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1

Coupled fixed point theorem in b-fuzzy metric spaces

Došenović T, Hassanzadeh Z., Sedghi S.

Fasciculi Mathematici

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2018

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Nr 61

27--41

EN

The aim of this paper is to prove a coupled coincidence fixed point theorem in complete b-fuzzy metric space using the concept of mixed monotone mappings, which represents a generalization of some recent results.

2

On some properties of (h,e)-implications. distributivities with t-norms and t-conorms.

Massanet S., Torrens J.

Journal of Artificial Intelligence and Soft Computing Research

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2012

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Vol. 2, No. 2

109--123

EN

In this paper some basic properties of (h, e)-implications are studied. This kind of implications has been recently introduced (see [29]). They are implications generated from an additive generator of a representable uninorm in a similar way of Yager’s f- and gimplications which are generated from additive generators of continuous Archimedean t-norms and t-conorms, respectively. In addition, they satisfy a classical property of some types of implications derived from uninorms that is I(e,y) = y for all y ∈ [0,1]. Moreover they are examples of fuzzy implications satisfying the exchange principle but not the law of importation for any t-norm, in fact for any function F : [0,1] 2 → [0,1]. On the other hand, the distributivities with conjunctions and disjunctions (t-norms and t-conorms) are also studied leading to new solutions of the corresponding functional equations. Finally, it is proved that they do not intersect with any of the most used classes of implications.

3

A Common Fixed Point Theorem for Set-valued Contraction Mappings in Menger Space

Pant B. D., Chauhan S., Kumar S.

Commentationes Mathematicae

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2012

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Vol. 52, [Z] 1

61-71

EN

The aim of this paper is to prove a common fixed point theorem for even number of single-valued and two set-valued mappings in complete Menger space using implicit relation. Our result improves and extends the result of Chen and Chang [Common fixed point theorems in Menger spaces, Int. J. Math. Math. Sci. 2006, Art. ID 75931, 15 pp].

4

A Note on Axiom System for SBL-algebras

Halaš R.

Fundamenta Informaticae

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2009

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Vol. 90, nr 1-2

87-92

EN

In the paper we resolve an open problem posed by D.Ciucci in [1] on the independence of axioms for SBL-algebras. The main aim is to present its solution which is, in contrast to the one presented in [4], simple, transparent and easily verifiable.

5

On the Axiomatic System of SBL- algebras

Švrček F.

Fundamenta Informaticae

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2008

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Vol. 89, nr 2-3

345-368

EN

SBL-algebras were introduced as algebraic models for the basic strict fuzzy logic SBL extended with an involutive negation. The open problemof a minimal independent axiomatic system of the SBL-algebras is resolved in the paper.

6

Granular entropy and granulation procee

Rybalov A.

Archives of Control Sciences

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2002

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Vol. 12, no. 4

457-467

EN

People use granulation to represent original data as a set of entities that are better suited for managing resulting subtasks. Concept that are introduced in this paper are based on two features of granulation: the revelance of all the points in a granule and relative number of points in every granule. Based on these features several concepts are introduced that include granular relevance, defined as sum of relevancies of all the points in the granule and granular entropy, that is similar to information entropy and reflects the dispersion of relevant points across granules. Using these concepts granulation process is represented as solution of optimization problem where objective function is granular entropy. To this end the theorem, that shows how the change in relevance of points in a granule affects granular entropy, was proved. The last two sections of the paper show how leverage over the granulation process can be achieved by using t-norm and uni-norm operators.

7

Data granulation through optimization of similarity measure

Bargiela A., Pedrycz W., Hirota K.

Archives of Control Sciences

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2002

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Vol. 12, no. 4

469-491

EN

We introduce a logic-driven clustering in which prototypes are formed and evaluated in a sequential manner. The way of revealing a structure in data is realized by maximizing a certain performance index (objective function) that takes into consideration an overall level of matching and a similarity level between the prototypes. It is shown how the relevance of the prototypes translates into their granularity. The clustering method helps identify and quantify anisotropy of the feature space. We also show how each prototype is equipped with its own weight vector describing the anisotropy property and thus implying some ranking of the features in the data space.

8

Necessity measures and parametric inclusion relations of fuzzy sets

Inuiguchi M., Tanino T.

Fundamenta Informaticae

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2000

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Vol. 42, nr 3,4

279-302

EN

A necessity measure N is defined by an implication function. However, specification of an implication function is difficult. Necessity measures are closely related to inclusion relations. In this paper, we propose an approach to necessity measure specification by giving a parametric inclusion relation between fuzzy sets A and B which is equivalent to NA(B) > h. It is shown that, in such a way, we can specify a necessity measure, i.e., an implication function. Moreover, when a necessity measure or equivalently, an implication function is given, then the derivation of an associated parametric inclusion relation is discussed. The associated parametric inclusion relation cannot be obtained for any implication function but only for implication functions which satisfy certain conditions. Applying our results to necessity measures defined by S-, R- and reciprocal R-implications with continuous Archimedean t-norms, associated parametric inclusion relations are shown.

9

On common fixed point theorems of compatible mappings in Menger spaces

Rashwan R., Hedar A.

Demonstratio Mathematica

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1998

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Vol. 31, nr 3

537-546