Similarity in fuzzy systems

Pal, A. K.; Mondal, Bapin; Bhattacharyya, Namrata; Raha, Sanghamitra

doi:10.1186/s40467-014-0018-0

Cited by 12 publications

(7 citation statements)

References 31 publications

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“…A fuzzy measure based on matching functions [17] is also included in Table I as it uses the maximum t-conorm. A detailed discussion of set-theoretic similarity measures for fuzzy sets can be found in [20] and [21].…”

Section: Fuzzy Set-theoretic Similarity Measuresmentioning

confidence: 99%

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A Bidirectional Subsethood Based Similarity Measure for Fuzzy Sets

Kabir

Wagner

Havens

et al. 2018

2018 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

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Similarity measures are useful for reasoning about fuzzy sets. Hence, many classical set-theoretic similarity measures have been extended for comparing fuzzy sets. In previous work, a set-theoretic similarity measure considering the bidirectional subsethood for intervals was introduced. The measure addressed specific concerns of many common similarity measures, and it was shown to be bounded above and below by Jaccard and Dice measures respectively. Herein, we extend our prior measure from similarity on intervals to fuzzy sets. Specifically, we propose a vertical-slice extension where two fuzzy sets are compared based on their membership values. We show that the proposed extension maintains all common properties (i.e., reflexivity, symmetry, transitivity, and overlapping) of the original fuzzy similarity measure. We demonstrate and contrast its behaviour along with common fuzzy set-theoretic measures using different types of fuzzy sets (i.e., normal, non-normal, convex, and non-convex) in respect to different discretization levels.

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Section: Fuzzy Set-theoretic Similarity Measuresmentioning

confidence: 99%

“…We note that Eq. (7)behaves like a fuzzy measure mentioned in[21] for the minimum t-norm, though the origin of this measure is unknown.…”

mentioning

confidence: 99%

A Bidirectional Subsethood Based Similarity Measure for Fuzzy Sets

Kabir

Wagner

Havens

et al. 2018

2018 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

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“…This motivates the introduction of similarity based reasoning techniques as proposed in [12] [13] [14]. A brief review work on similarity based approximate reasoning, in general, can be found in [10] [15]. A detailed description of similarity related reasoning can also be found in [12].…”

Section: Similarity Based Fuzzy System (Sbfs)mentioning

confidence: 99%

“…We interpret the result as a conditional fuzzy relation. Then, the similarity value is used to modify the conditional relation [10]. Such a modification of relation may also be performed in many ways.…”

Section: Introductionmentioning

confidence: 99%

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A Similarity Based Fuzzy System as a Function Approximator

Pal¹,

Karim²,

Mondal³

et al. 2018

IJIS

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In this paper, an attempt is made to prove that some similarity based fuzzy systems can be found to behave as function approximators. A typical similarity based fuzzy system is proposed and its behaviour is shown to have the said property. It elucidates the connection between similarity relation and similarity measure of fuzzy sets to fuzzy inference methodology. The concept of similarity relation is used in fuzzification of crisp input values. Similarity index is used in measuring approximate equality of fuzzy sets over a given universe of discourse of a linguistic variable. The similarity between the observation(s) and the antecedent of a rule is used in selecting rule(s) for possible firing and also in modifying the relation between the antecedent and consequent of the rule based on the specific observation. Inference is drawn through the usual composition and subsequently by projecting the modified fuzzy restriction acting on the variables of interest on the universe of the linguistic variable in the consequent of the rule. A specificity based defuzzification scheme is proposed for multiple-rule firing. It has been proved systematically that such a similarity based fuzzy system can uniformly approximate continuous functions to any desired degree of accuracy on a closed and bounded interval. Simulation results are presented for the well-known dc-motor problem. A comparative study is made to establish the validity and efficiency of the proposed similarity based fuzzy system.

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Fuzziness in Information Extracted from Social Media Keywords

Shahbazova

Shahbazzade

2018

Communications in Computer and Information Science

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Similarity in fuzzy systems

Cited by 12 publications

References 31 publications

A Bidirectional Subsethood Based Similarity Measure for Fuzzy Sets

A Bidirectional Subsethood Based Similarity Measure for Fuzzy Sets

A Similarity Based Fuzzy System as a Function Approximator

Fuzziness in Information Extracted from Social Media Keywords

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