Gray Level Image Threshold Using Neutrosophic Shannon Entropy

This article presents a new method of segmenting grayscale images by minimizing Shannon's neutrosophic entropy. For the proposed segmentation method, the neutrosophic information components, i.e., the degree of truth, the degree of neutrality and the degree of falsity are defined taking into account the belonging to the segmented regions and at the same time to the separation threshold area. The principle of the method is simple and easy to understand and can lead to multiple thresholds. The efficacy of the method is illustrated using some test gray level images. The experimental results show that the proposed method has good performance for segmentation with optimal gray level thresholds.

Shannon Entropy for Neutrosophic Information

The paper presents an extension of Shannon entropy for neutrosophic information. This extension uses a new formula for distance between two neutrosophic triplets. In addition, the obtained results are particularized for bifuzzy, intuitionistic and paraconsistent fuzzy information.

Shannon entropy for intuitionistic fuzzy information

The paper presents an extension of Shannon fuzzy entropy for intuitionistic fuzzy one. Firstly, we presented a new formula for calculating the distance and similarity of intuitionistic fuzzy information. Then, we constructed measures for information features like score, certainty and uncertainty. Also, a new concept was introduced, namely escort fuzzy information. Then, using the escort fuzzy information, Shannon's formula for intuitionistic fuzzy information was obtained. It should be underlined that Shannon's entropy for intuitionistic fuzzy information verifies the four defining conditions of intuitionistic fuzzy uncertainty. The measures of its two components were also identified: fuzziness (ambiguity) and incompleteness (ignorance).

Entropy, neutro-entropy and anti-entropy for neutrosophic information

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 complexity. This deca-valued structure led to construction of two new concepts for the neutrosophic information: neutro-entropy and anti-entropy. These two concepts are added to the two existing: entropy and non-entropy. Thus, we obtained the following triad: entropy, neutro-entropy and anti-entropy.

Penta and Hexa Valued Representation of Neutrosophic Information

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 truth, index of falsity, index of ignorance, index of contradiction and index of hesitation. Also, it was constructed an associated penta valued logic and then using this logic, it was defined for the proposed penta valued structure the following operators: union, intersection, negation, complement and dual. Then, the penta valued representation is extended to a hexa valued one, adding the sixth component, namely the index of ambiguity.

Entropy and Syntropy in the Context of Five-Valued Logics

This paper presents a five-valued representation of bifuzzy sets. This representation is related to a five-valued logic that uses the following values: true, false, inconsistent, incomplete and ambiguous. In the framework of five-valued representation, formulae for similarity, entropy and syntropy of bifuzzy sets are constructed.

Similarity, Cardinality and Entropy for Bipolar Fuzzy Set in the Framework of Penta-valued Representation

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 representations and are based on a penta-valued logic that uses the following logical values: true, false, unknown, contradictory and ambiguous. Also a new distance for bounded real interval was defined.

New HSL Distance Based Colour Clustering Algorithm

In this paper, we define a distance for the HSL colour system. Next, the proposed distance is used for a fuzzy colour clustering algorithm construction. The presented algorithm is related to the well-known fuzzy c-means algorithm. Finally, the clustering algorithm is used as colour reduction method. The obtained experimental results are presented to demonstrate the effectiveness of our approach.

Multi-valued Color Representation Based on Frank t-norm Properties

In this paper two knowledge representation models are proposed, FP4 and FP6. Both combine ideas from fuzzy sets and four-valued and hexa-valued logics. Both represent imprecise properties whose accomplished degree is unknown or contradictory for some objects. A possible application in the color analysis and color image processing is discussed.

A New Penta-valued Logic Based Knowledge Representation

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 some objects. Basic operations of conjunction, disjunction and negation are introduced. Relations to other representation models like fuzzy sets, intuitionistic, paraconsistent and bipolar fuzzy sets are discussed.