The 12th International Conference on Fuzzy Systems and Data Mining (FSDM 2026)

Abstract: As a generalization of the classical Lebesgue integral, set-valued integrals had been greatly developed, and widely applied in the fields such as Mathematical Economy, Control Theory, Optimization Theory. In recent years, based on nonadditive integrals, various kinds of set-valued nonadditive integrals were developed. As a powerful tool for modeling nondeterministic problems and a typical nonadditive integral, the Choquet integral has attracted much attention. This lecture gives an overview of several existing set-valued Choquet integrals: (i) Choquet integrals of set-valued functions with respect to set-valued fuzzy measures, which include the special cases of Choquet integrals of set-valued functions with respect to fuzzy measures and of single-valued functions with respect to set-valued fuzzy measures; (ii) Generalized Choquet type set-valued integral (GCTSI) of single-valued functions with respect to set-multifunctions and additive measures; (iii) Double set-function multi-valued Choquet integral (DSMVCI) for single-valued functions with respect to set-multifunctions and fuzzy measures. Various kinds of their properties and convergence theorems are shown, and some set-valued type inequalities, such as Jensen's and Markov's are given. Related to many applications in different fields, such as decision making are provided.

Biography: Deli Zhang is a first-class professor and doctoral supervisor. He formerly served as the vice president of Changchun Normal University. He also holds the positions of director of the Jilin Provincial Key Laboratory of Mathematical Soft Computing and Applications and provincial education inspector for the Jilin Provincial Government. He is recognized as a high-level Category A talent of Jilin Province, a member of the Second Expert Working Committee on Basic Education Curriculum and Textbooks of the Ministry of Education, the vice chairman of the First Professional Committee on Mathematical Teaching Guidance for Basic Education of the Ministry of Education, the vice chairman of the Fuzzy Mathematics and Fuzzy Systems Professional Committee of the Chinese Society of Systems Engineering, and the vice president of the Jilin Mathematical Society. His accolades include one second prize of the National Teaching Achievement Award, one first prize of the Jilin Provincial Natural Science Award, one second prize of the Jilin Provincial Scientific and Technological Progress Award, one special prize of the Jilin Provincial Teaching Achievement Award. His primary research areas encompass non-additive measure theory, fuzzy mathematics, and mathematics education. He has published over 100 research papers, more than 50 of which have been indexed by SCI and CCSCI, and has authored two monographs: "Generalized Integral Theory" and "Fuzzy Integral Theory," as well as served as the editor-in-chief of over 50 books and textbooks. He currently serves as a reviewer for the "American Mathematical Review," and as an editorial board member for "Fuzzy Systems and Mathematics," "American Journal of Applied Mathematics," and "Mathematics and Computer Science." He has led or participated in four general research projects funded by the National Natural Science Foundation of China and three general research projects funded by the Jilin Provincial Natural Science Foundation.