Distances between Interval-valued Fuzzy Sets Taking into Account the Width of the Intervals

In this work we propose a new axiomatic definition of distance between interval-valued fuzzy sets which takes into account the width of the membership intervals and linear orders. We discuss some construction methods using aggregation functions which are defined in terms of admissible orders.

[1]  Humberto Bustince,et al.  Image Magnification Using Interval Information , 2011, IEEE Transactions on Image Processing.

[2]  Humberto Bustince,et al.  An IVFS-based image segmentation methodology for rat gait analysis , 2011, Soft Comput..

[3]  Humberto Bustince,et al.  Relationship between restricted dissimilarity functions, restricted equivalence functions and normal EN-functions: Image thresholding invariant , 2008, Pattern Recognit. Lett..

[4]  Francisco Herrera,et al.  IVTURS: A Linguistic Fuzzy Rule-Based Classification System Based On a New Interval-Valued Fuzzy Reasoning Method With Tuning and Rule Selection , 2013, IEEE Transactions on Fuzzy Systems.

[5]  Humberto Bustince,et al.  Construction theorems for intuitionistic fuzzy sets , 1996, Fuzzy Sets Syst..

[6]  Wenyi Zeng,et al.  Distance and similarity measures of Pythagorean fuzzy sets and their applications to multiple criteria group decision making , 2018, Int. J. Intell. Syst..

[7]  Chris Cornelis,et al.  Implication in intuitionistic fuzzy and interval-valued fuzzy set theory: construction, classification, application , 2004, Int. J. Approx. Reason..

[8]  Humberto Bustince,et al.  Decision making with an interval-valued fuzzy preference relation and admissible orders , 2015, Appl. Soft Comput..

[9]  Palash Dutta,et al.  Medical Diagnosis Based on Distance Measures Between Picture Fuzzy Sets , 2018, Int. J. Fuzzy Syst. Appl..

[10]  Humberto Bustince,et al.  Generation of linear orders for intervals by means of aggregation functions , 2013, Fuzzy Sets Syst..

[11]  Humberto Bustince,et al.  Indicator of inclusion grade for interval-valued fuzzy sets. Application to approximate reasoning based on interval-valued fuzzy sets , 2000, Int. J. Approx. Reason..

[12]  Humberto Bustince,et al.  Construction of interval-valued fuzzy preference relations from ignorance functions and fuzzy preference relations. Application to decision making , 2014, Knowl. Based Syst..

[13]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[14]  Hyemi Choi,et al.  A MEDICAL DIAGNOSIS BASED ON INTERVAL-VALUED FUZZY SETS , 2012 .

[15]  Qing Guo,et al.  Ensemble Interval-Valued Fuzzy Cognitive Maps , 2018, IEEE Access.

[16]  Zeshui Xu,et al.  Some geometric aggregation operators based on intuitionistic fuzzy sets , 2006, Int. J. Gen. Syst..

[17]  Humberto Bustince,et al.  A review of the relationships between implication, negation and aggregation functions from the point of view of material implication , 2016, Inf. Sci..

[18]  Oscar Castillo,et al.  A review on interval type-2 fuzzy logic applications in intelligent control , 2014, Inf. Sci..

[19]  Humberto Bustince,et al.  Construction of Interval-Valued Fuzzy Relations With Application to the Generation of Fuzzy Edge Images , 2011, IEEE Transactions on Fuzzy Systems.

[20]  Francisco Herrera,et al.  A Historical Account of Types of Fuzzy Sets and Their Relationships , 2016, IEEE Transactions on Fuzzy Systems.

[21]  Danna Zhou,et al.  d. , 1934, Microbial pathogenesis.

[22]  Humberto Bustince,et al.  Interval-valued fuzzy sets constructed from matrices: Application to edge detection , 2009, Fuzzy Sets Syst..

[23]  Maria J. Asiain,et al.  Negations With Respect to Admissible Orders in the Interval-Valued Fuzzy Set Theory , 2018, IEEE Transactions on Fuzzy Systems.

[24]  Martin Hofmann,et al.  On the non-sequential nature of the interval-domain model of real-number computation , 2004, Mathematical Structures in Computer Science.