Representations of a Comparison Measure between Two Fuzzy Sets
This paper analyzes the representation behaviors of a comparison measure between two compared fuzzy sets. Three types of restrictions on two fuzzy sets are considered in this paper: two disjoint union fuzzy sets, two disjoint fuzzy sets and two general fuzzy sets. Differences exist among the numbers...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-12-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/12/12/2008 |
| _version_ | 1797545603134128128 |
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| author | Juin-Han Chen Hui-Chin Tang |
| author_facet | Juin-Han Chen Hui-Chin Tang |
| author_sort | Juin-Han Chen |
| collection | DOAJ |
| description | This paper analyzes the representation behaviors of a comparison measure between two compared fuzzy sets. Three types of restrictions on two fuzzy sets are considered in this paper: two disjoint union fuzzy sets, two disjoint fuzzy sets and two general fuzzy sets. Differences exist among the numbers of possible representations of a comparison measure for the three types of fuzzy sets restrictions. The value of comparison measure is constant for two disjoint union fuzzy sets. There are 49 candidate representations of a comparison measure for two disjoint fuzzy sets, of which 13 candidate representations with one or two terms are obtained. For each candidate representation, a variant of the general axiomatic definition for a comparison measure is presented. Choosing the right candidate representation for a given application, we can easily and efficiently calculate and compare a comparison measure. |
| first_indexed | 2024-03-10T14:18:39Z |
| format | Article |
| id | doaj.art-9d9be5cec2d444cb9ca972187351bb91 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T14:18:39Z |
| publishDate | 2020-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-9d9be5cec2d444cb9ca972187351bb912023-11-20T23:35:59ZengMDPI AGSymmetry2073-89942020-12-011212200810.3390/sym12122008Representations of a Comparison Measure between Two Fuzzy SetsJuin-Han Chen0Hui-Chin Tang1Department of Industrial Engineering and Management, Cheng Shiu University, Kaohsiung 83347, TaiwanDepartment of Industrial Engineering and Management, National Kaohsiung University of Science and Technology, Kaohsiung 80778, TaiwanThis paper analyzes the representation behaviors of a comparison measure between two compared fuzzy sets. Three types of restrictions on two fuzzy sets are considered in this paper: two disjoint union fuzzy sets, two disjoint fuzzy sets and two general fuzzy sets. Differences exist among the numbers of possible representations of a comparison measure for the three types of fuzzy sets restrictions. The value of comparison measure is constant for two disjoint union fuzzy sets. There are 49 candidate representations of a comparison measure for two disjoint fuzzy sets, of which 13 candidate representations with one or two terms are obtained. For each candidate representation, a variant of the general axiomatic definition for a comparison measure is presented. Choosing the right candidate representation for a given application, we can easily and efficiently calculate and compare a comparison measure.https://www.mdpi.com/2073-8994/12/12/2008fuzzy setcomparison measurerepresentationdisjoint |
| spellingShingle | Juin-Han Chen Hui-Chin Tang Representations of a Comparison Measure between Two Fuzzy Sets Symmetry fuzzy set comparison measure representation disjoint |
| title | Representations of a Comparison Measure between Two Fuzzy Sets |
| title_full | Representations of a Comparison Measure between Two Fuzzy Sets |
| title_fullStr | Representations of a Comparison Measure between Two Fuzzy Sets |
| title_full_unstemmed | Representations of a Comparison Measure between Two Fuzzy Sets |
| title_short | Representations of a Comparison Measure between Two Fuzzy Sets |
| title_sort | representations of a comparison measure between two fuzzy sets |
| topic | fuzzy set comparison measure representation disjoint |
| url | https://www.mdpi.com/2073-8994/12/12/2008 |
| work_keys_str_mv | AT juinhanchen representationsofacomparisonmeasurebetweentwofuzzysets AT huichintang representationsofacomparisonmeasurebetweentwofuzzysets |