Selection principles in the context of soft sets: Menger spaces

This paper aims to extend the Interval-valued Intuitionistic Hesitant Fuzzy Set to a Generalized Interval-valued Hesitant Intuitionistic Fuzzy Soft Set (GIVHIFSS). Definition of a GIVHIFSS and some of their operations are defined, and some of their properties are studied. In these GIVHIFSSs, the authors have defined complement, null, and absolute. Soft binary operations like operations union, intersection, a subset are also defined. Here is also verified De Morgan’s laws and the algebraic structure of GIVHIFSSs. Finally, by using the comparison table, a different approach to GIVHIFSS based decision-making is presented.

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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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An algebraic approach to N-soft sets with application in decision-making using TOPSIS

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-202717 ◽

2021 ◽

pp. 1-21

Author(s):

Muhammad Shabir ◽

Rimsha Mushtaq ◽

Munazza Naz

Keyword(s):

Decision Making ◽

Mathematical Models ◽

Real World ◽

Algebraic Approach ◽

Multi Criteria Decision Making ◽

Commutative Monoids ◽

Soft Sets ◽

Algebraic Properties ◽

Different Types ◽

Selection Of

In this paper, we focus on two main objectives. Firstly, we define some binary and unary operations on N-soft sets and study their algebraic properties. In unary operations, three different types of complements are studied. We prove De Morgan’s laws concerning top complements and for bottom complements for N-soft sets where N is fixed and provide a counterexample to show that De Morgan’s laws do not hold if we take different N. Then, we study different collections of N-soft sets which become idempotent commutative monoids and consequently show, that, these monoids give rise to hemirings of N-soft sets. Some of these hemirings are turned out as lattices. Finally, we show that the collection of all N-soft sets with full parameter set E and collection of all N-soft sets with parameter subset A are Stone Algebras. The second objective is to integrate the well-known technique of TOPSIS and N-soft set-based mathematical models from the real world. We discuss a hybrid model of multi-criteria decision-making combining the TOPSIS and N-soft sets and present an algorithm with implementation on the selection of the best model of laptop.

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Some Modifications of Pairwise Soft Sets and Some of Their Related Concepts

Mathematics ◽

10.3390/math9151781 ◽

2021 ◽

Vol 9 (15) ◽

pp. 1781

Author(s):

Samer Al Ghour

Keyword(s):

Topological Space ◽

Sufficient Conditions ◽

Soft Sets ◽

New Concepts ◽

Bitopological Spaces ◽

The Relationship ◽

Soft Topological Space

In this paper, we first define soft u-open sets and soft s-open as two new classes of soft sets on soft bitopological spaces. We show that the class of soft p-open sets lies strictly between these classes, and we give several sufficient conditions for the equivalence between soft p-open sets and each of the soft u-open sets and soft s-open sets, respectively. In addition to these, we introduce the soft u-ω-open, soft p-ω-open, and soft s-ω-open sets as three new classes of soft sets in soft bitopological spaces, which contain soft u-open sets, soft p-open sets, and soft s-open sets, respectively. Via soft u-open sets, we define two notions of Lindelöfeness in SBTSs. We discuss the relationship between these two notions, and we characterize them via other types of soft sets. We define several types of soft local countability in soft bitopological spaces. We discuss relationships between them, and via some of them, we give two results related to the discrete soft topological space. According to our new concepts, the study deals with the correspondence between soft bitopological spaces and their generated bitopological spaces.

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