Related papers: Entropy and Syntropy in the Context of Five-Valued…
In this paper one presents new similarity, cardinality and entropy measures for bipolar fuzzy set and for its particular forms like intuitionistic, paraconsistent and fuzzy set. All these are constructed in the framework of multi-valued…
This paper presents two variants of penta-valued representation for neutrosophic entropy. The first is an extension of Kaufmann's formula and the second is an extension of Kosko's formula. Based on the primary three-valued information…
In this paper a knowledge representation model are proposed, FP5, which combine the ideas from fuzzy sets and penta-valued logic. FP5 represents imprecise properties whose accomplished degree is undefined, contradictory or indeterminate for…
This approach presents a multi-valued representation of the neutrosophic information. It highlights the link between the bifuzzy information and neutrosophic one. The constructed deca-valued structure shows the neutrosophic information…
The paper presents some steps for multi-valued representation of neutrosophic information. These steps are provided in the framework of multi-valued logics using the following logical value: true, false, neutral, unknown and saturated.…
In this paper we deal with a new approach to probabilistic reasoning in a logical framework. Nearly almost all logics of probability that have been proposed in the literature are based on classical two-valued logic. After making clear the…
To deal with uncertainty in reasoning, interval-valued logic has been developed. But uniform intervals cannot capture the difference in degrees of belief for different values in the interval. To salvage the problem triangular and…
This paper mainly focuses on (1) a generalized treatment of fuzzy sets of type $n$, where $n$ is an integer larger than or equal to $1$, with an example, mathematical discussions, and real-life interpretation of the given mathematical…
In fuzzy propositional logic, to a proposition a partial truth in [0,1] is assigned. It is well known that under certain circumstances, fuzzy logic collapses to classical logic. In this paper, we will show that under dual conditions, fuzzy…
The increasing rise in artificial intelligence has made the use of imprecise language in computer programs like ChatGPT more prominent. Fuzzy logic addresses this form of imprecise language by introducing the concept of fuzzy sets, where…
Starting from the primary representation of neutrosophic information, namely the degree of truth, degree of indeterminacy and degree of falsity, we define a nuanced representation in a penta valued fuzzy space, described by the index of…
In this article, we have introdued D-fuzzy sets. We have discussed the notions of inclusion, union, intersection, complementation and convexity of such D-fuzzy sets. Also we have proved separation theorem of convex D-fuzzy sets.
We locate the relevant degrees of freedom for the entanglement entropy on some 2+1 fuzzy models. It is found that the entropy is stored in the near boundary degrees of freedom. We give a simple analytical derivation for the area law using…
In this book we introduce the plithogenic set (as generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets), plithogenic logic (as generalization of classical, fuzzy, intuitionistic fuzzy, and neutrosophic logics),…
Entropy can signify different things: For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced and it can be difficult to ascertain their different importance and…
We propose a new definition of the representation theorem for many-valued logics, with modal operators as well, and define the stronger relationship between algebraic models of a given logic and relational structures used to define the…
Entropy has emerged as a dynamic, interdisciplinary, and widely accepted quantitative measure of uncertainty across different disciplines. A unified understanding of entropy measures, supported by a detailed review of their theoretical…
Crisp and $L$-fuzzy ambiguous representations of closed subsets of one space by closed subsets of another space are introduced. It is shown that, for each pair of compact Hausdorff spaces, the set of (crisp or $L$-fuzzy) ambiguous…
The routine definitions of both entropy, and differential entropy show inconsistencies that make them not reciprocally coherent. We propose a few possible modifications of these quantities so that 1) they no longer show incongruities, 2)…
Real-world phenomena often exhibit vagueness, partial truth, and incomplete information. To model such uncertainty in a mathematically rigorous way, many generalized set-theoretic frameworks have been introduced, including Fuzzy Sets [1],…