Some Fuzzy Measures Constructing Paradigm and Methods From Given Measure Spaces and Evaluation Information

With some theoretical derivation and practical decision-making problems, in this article, we propose a constructing paradigm for generating fuzzy measures in some certain decision situations, such as in risk evaluation and decision making. The constructing paradigm involves four constructing factors: source measure space, construction function, construction choice, and object/constructed measure space. We use some strict and consistent formulation to reinvent the processes of constructing the well-known belief measure and plausibility measure. In this a, the belief measure and plausibility measure are regarded as the two extremities of some pessimism–optimism preferences, and we further propose two construction choices to construct the families of fuzzy measures to generalize and seamlessly connect them. We also propose three different ways to determine construction functions in some certain decisional situations. Several relevant mathematical properties and numerical examples are also presented.