New Similarity Measure Between Single-Valued Neutrosophic Sets and Decision-Making Applications in Professional Proficiencies

New Similarity Measure Between Single-Valued Neutrosophic Sets and Decision-Making Applications in Professional Proficiencies

Memet Şahin (Gaziantep University, Turkey) and Abdullah Kargın (Gaziantep University, Turkey)
Copyright: © 2020 |Pages: 21
DOI: 10.4018/978-1-7998-2555-5.ch007


In this study, a new similarity measure for single valued neutrosophic numbers is defined. It is shown that this new similarity measure satisfies the conditions of similarity measure. This new similarity measure is used to assess professional proficiencies. In making this assessment, it is assumed that there is an imaginary ideal worker, and the authors determined the criteria of this ideal worker. Then, the rate of similarity of each worker to the ideal worker is determined with the new similarity measure. Thus, with the help of the new similarity measure, a more objective professional proficiency assessment is made.
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1 Introduction

There are many uncertainties in daily life. The logic of classical mathematics is often insufficient to explain these uncertainties. Because it is not always possible to call a situation or event absolutely right or wrong. For example, we cannot always call the weather cold or hot. It can be hot for some, cold for some and cool for others. Similar situations in which we remain indecisive may appear in the professional proficiency assessment. It is often difficult to determine whether a work done or a product produced is always definite good or definite bad. Such a situation reduces the reliability of evaluating professional proficiencies. In order to cope with these uncertainties, Smarandache (1999) defined the concept of neutrosophic logic and neutrosophic set. In the concept of neutrosophic logic and neutrosophic sets, there is T degree of membership, I degree of undeterminacy and F degree of non-membership. These degrees are defined independently of each other. A neutrosophic value is shown by (T, I, F). In other words, a condition is handled according to both its accuracy and its inaccuracy and its uncertainty. Therefore, neutrosophic logic and neutrosophic set help us to explain many uncertainties in our lives. In addition, many researchers have made studies on this theory (Şahin M., Kargın A., 2019a; Olgun N., Çelik M., 2019; Şahin M., Kargın A, 2019b; Şahin M., Kargın A., 2019c; Smarandache F., Ali M., 2016; Şahin M., Kargın A., 2019d; Şahin M., Kargın A., 2019e; Uluçay V., Şahin M., Hassan N., 2018; Uluçay V., Kiliç A., Yildiz I., Sahin M. 2018; Ulucay V., Şahin M., Olgun N. 2018; Şahin M., Olgun N., Kargın A., Uluçay V. 2018; Liu P., Shi L. 2015a; Liu P., Shi L. 2015b; Liu P., Tang G. 2016a; Liu P., Tang G. 2016b; Liu P., Wang Y. 2016; Liu P., Teng F. 2015; Liu P., Zhang L., Liu X., Wang P. 2016; Sahin M., Deli I., Ulucay V., 2016; Şahin M., Kargın A., 2017; Smarandache F., Şahin M., Kargın A., 2018; Hassan N., Uluçay, V., Şahin M. 2018; Şahin M., Kargın A., Çoban M. A., 2018; Şahin M., Kargın A., 2018; Şahin, M., Uluçay, V., Olgun, N., & Kilicman A., 2017). In fact, in the concept of fuzzy logic and fuzzy sets (Zadeh A. L., 1965), there is only a degree of membership. In addition, the concept of intuitionistic fuzzy logic and intuitionistic fuzzy set (Atanassov T. K., 1986) includes membership degree, degree of undeterminacy and degree of non-membership. But these degrees are defined dependently of each other. Therefore, neutrosophic set is a generalized state of fuzzy and intuitionistic fuzzy set. Also, single valued neutrosophic set (Wang H., Smarandache F., Zhang Y. Q., Sunderraman R., 2010) is a special set of neutrosophic sets. In single valued neutrosophic set, values ​​of membership, indeterminacy and non – membership are in the [0, 1] closed interval. Similarity measure is a measure of how similar other entities look to an asset whose properties are known. The performance of a human being, a cancer cell, a machine can be an example of the entities we are talking about. For example, by comparing the properties of a tissue known to carry definite disease to other tissues suspected to be disease, it can be found which tissue is similar to the diseased tissue. Thus, a decision can be made as to whether the suspicious tissues carry this disease. Furthermore, many researchers have made studies on similarity measure. Recently; a new similarity measure on single valued neutrosophic sets and applications to pattern recognition (Şahin M., Olgun N., Uluçay V., Kargın A., Smarandache F., 2017); some new generalized aggregation operators based on centroid single valued triangular neutrosophic numbers and their applications (Şahin M., Ecemiş O., Uluçay V., Kargın A., 2017); similarity measures in neutrosophic sets-I (Chatterjee R., Majumdar P., Samanta S. K. 2019); similarity measures of single valued neutrosophic rough sets (Mohana K., Mohanasundari M. 2019); word-level neutrosophic sentiment similarity (Smarandache F., et al., 2019) and similarity measures between interval neutrosophic sets and their applications (Ye J., 2014) were obtained.

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