Negations With Respect to Admissible Orders in the Interval-Valued Fuzzy Set Theory

Asiain, Maria José; Bustince, Humberto; Mesiar, Radko; Kolesárová, Anna; Takáč, Zdenko

doi:10.1109/tfuzz.2017.2686372

Cited by 50 publications

(20 citation statements)

References 40 publications

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“…The second construction method is based on the next theorem. Recall that an interval-valued fuzzy negation N IV is an antytonic operation that satisfies N IV ( ) = and N IV ( ) = [43,44].…”

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

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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.

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“…The second construction method is based on the next theorem. Recall that an interval-valued fuzzy negation N IV is an antytonic operation that satisfies N IV ( ) = and N IV ( ) = [43,44].…”

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

Self Cite

View full text Add to dashboard Cite

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“…In this section, we introduce several well known notions and results which are necessary for our subsequent developments. We consider closed subintervals of the unit interval [0,1]. In this sense, we denote:…”

Section: Preliminariesmentioning

confidence: 99%

“…This is the order relation most widely used in the literature [15]. We denote by ≤ L any order in L([0, 1]) (which can be partial or total) with 0 L = [0, 0] as its minimal element and 1 L = [1,1] as its maximal element. To denote a total order in L([0, 1]) with these minimal and maximal elements, we use the notation ≤ TL .…”

Section: Definition 1: An Order Relation On L(mentioning

confidence: 99%

“…Distance measures and entropies are significant notions in fuzzy sets theory due to their high applicability [18], [26], [29], [31], [35], [43], [45]. At the same time, interval-valued fuzzy sets [12] in many cases improve the results of fuzzy sets in different applications [1]- [4], [6], [7], [11], [14], [16], [17], [22], [34], [42], since they allow us to take into account the uncertainty linked to the construction of a precise membership function. For this reason, there exists a wide interest in the literature for extending the notions of distance measure and entropy to deal with interval-valued fuzzy sets and entropies [5], [23], [37], [38].…”

Section: Introductionmentioning

confidence: 99%

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Width-Based Interval-Valued Distances and Fuzzy Entropies

et al. 2019

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In this paper, we study distance measures between interval-valued fuzzy sets and entropies of interval-valued fuzzy sets. These are well-known and widely used notions in the fuzzy sets theory. The novelty of our approach is twofold: on one hand, it considers the width of intervals in order to connect the uncertainty of the output with the uncertainty of the inputs. On the other hand, it makes use of total orders between intervals, instead of partial ones, so that the usefulness of the notions related with some kind of monotonicity is fully recovered in the interval-valued setting. The construction of distance measures and entropies is done by aggregating interval-valued restricted dissimilarity functions and interval-valued normal E N-functions. For this reason, we first study these functions, both in line with the two above stated considerations. Finally, we present an illustrative example in image thresholding using an expression of the proposed interval-valued entropy to show the validity of our approach. INDEX TERMS Admissible order, interval-valued distance, interval-valued entropy, interval-valued restricted dissimilarity function. INÉS COUSO received the Ph.D. degree in mathematics from the University of Oviedo, Spain, in 1999. She was an Invited Researcher with the

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“…Therefore, the PyFS is the generalization of the IFS because the domain of the PyFS is larger than the IFS. For some other recent studies on IFSs and PyFSs, one may refer to Asiain et al [5], Mahmood et al [6], Li [7], Peng and Yang [8], Garg [9], Wei and Lu [10] and Lu et al [11,12].…”

Section: Introductionmentioning

confidence: 99%

Similarity Measures for Fractional Orthotriple Fuzzy Sets Using Cosine and Cotangent Functions and Their Application in Accident Emergency Response

et al. 2020

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The fractional orthotriple fuzzy set (FOFS) is more generalized than the spherical fuzzy set (SFS) and picture fuzzy set (PFS) to cope with awkward and complex information in fuzzy set (FS) theory. The FOFS is a more powerful technique with respect to the existing drawbacks because of its conditions, i.e., the sum of the f powers of positive, neutral, and negative grades is bounded to [0,1]. With the advantages of the FOFS, in this paper, we study the basic definitions and some existing similarity measures (SMs) of intuitionistic fuzzy sets (IFSs), PFSs, Pythagorean fuzzy sets (PyFSs) and SFSs. The existing approaches have certain limitations and cannot be applied to problems that are in the form of FOFSs. The goal of this paper is to propose the idea of some new SMs including cosine SMs for FOFSs, SMs for FOFSs based on the cosine function, and SMs for FOFSs based on the cotangent function. Further, some weighted SMs (WSMs) are also proposed for which the weight of the attributes is considered. Then, we apply these SMs and WSMs to the pattern recognition problem. Finally, the comparative study of the new SMs for FOFSs is established with existing SMs, and also, some advantages of the proposed work are discussed.

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Negations With Respect to Admissible Orders in the Interval-Valued Fuzzy Set Theory

Cited by 50 publications

References 40 publications

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

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

Width-Based Interval-Valued Distances and Fuzzy Entropies

Similarity Measures for Fractional Orthotriple Fuzzy Sets Using Cosine and Cotangent Functions and Their Application in Accident Emergency Response

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