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This paper discusses the trapezoidal fuzzy number(TrFN); Interval-valued intuitionistic fuzzy number(IVIFN); neutrosophic set and its operational laws; and, trapezoidal neutrosophic set(TrNS) and its operational laws. Based on the…
This paper focuses on designing expert systems to support decision making in complex, uncertain environments. In this context, our research indicates that strictly probabilistic representations, which enable the use of decision-theoretic…
A concept of multi-valued cognitive maps is introduced in this paper. The concept expands the fuzzy one. However, all variables and weights are not linearly ordered in the concept, but are only partially-ordered. Such an ap- proach allows…
Large Language Models (LLMs) excel in text generation, reasoning, and decision-making, enabling their adoption in high-stakes domains such as healthcare, law, and transportation. However, their reliability is a major concern, as they often…
In many situations humans have to reason with inconsistent knowledge. These inconsistencies may occur due to not fully reliable sources of information. In order to reason with inconsistent knowledge, it is not possible to view a set of…
A characterization of flat ideals in the unit interval with the canonical fuzzy order is obtained with the help of the ordinal sum decomposition of continuous t-norms. This characterization will be useful in the study of topological and…
Fuzzy answer set programming is a declarative framework for representing and reasoning about knowledge in fuzzy environments. However, the unavailability of fuzzy aggregates in disjunctive fuzzy logic programs, DFLP, with fuzzy answer set…
This contribution reviews critically the existing entropy measures for probabilistic hesitant fuzzy sets (PHFSs), and demonstrates that these entropy measures fail to effectively distinguish a variety of different PHFSs in some cases. In…
Fuzzy time series forecasting methods are very popular among researchers for predicting future values as they are not based on the strict assumptions of traditional time series forecasting methods. Non-stochastic methods of fuzzy time…
Following the definition of intuitionistic fuzzy n-norm [ 3 ], we have introduced the definition of intuitionistic fuzzy norm (in short IFN) over a linear space and there after a few results on intuitionistic fuzzy normed linear space and…
In this contribution we describe a novel procedure to represent fuzziness in rating scales in terms of fuzzy numbers. Following the rationale of fuzzy conversion scale, we adopted a two-step procedure based on a psychometric model (i.e.,…
Logical propositions with the fuzzy modality "Probably" are shown to obey an uncertainty principle very similar to that of Quantum Optics. In the case of such propositions, the partial truth values are in fact probabilities. The…
Shannon entropy was defined for probability distributions and then its using was expanded to measure the uncertainty of knowledge for systems with complete information. In this article, it is proposed to extend the using of Shannon entropy…
This research introduces a new constraint domain for reasoning about data with uncertainty. It extends convex modeling with the notion of p-box to gain additional quantifiable information on the data whereabouts. Unlike existing approaches,…
A reason maintenance system which extends an ATMS through Mukaidono's fuzzy logic is described. It supports a problem solver in situations affected by incomplete information and vague data, by allowing nonmonotonic inferences and the…
In this article, we describe the fuzzy logic, fuzzy language and algorithms as the basis of fuzzy reasoning, one of the intelligent information processing method, and then describe the general fuzzy reasoning method.
This note is concerned with a formal analysis of the problem of non-monotonic reasoning in intelligent systems, especially when the uncertainty is taken into account in a quantitative way. A firm connection between logic and probability is…
In the digital age of information overload and uncertainty, the authors propose the tDTSW model based on fuzzy logic to navigate governance complexities. This model transcends binary thinking, analyzes democracy, transparency, and social…
Prediction sets offer a binary inclusion/exclusion for each element at the same fixed confidence level. We generalize to fuzzy prediction sets, which exclude elements at their own data-driven confidence level. Our key insight is that a…
The concept of uncertainty is posed in almost any complex system including parallel robots as an outstanding instance of dynamical robotics systems. As suggested by the name, uncertainty, is some missing information that is beyond the…