief structure, the proposed structure can model both symbolic and numerical uncertainty. Based on the above, the conjunctive and disjunctive combination rules in Dempster-Shafer theory are extended to random permutation set theory. Through properties analysis and simulation demonstration, we demonstrate that the proposed methods can not only resolve the counter-intuitive results of orthogonal sums, but make full use of order information in distributions as well. In addition, we also extend the product space operations and discounting methods based on the proposed methods, and give a general framework of multi-source information fusion under the random permutation set theory.Öğe From Fuzzy Rule-Based Models to Granular Models(Institute of Electrical and Electronics Engineers Inc., 2025) Cui, Ye; Hanyu, E.; Pedrycz, Witold; Li, ZhiwuFuzzy rule-based models constructed in the presence of numeric data are nonlinear numeric models producing for any input some numeric output. There are no ideal models so the obtained numeric output could create a false illusion of achieved accuracy. A desirable approach is to augment the results with some measure of confidence (credibility) by admitting a granular rather than numeric format of the produced output values of the model. Our focus of this study is on fuzzy Takagi–Sugeno rule-based models whose conclusions are constant. The ultimate objective is to extend such models to the generalized granular structure with the conclusions formed as information granules. We study information granules described by intervals and fuzzy sets as well as probabilistic Gaussian information granules. The original design of the granular model is realized by involving the principle of justifiable granularity. Using this principle, we also show how to determine the equivalence between information granules. The construction of probabilistic information granules of the model is completed with the aid of optimized Gaussian process models. The granular models built in this way constitute a substantial and application-oriented departure from the numeric fuzzy models by offering a comprehensive insight into the quality of the produced results. The experimental studies based on synthetic and publicly available data demonstrate the design process and discuss the quality of the obtained results. © 2024 IEEE.