Interval-valued implications and interval-valued strong equality index with admissible orders

Zapata, Hugo; Bustince, Humberto; Montes, Susana; Bedregal, Benjamín R. C.; Dimuro, Graçaliz Pereira; Takáč, Zdenko; Baczyński, Michał; Fernández, Javier

doi:10.1016/j.ijar.2017.05.009

Cited by 73 publications

(26 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Some distance measures, based on the so-called "normalized Hamming distance" ( [4], [5], [22]), or other distances based on the Hausdorff metric [22], as well as the concepts of implication operations and strong equality indices in intervalvalued fuzzy sets ( [46]) can be seen as some examples of this general construction.…”

Section: A Construction Methods Of Scalar Extensionsmentioning

confidence: 99%

From Fuzzy Sets to Interval-Valued and Atanassov Intuitionistic Fuzzy Sets: A Unified View of Different Axiomatic Measures

Couso

Bustince

2019

IEEE Trans. Fuzzy Syst.

Self Cite

View full text Add to dashboard Cite

We examine a broad collection of axiomatic definitions from various and diverse contexts, within the domain of fuzzy sets. We evaluate their respective extensions to the case of interval-valued fuzzy sets and intuitionistic fuzzy sets, from a purely formal point of view. We conclude that a large number of such extensions follow similar formal procedures This fact allows us to formulate a general procedure which encompasses all the reviewed extensions as particular cases of it. The new general formulation allows us to identify three different procedures to derive the corresponding extension to the field of interval-valued fuzzy sets or to the field of intuitionistic fuzzy sets from a specific real-valued measure in the context of fuzzy sets. These three processes agglutinate a multitude of particular constructions found in the literature.

show abstract

Section: A Construction Methods Of Scalar Extensionsmentioning

confidence: 99%

From Fuzzy Sets to Interval-Valued and Atanassov Intuitionistic Fuzzy Sets: A Unified View of Different Axiomatic Measures

Couso

Bustince

2019

IEEE Trans. Fuzzy Syst.

Self Cite

View full text Add to dashboard Cite

show abstract

“…We are interested in extending the partial order ⩽ L I to a linear order, solving the problem of existence of incomparable elements. We recall the notion of an admissible order, which was introduced in [28] and studied, for example, in [29] and [30]. The linearity of the order is needed in many applications of real problems, in order to be able to compare any two interval data [31].…”

Section: Orders In the Interval-valued Fuzzy Settingmentioning

confidence: 99%

“…is an interval-valued aggregation function on L I with respect to ⩽ Lex1 , ⩽ Lex2 and ⩽ XY for x, y ∈ L I and ∈ [0, 1] (cf. [30]).…”

Section: Remarkmentioning

confidence: 99%

Interval Subsethood Measures with Respect to Uncertainty for the Interval-Valued Fuzzy Setting

Pękala¹,

Bentkowska²,

Sesma‐Sara³

et al. 2020

IJCIS

View full text Add to dashboard Cite

In this paper, the problem of measuring the degree of subsethood in the interval-valued fuzzy setting is addressed. Taking into account the widths of the intervals, two types of interval subsethood measures are proposed. Additionally, their relation and main properties are studied. These developments are made both with respect to the regular partial order of intervals and with respect to admissible orders. Finally, some construction methods of the introduced interval subsethood measures with the use interval-valued aggregation functions are examined.

show abstract

“…Specific total order was introduced for comparing any two intuitionistic fuzzy sets [61]. Moreover, admissible order, which refined both the total order and the classical product order, was defined on the interval-valued number set [62][63][64]. We recall the definition of admissible order on below.…”

Section: Basic Operation and Order Relation On The Set Of All Intervamentioning

confidence: 99%

Resolution of Max‐Product Fuzzy Relation Equation with Interval‐Valued Parameter

et al. 2019

View full text Add to dashboard Cite

Considering the application background on P2P network system, we investigate the max-product fuzzy relation equation with interval-valued parameter in this paper. Order relation on the set of all interval-valued numbers plays key role in the construction and resolution of the interval-valued-parameter fuzzy relation equation (IPFRE). The basic operations supremum (a∨b) and infimum (a∧b) in the IPFRE should be defined depending on the order relation. A novel total order is introduced for establishing the IPFRE. We also discuss some properties of the IPFRE system, including the consistency and structure of the complete solution set. Concepts of close index set and open index set are defined, helping us to construct the resolution method of the IPFRE system. We further provide a detailed algorithm for obtaining the complete solution set. Besides, the solution set is compared to that of the classical max-T fuzzy relation equations system.

show abstract

Interval-valued implications and interval-valued strong equality index with admissible orders

Cited by 73 publications

References 26 publications

From Fuzzy Sets to Interval-Valued and Atanassov Intuitionistic Fuzzy Sets: A Unified View of Different Axiomatic Measures

From Fuzzy Sets to Interval-Valued and Atanassov Intuitionistic Fuzzy Sets: A Unified View of Different Axiomatic Measures

Interval Subsethood Measures with Respect to Uncertainty for the Interval-Valued Fuzzy Setting

Resolution of Max‐Product Fuzzy Relation Equation with Interval‐Valued Parameter

Contact Info

Product

Resources

About