Generalized Distance-Based Entropy and Dimension Root Entropy for Simplified Neutrosophic Sets PDF Download
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Author: Wen-Hua Cui
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 12
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Book Description
In order to quantify the fuzziness in the simplified neutrosophic setting, this paper proposes a generalized distance-based entropy measure and a dimension root entropy measure of simplified neutrosophic sets (NSs) (containing interval-valued and single-valued NSs) and verifies their properties. Then, comparison with the existing relative interval-valued NS entropy measures through a numerical example is carried out to demonstrate the feasibility and rationality of the presented generalized distance-based entropy and dimension root entropy measures of simplified NSs. Lastly, a decision-making example is presented to illustrate their applicability, and then the decision results indicate that the presented entropy measures are effective and reasonable. Hence, this study enriches the simplified neutrosophic entropy theory and measure approaches.
Author: Wen-Hua Cui
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 12
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Book Description
In order to quantify the fuzziness in the simplified neutrosophic setting, this paper proposes a generalized distance-based entropy measure and a dimension root entropy measure of simplified neutrosophic sets (NSs) (containing interval-valued and single-valued NSs) and verifies their properties. Then, comparison with the existing relative interval-valued NS entropy measures through a numerical example is carried out to demonstrate the feasibility and rationality of the presented generalized distance-based entropy and dimension root entropy measures of simplified NSs. Lastly, a decision-making example is presented to illustrate their applicability, and then the decision results indicate that the presented entropy measures are effective and reasonable. Hence, this study enriches the simplified neutrosophic entropy theory and measure approaches.
Author: Florentin Smarandache
Publisher: Infinite Study
ISBN:
Category : Antiques & Collectibles
Languages : en
Pages : 47
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Book Description
Papers on neutrosophic and plithogenic sets, logics, probabilities and statistics, on NeutroAlgebra and AntiAlgebra, NeutroGeometry and AntiGeometry, SuperHyperAlgebra and Neutrosophic SuperHyperAlgebra, etc…
Author: NANCY
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 306
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Book Description
Multiple-criteria decision-making (MCDM) problems are the imperative part of modern decision theory where a set of alternatives has to be assessed against the multiple influential attributes before the best alternative is selected. In a decision-making(DM) process, an important problem is how to express the preference value. Due to the increasing complexity of the socioeconomic environment and the lack of knowledge or the data about the DM problems, it is difficult for the decision maker to give the exact decision as there is always an imprecise, vague or uncertain information.
Author: Jun Ye
Publisher: Infinite Study
ISBN:
Category :
Languages : en
Pages : 10
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Book Description
Entropy is one of many important mathematical tools for measuring uncertain/fuzzy information. As a subclass of neutrosophic sets (NSs), simplified NSs (including single-valued and interval-valued NSs) can describe incomplete, indeterminate, and inconsistent information. Based on the concept of fuzzy exponential entropy for fuzzy sets, this work proposes exponential entropy measures of simplified NSs (named simplified neutrosophic exponential entropy (SNEE) measures), including single-valued and interval-valued neutrosophic exponential entropy measures, and investigates their properties.
Author: Han Yang
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 10
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Book Description
Information measures play an important role in the interval neutrosophic sets (INS) theory. The main purpose of this paper is to study the similarity and entropy of INS and its application in multi-attribute decision-making. We propose a new inclusion relation between interval neutrosophic sets where the importance of the three membership functions may be different. Then, we propose the axiomatic definitions of the similarity measure and entropy of the interval neutrosophic set (INS) based on the new inclusion relation. Based on the Hamming distance, cosine function and cotangent function, some new similarity measures and entropies of INS are constructed. Finally, based on the new similarity and entropy, we propose a multi-attribute decision-making method and illustrate that these new similarities and entropies are reasonable and effective.
Author: Xindong Peng
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 57
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Book Description
Neutrosophic set, initiated by Smarandache, is a novel tool to deal with vagueness considering the truth-membership T, indeterminacy-membership I and falsity-membership F satisfying the condition 0 ≤ T + I + F ≤ 3. It can be used to characterize the uncertain information more sufficiently and accurately than intuitionistic fuzzy set. Neutrosophic set has attracted great attention of many scholars that have been extended to new types and these extensions have been used in many areas such as aggregation operators, decision making, image processing, information measures, graph and algebraic structures.
Author: Hongjun Guan
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 15
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Book Description
Most existing high-order prediction models abstract logical rules that are based on historical discrete states without considering historical inconsistency and fluctuation trends. In fact, these two characteristics are important for describing historical fluctuations. This paper proposes a model based on logical rules abstracted from historical dynamic fluctuation trends and the corresponding inconsistencies. In the logical rule training stage, the dynamic trend states of up and down are mapped to the two dimensions of truth-membership and false-membership of neutrosophic sets, respectively. Meanwhile, information entropy is employed to quantify the inconsistency of a period of history, which is mapped to the indeterminercy-membership of the neutrosophic sets. In the forecasting stage, the similarities among the neutrosophic sets are employed to locate the most similar left side of the logical relationship. Therefore, the two characteristics of the fluctuation trends and inconsistency assist with the future forecasting. The proposed model extends existing high-order fuzzy logical relationships (FLRs) to neutrosophic logical relationships (NLRs). When compared with traditional discrete high-order FLRs, the proposed NLRs have higher generality and handle the problem caused by the lack of rules. The proposed method is then implemented to forecast Taiwan Stock Exchange CapitalizationWeighted Stock Index and Heng Seng Index. The experimental conclusions indicate that the model has stable prediction ability for different data sets. Simultaneously, comparing the prediction error with other approaches also proves that the model has outstanding prediction accuracy and universality.
Author: Florentin Smarandache
Publisher: Infinite Study
ISBN: 1599730804
Category : Mathematics
Languages : en
Pages : 157
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Book Description
N-Norm and N-conorm are extended in Neutrosophic Logic/Set.
Author: Amin Vafadarnikjoo
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 18
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Book Description
The analytic hierarchy process (AHP) is recognised as one of the most commonly applied methods in the multiple attribute decision-making (MADM) literature. In the AHP, encompassing uncertainty feature necessitates using suitable uncertainty theories, since dealing efficiently with uncertainty in subjective judgements is of great importance in real-world decision-making problems. The neutrosophic set (NS) theory and grey systems are two reliable uncertainty theories which can bring considerable benefits to uncertain decision-making. Thea im of this study is to improve uncertain decision-making by incorporating advantages of the NS and grey systems theories with the AHP in investigating sustainability through agility readiness evaluation in large manufacturing plants.
Author: Tomasa Calvo
Publisher: Physica
ISBN: 3790817872
Category : Computers
Languages : en
Pages : 361
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Book Description
1. The increasing number of research papers appeared in the last years that either make use of aggregation functions or contribute to its theoretieal study asses its growing importance in the field of Fuzzy Logie and in others where uncertainty and imprecision play a relevant role. Since these papers are pub lished in many journals, few books and several proceedings of conferences, books on aggregation are partieularly welcome. To my knowledge, "Agrega tion Operators. New Trends and Applications" is the first book aiming at generality , and I take it as a honour to write this Foreword in response to the gentle demand of its editors, Radko Mesiar, Tomasa Calvo and Gaspar Mayor. My pleasure also derives from the fact that twenty years aga I was one of the first Spaniards interested in the study of aggregation functions, and this book includes work by several Spanish authors. The book contains nice and relevant original papers, authored by some of the most outstanding researchers in the field, and since it can serve, as the editors point out in the Preface, as a small handbook on aggregation, the book is very useful for those entering the subject for the first time. The book also contains apart dealing with potential areas of application, so it can be helpful in gaining insight on the future developments.
