The credibility theory was introduced by B. Liu as a new way to describe the fuzzy uncertainty. The credibility measure is the fundamental notion of the credibility theory. Recently, L.Yang and K. Iwamura extended the credibility measure by defining the parametric measure $m_{\lambda}$ ($\lambda$ is a real parameter in the interval $[0,1]$ and for $\lambda= 1/2$ we obtain as a particular case the notion of credibility measure). By using the $m_{\lambda}$-measure, we studied in this paper a risk neutral multi-item inventory problem. Our construction generalizes the credibilistic inventory model developed by Y. Li and Y. Liu in 2019. In our model, the components of demand vector are fuzzy variables and the maximization problem is formulated by using the notion of $m_{\lambda}$-expected value. We shall prove a general formula for the solution of optimization problem, from which we obtained effective formulas for computing the optimal solutions in the particular cases where the demands are trapezoidal and triangular fuzzy numbers. For $\lambda=1/2$ we obtain as a particular case the computation formulas of the optimal solutions of the credibilistic inventory problem of Li and Liu. These computation formulas are applied for some $m_{\lambda}$-models obtained from numerical data.

The need for fully human-understandable models is increasingly being recognised as a central theme in AI research. The acceptance of AI models to assist in decision making in sensitive domains will grow when these models are interpretable, and this trend towards interpretable models will be amplified by upcoming regulations. One of the killer applications of interpretable AI is medical practice, which can benefit from accurate decision support methodologies that inherently generate trust. In this work, we propose FPT, (MedFP), a novel method that combines probabilistic trees and fuzzy logic to assist clinical practice. This approach is fully interpretable as it allows clinicians to generate, control and verify the entire diagnosis procedure; one of the methodology's strength is the capability to decrease the frequency of misdiagnoses by providing an estimate of uncertainties and counterfactuals. Our approach is applied as a proof-of-concept to two real medical scenarios: classifying malignant thyroid nodules and predicting the risk of progression in chronic kidney disease patients. Our results show that probabilistic fuzzy decision trees can provide interpretable support to clinicians, furthermore, introducing fuzzy variables into the probabilistic model brings significant nuances that are lost when using the crisp thresholds set by traditional probabilistic decision trees. We show that FPT and its predictions can assist clinical practice in an intuitive manner, with the use of a user-friendly interface specifically designed for this purpose. Moreover, we discuss the interpretability of the FPT model.

Municipal solid waste management (MSWM) is a challenging issue of urban development in developing countries. Each country having different socio-economic-environmental background, might not accept a particular disposal method as the optimal choice. Selection of suitable disposal method in MSWM, under vague and imprecise information can be considered as multi criteria decision making problem (MCDM). In the present paper, TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) methodology is extended based on credibility theory for evaluating the performances of MSW disposal methods under some criteria fixed by experts. The proposed model helps decision makers to choose a preferable alternative for their municipal area. A sensitivity analysis by our proposed model confirms this fact.

The role of inferencing with uncertainty is becoming more important in rule-based expert systems (ES), since knowledge given by a human expert is often uncertain or imprecise. We have succeeded in designing a VLSI chip which can perform an entire inference process based on fuzzy logic. The design of the VLSI fuzzy inference engine emphasizes simplicity, extensibility, and efficiency (operational speed and layout area). It is fabricated in 2.5 um CMOS technology. The inference engine consists of three major components; a rule set memory, an inference processor, and a controller. In this implementation, a rule set memory is realized by a read only memory (ROM). The controller consists of two counters. In the inference processor, one data path is laid out for each rule. The number of the inference rule can be increased adding more data paths to the inference processor. All rules are executed in parallel, but each rule is processed serially. The logical structure of fuzzy inference proposed in the current paper maps nicely onto the VLSI structure. A two-phase nonoverlapping clocking scheme is used. Timing tests indicate that the inference engine can operate at approximately 20.8 MHz. This translates to an execution speed of approximately 80,000 Fuzzy Logical Inferences Per Second (FLIPS), and indicates that the inference engine is suitable for a demanding real-time application. The potential applications include decision-making in the area of command and control for intelligent robot systems, process control, missile and aircraft guidance, and other high performance machines.

A major aspect of human reasoning involves the use of approximations. Particularly in situations where the decision-making process is under stringent time constraints, decisions are based largely on approximate, qualitative assessments of the situations. Our work is concerned with the application of approximate reasoning to real-time control. Because of the stringent processing speed requirements in such applications, hardware implementations of fuzzy logic inferencing are being pursued. We describe a programming environment for translating fuzzy control rules into hardware realizations. Two methods of hardware realizations are possible. The First is based on a special purpose chip for fuzzy inferencing. The second is based on a simple memory chip. The ability to directly translate a set of decision rules into hardware implementations is expected to make fuzzy control an increasingly practical approach to the control of complex systems.