Three-way Decision Models of Cognitive Computing in Pythagorean Fuzzy Environments

Three-way decisions in generalized intuitionistic fuzzy environments: survey and challenges

Enhancing decision-making under risks is crucial in various fields, and three-way decision (3WD) methods have been extensively utilized and proven to be effective in numerous scenarios. However, traditional methods may not be sufficient when addressing intricate decision-making scenarios characterized by uncertain and ambiguous information. In response to this challenge, the generalized intuitionistic fuzzy set (IFS) theory extends the conventional fuzzy set theory by introducing two pivotal concepts, i.e., membership degrees and non-membership degrees. These concepts offer a more comprehensive means of portraying the relationship between elements and fuzzy concepts, thereby boosting the ability to model complex problems. The generalized IFS theory brings about heightened flexibility and precision in problem-solving, allowing for a more thorough and accurate description of intricate phenomena. Consequently, the generalized IFS theory emerges as a more refined tool for articulating fuzzy phenomena. The paper offers a thorough review of the research advancements made in 3WD methods within the context of generalized intuitionistic fuzzy (IF) environments. First, the paper summarizes fundamental aspects of 3WD methods and the IFS theory. Second, the paper discusses the latest development trends, including the application of these methods in new fields and the development of new hybrid methods. Furthermore, the paper analyzes the strengths and weaknesses of research methods employed in recent years. While these methods have yielded impressive outcomes in decision-making, there are still some limitations and challenges that need to be addressed. Finally, the paper proposes key challenges and future research directions. Overall, the paper offers a comprehensive and insightful review of the latest research progress on 3WD methods in generalized IF environments, which can provide guidance for scholars and engineers in the intelligent decision-making field with situations characterized by various uncertainties.

A three-way decisions approach based on double hierarchy linguistic aggregation operators of strict t-norms and t-conorms

With the massive increase in uncertainty of linguistic information in realistic decision making, there is a great challenge for people to make decisions in the complex linguistic environment. To overcome this challenge, this paper proposes a three-way decisions method based on aggregation operators of strict t-norms and t-conorms under double hierarchy linguistic environment. By mining the double hierarchy linguistic information, strict t-norms and t-conorms are introduced to define the operation rules and their operation examples are also given. Then, the double hierarchy linguistic weighted average (DHLWA) operator and weighted geometric (DHLWG) operator are proposed based on strict t-norms and t-conorms. Besides, some of their important properties are also proved and derived, such as idempotency, boundedness and monotonicity. Next, DHLWA and DHLWG are integrated with three-way decisions to construct our three-way decisions model. Specifically, the double hierarchy linguistic decision theoretic rough set (DHLDTRS) model is constructed by incorporating the computational model of expected loss with DHLWA and DHLWG, which can consider the various decision attitudes from decision makers more adequately. Furthermore, we also propose a novel entropy weight calculation formula to improve the entropy weight method for obtaining the weights more objectively, and integrate grey relational analysis (GRA) method to calculate the conditional probability. Based on the Bayesian minimum-loss decision rules, the solving method of our model is also propounded and the corresponding algorithm is designed. Finally, an illustrative example and experimental analysis are presented, which can validate the rationality, robustness as well as superiority of our method.