On nonlinear fuzzy set-valued $ \Theta $-contractions with applications

<abstract><p>Among various improvements in fuzzy set theory, a progressive development has been in process to investigate fuzzy analogues of fixed point theorems of the classical fixed point results. In this direction, taking the ideas of $ \theta $-contractions as well as Feng-Liu's approach into account, some new fuzzy fixed point results for nonlinear fuzzy set-valued $ \theta $-contractions in the framework of metric-like spaces are introduced in this paper without using the usual Pompeiu-Hausorff distance function. Our established concepts complement, unify and generalize a few important fuzzy and classical fixed point theorems in the corresponding literature. A handful of these special cases of our notions are pointed and analyzed. Some of the main results herein are further applied to derive their analogues in metric-like spaces endowed with partial ordering and binary relations. Comparisons and nontrivial examples are given to authenticate the hypotheses and significance of the obtained ideas.</p></abstract>

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On soft set-valued maps and integral inclusions

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-202154 ◽

2021 ◽

pp. 1-15

Author(s):

Monairah Alansari ◽

Shehu Shagari Mohammed ◽

Akbar Azam

Keyword(s):

Fixed Point ◽

Set Theory ◽

Fuzzy Set Theory ◽

Fixed Point Theorems ◽

Soft Set ◽

Mathematical Tool ◽

Multivalued Maps ◽

Soft Sets ◽

Special Cases ◽

New Development

As an improvement of fuzzy set theory, the notion of soft set was initiated as a general mathematical tool for handling phenomena with nonstatistical uncertainties. Recently, a novel idea of set-valued maps whose range set lies in a family of soft sets was inaugurated as a significant refinement of fuzzy mappings and classical multifunctions as well as their corresponding fixed point theorems. Following this new development, in this paper, the concepts of e-continuity and E-continuity of soft set-valued maps and αe-admissibility for a pair of such maps are introduced. Thereafter, we present some generalized quasi-contractions and prove the existence of e-soft fixed points of a pair of the newly defined non-crisp multivalued maps. The hypotheses and usability of these results are supported by nontrivial examples and applications to a system of integral inclusions. The established concepts herein complement several fixed point theorems in the framework of point-to-set-valued maps in the comparable literature. A few of these special cases of our results are highlighted and discussed.

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APPLICATIONS OF FUZZY SET THEORY AND RECENT DEVELOPMENT IN FIXED POINT THEORY IN FUZZY METRIC SPACES

10.1063/1.3525221 ◽

2010 ◽

Author(s):

Sushil Sharma

Keyword(s):

Fixed Point ◽

Set Theory ◽

Fuzzy Set ◽

Fuzzy Set Theory ◽

Metric Spaces ◽

Fixed Point Theory ◽

Point Theory ◽

Fuzzy Metric Spaces ◽

Fuzzy Metric

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Generalized dice similarity measures for complex q-Rung Orthopair fuzzy sets and its application

Complex & Intelligent Systems ◽

10.1007/s40747-020-00203-x ◽

2020 ◽

Author(s):

Harish Garg ◽

Zeeshan Ali ◽

Tahir Mahmood

Keyword(s):

Set Theory ◽

Fuzzy Set ◽

Fuzzy Set Theory ◽

Intuitionistic Fuzzy Set ◽

Similarity Measures ◽

Membership Degree ◽

Pythagorean Fuzzy Set ◽

Numerical Examples ◽

Medical Diagnoses ◽

Special Cases

AbstractComplex q-rung orthopair fuzzy set (Cq-ROFS) is an extension of Complex fuzzy set, intuitionistic fuzzy set, Pythagorean fuzzy set, to cope with complicated and inconsistence information in the environment of fuzzy set theory with a wider domain. In Cq-ROFS, each attribute is characterized by the degree of membership and non-membership degree over the unit-disc of the complex plan. Keeping the advantages of Cq-ROFSs, in this manuscript, we present a concept of the dice similarity and generalized dice similarity measures between the pairs of the sets. The basic axioms and properties are also stated. Further, we extend the proposed measures to weighted dice similarity measures and investigated their properties. The certain properties and the special cases of the proposed work are also derived. The applicability of the proposed measures is demonstrated with some numerical examples related to medical diagnoses and pattern recognition. The superiority and advantages of the measures over the existing ones are also illustrated with certain numerical examples.

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