scholarly journals A BILATTICE-BASED FRAMEWORK FOR HANDLING GRADED TRUTH AND IMPRECISION

2007 ◽  
Vol 15 (01) ◽  
pp. 13-41 ◽  
Author(s):  
GLAD DESCHRIJVER ◽  
OFER ARIELI ◽  
CHRIS CORNELIS ◽  
ETIENNE E. KERRE
Keyword(s):  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
The Other ◽  
Exact Nature ◽  
Conflicting Information ◽  
Intuitive Appeal ◽  
Application Potential ◽  
Logical Connectives ◽  
The Relationship ◽  
Interval Valued

We present a family of algebraic structures, called rectangular bilattices, which serve as a natural accommodation and powerful generalization to both intuitionistic fuzzy sets (IFSs) and interval-valued fuzzy sets (IVFSs). These structures are useful on one hand to clarify the exact nature of the relationship between the above two common extensions of fuzzy sets, and on the other hand provide an intuitively attractive framework for the representation of uncertain and potentially conflicting information. We also provide these structures with adequately defined graded versions of the basic logical connectives, and study their properties and relationships. Application potential and intuitive appeal of the proposed framework are illustrated in the context of preference modeling.

scholarly journals On Neutrosophic Offuninorms

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1136 ◽  
Author(s):  
Erick González Caballero ◽  
Florentin Smarandache ◽  
Maikel Leyva Vázquez
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Theory ◽  
Intuitionistic Fuzzy Sets ◽  
Membership Functions ◽  
Neutrosophic Sets ◽  
Intuitionistic Fuzzy ◽  
Wide Range ◽  
The Relationship ◽  
Interval Valued ◽  
Important Kind

Uninorms comprise an important kind of operator in fuzzy theory. They are obtained from the generalization of the t-norm and t-conorm axiomatic. Uninorms are theoretically remarkable, and furthermore, they have a wide range of applications. For that reason, when fuzzy sets have been generalized to others—e.g., intuitionistic fuzzy sets, interval-valued fuzzy sets, interval-valued intuitionistic fuzzy sets, or neutrosophic sets—then uninorm generalizations have emerged in those novel frameworks. Neutrosophic sets contain the notion of indeterminacy—which is caused by unknown, contradictory, and paradoxical information—and thus, it includes, aside from the membership and non-membership functions, an indeterminate-membership function. Also, the relationship among them does not satisfy any restriction. Along this line of generalizations, this paper aims to extend uninorms to the framework of neutrosophic offsets, which are called neutrosophic offuninorms. Offsets are neutrosophic sets such that their domains exceed the scope of the interval [0,1]. In the present paper, the definition, properties, and application areas of this new concept are provided. It is necessary to emphasize that the neutrosophic offuninorms are feasible for application in several fields, as we illustrate in this paper.

Width-based distance measures on interval-valued intuitionistic fuzzy sets

2021 ◽  
pp. 1-13
Author(s):  
Xi Li ◽  
Chunfeng Suo ◽  
Yongming Li
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Medical Diagnosis ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Intuitionistic Fuzzy ◽  
Interval Valued ◽  
Dissimilarity Function ◽  
Better Than

An essential topic of interval-valued intuitionistic fuzzy sets(IVIFSs) is distance measures. In this paper, we introduce a new kind of distance measures on IVIFSs. The novelty of our method lies in that we consider the width of intervals so that the uncertainty of outputs is strongly associated with the uncertainty of inputs. In addition, better than the distance measures given by predecessors, we define a new quaternary function on IVIFSs to construct the above-mentioned distance measures, which called interval-valued intuitionistic fuzzy dissimilarity function. Two specific methods for building the quaternary functions are proposed. Moreover, we also analyzed the degradation of the distance measures in this paper, and show that our measures can perfectly cover the measures on a simpler set. Finally, we provide illustrative examples in pattern recognition and medical diagnosis problems to confirm the effectiveness and advantages of the proposed distance measures.

On a Relationship Between Fuzzy Measures and AIFS

2016 ◽  
Vol 24 (06) ◽  
pp. 847-858 ◽  
Author(s):  
VicenÇ Torra ◽  
Yasuo Narukawa ◽  
Ronald R. Yager
Keyword(s):  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Fuzzy Measures ◽  
Intuitionistic Fuzzy ◽  
Atanassov Intuitionistic Fuzzy Sets ◽  
Interval Valued

The literature discusses several extensions of fuzzy sets. AIFS, IVFS, HFS, type-2 fuzzy sets are some of them. Interval valued fuzzy sets is one of the extensions where the membership is not a single value but an interval. Atanassov Intuitionistic fuzzy sets, for short AIFS, are defined in terms of two values for each element: membership and non-membership. In this paper we discuss AIFS and their relationship with fuzzy measures. The discussion permits us to define counter AIFS (cIFS) and discretionary AIFS (dIFS). They are extensions of fuzzy sets that are based on fuzzy measures.

scholarly journals Constructions for t-conorms and t-norms on interval-valued and interval-valued intuitionistic fuzzy sets by paving

2020 ◽  
Vol 26 (3) ◽  
pp. 1-12
Author(s):  
Martin Kalina ◽  
Keyword(s):  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Construction Method ◽  
Unit Interval ◽  
The Real ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

Paving is a method for constructing new operations from a given one. Kalina and Kral in 2015 showed that on the real unit interval this method can be used to construct associative, commutative and monotone operations from particular given operations (from basic ‘paving stones’). In the present paper we modify the construction method for interval-valued fuzzy sets. From given (possibly representable) t-norms and t-conorms we construct new, non-representable operations. In the last section, we modify the presented construction method for interval-valued intuitionistic fuzzy sets.

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