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Logarithmic Similarity Measure between Interval-Valued Fuzzy Sets and Its Fault Diagnosis Method

Logarithmic Similarity Measure between Interval-Valued Fuzzy Sets and Its Fault Diagnosis Method
Author: Zhikang Lu
Publisher: Infinite Study
Total Pages: 12
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ISBN:
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Fault diagnosis is an important task for the normal operation and maintenance of equipment. In many real situations, the diagnosis data cannot provide deterministic values and are usually imprecise or uncertain. Thus, interval-valued fuzzy sets (IVFSs) are very suitable for expressing imprecise or uncertain fault information in real problems.

A Novel Similarity Measure for Interval-Valued Intuitionistic Fuzzy Sets and Its Applications

A Novel Similarity Measure for Interval-Valued Intuitionistic Fuzzy Sets and Its Applications
Author: Minxia Luo
Publisher: Infinite Study
Total Pages: 13
Release:
Genre: Mathematics
ISBN:
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In this paper, a novel similarity measure for interval-valued intuitionistic fuzzy sets is introduced, which is based on the transformed interval-valued intuitionistic triangle fuzzy numbers. Its superiority is shown by comparing the proposed similarity measure with some existing similarity measures by some numerical examples. Furthermore, the proposed similarity measure is applied to deal with pattern recognition and medical diagnosis problems.

Hybrid Binary Logarithm Similarity Measure for MAGDM Problems under SVNS Assessments

Hybrid Binary Logarithm Similarity Measure for MAGDM Problems under SVNS Assessments
Author: Kalyan Mondal
Publisher: Infinite Study
Total Pages: 14
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Single valued neutrosophic set is an important mathematical tool for tackling uncertainty in scientific and engineering problems because it can handle situation involving indeterminacy. In this research, we introduce new similarity measures for single valued neutrosophic sets based on binary logarithm function.

Entropy and Similarity Measure for T2SVNSs and Its Application

Entropy and Similarity Measure for T2SVNSs and Its Application
Author: Geng Juan-Juan
Publisher: Infinite Study
Total Pages: 16
Release:
Genre: Mathematics
ISBN:
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The objective of this paper is to present a new approach for solving the multi-criteria group decision-making (MCGDM) problems in type-2 single valued neutrosophic set (T2SVNS) environment. Firstly, we give the concepts SVNS, T2SVNS and tangent similarity measure with T2SVN information. Secondly, we define a new entropy function for determining unknown attribute weights.

Neutrosophic Sets and Systems

Neutrosophic Sets and Systems
Author: Florentin Smarandache
Publisher: Infinite Study
Total Pages: 133
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Genre:
ISBN:
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“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc.

Neutrosophic Sets and Systems: An International Book Series in Information Science and Engineering, vol. 20 / 2018

Neutrosophic Sets and Systems: An International Book Series in Information Science and Engineering, vol. 20 / 2018
Author: Florentin Smarandache
Publisher: Infinite Study
Total Pages: 132
Release:
Genre: Mathematics
ISBN: 1599735601
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“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc.

New Trends in Aggregation Theory

New Trends in Aggregation Theory
Author: Radomír Halaš
Publisher: Springer
Total Pages: 348
Release: 2019-05-16
Genre: Technology & Engineering
ISBN: 3030194949
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This book collects the contributions presented at AGOP 2019, the 10th International Summer School on Aggregation Operators, which took place in Olomouc (Czech Republic) in July 2019. It includes contributions on topics ranging from the theory and foundations of aggregation functions to their various applications. Aggregation functions have numerous applications, including, but not limited to, data fusion, statistics, image processing, and decision-making. They are usually defined as those functions that are monotone with respect to each input and that satisfy various natural boundary conditions. In particular settings, these conditions might be relaxed or otherwise customized according to the user’s needs. Noteworthy classes of aggregation functions include means, t-norms and t-conorms, uninorms and nullnorms, copulas and fuzzy integrals (e.g., the Choquet and Sugeno integrals). This book provides a valuable overview of recent research trends in this area.

Distance Measures between the Interval-Valued Complex Fuzzy Sets

Distance Measures between the Interval-Valued Complex Fuzzy Sets
Author: Songsong Dai
Publisher: Infinite Study
Total Pages: 12
Release:
Genre: Mathematics
ISBN:
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Complex fuzzy set (CFS) is a recent development in the field of fuzzy set (FS) theory. The significance of CFS lies in the fact that CFS assigned membership grades from a unit circle in the complex plane, i.e., in the form of a complex number whose amplitude term belongs to a [0, 1] interval. The interval-valued complex fuzzy set (IVCFS) is one of the extensions of the CFS in which the amplitude term is extended from the real numbers to the interval-valued numbers. The novelty of IVCFS lies in its larger range comparative to CFS. We often use fuzzy distance measures to solve some problems in our daily life. Hence, this paper develops some series of distance measures between IVCFSs by using Hamming and Euclidean metrics. The boundaries of these distance measures for IVCFSs are obtained. Finally, we study two geometric properties include rotational invariance and reflectional invariance of these distance measures.

A novel divergence measure and its based TOPSIS method for multi criteria decision-making under single-valued neutrosophic environment

A novel divergence measure and its based TOPSIS method for multi criteria decision-making under single-valued neutrosophic environment
Author: Nancy
Publisher: Infinite Study
Total Pages: 15
Release:
Genre: Mathematics
ISBN:
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The theme of this work is to present an axiomatic definition of divergence measure for single-valued neutrosophic sets (SVNSs). The properties of the proposed divergence measure have been studied. Further, we develop a novel technique for order preference by similarity to ideal solution (TOPSIS) method for solving single-valued neutrosophic multi-criteria decision-making with incomplete weight information. Finally, a numerical example is presented to verify the proposed approach and to present its effectiveness and practicality.

Neutrosophic Sets and Systems, vol. 51/2022

Neutrosophic Sets and Systems, vol. 51/2022
Author: Florentin Smarandache
Publisher: Infinite Study
Total Pages: 970
Release: 2022-09-01
Genre: Mathematics
ISBN:
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“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc. Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. This theory considers every notion or idea together with its opposite or negation and with their spectrum of neutralities in between them (i.e. notions or ideas supporting neither nor ). The and ideas together are referred to as . Neutrosophy is a generalization of Hegel's dialectics (the last one is based on and only). According to this theory every idea tends to be neutralized and balanced by and ideas - as a state of equilibrium. In a classical way , , are disjoint two by two. But, since in many cases the borders between notions are vague, imprecise, Sorites, it is possible that , , (and of course) have common parts two by two, or even all three of them as well. Neutrosophic Set and Neutrosophic Logic are generalizations of the fuzzy set and respectively fuzzy logic (especially of intuitionistic fuzzy set and respectively intuitionistic fuzzy logic).