Generalized operations in soft set theory via relaxed conditions on parameters

Soft set theory has been evolved as a very useful mathematical tool to handle uncertainty and ambiguity associated with the real world data based structures. Parameters with certain conditions have been used to classify the data with the help of suitable functions. The aim of this paper is to relax conditions on parameters which lead us to propose some new concepts that consequently generalize existing comparable notions. We introduce the concepts of generalized finite soft equality (gf-soft equality), generalized finite soft union (gf-soft union) and generalized finite soft intersection (gf-soft intersection) of two soft sets. We prove results involving operations introduced herein. Moreover, with the help of examples, it is shown that these operations are proper generalizations of existing comparable operations.

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On generalized soft equality and soft Lattice structure

Filomat ◽

10.2298/fil1406191a ◽

2014 ◽

Vol 28 (6) ◽

pp. 1191-1203 ◽

Cited By ~ 1

Author(s):

Mujahid Abbas ◽

Basit Ali ◽

Salvador Romaguera

Keyword(s):

Real World ◽

Lattice Structure ◽

Mathematical Tool ◽

Lattice Structures ◽

Soft Sets ◽

Dependence Relation ◽

Real World Data ◽

World Data ◽

New Concepts

Molodtsov introduced soft sets as a mathematical tool to handle uncertainty associated with real world data based problems. In this paper we propose some new concepts which generalize existing comparable notions. We introduce the concept of generalized soft equality (denoted as g-soft equality) of two soft sets and prove that the so called lower and upper soft equality of two soft sets imply g-soft equality but the converse does not hold. Moreover we give tolerance or dependence relation on the collection of soft sets and soft lattice structures. Examples are provided to illustrate the concepts and results obtained herein.

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Trastuzumab-based palliative chemotherapy for HER2-positive gastric cancer: a single-center real-world data

BMC Cancer ◽

10.1186/s12885-021-08058-2 ◽

2021 ◽

Vol 21 (1) ◽

Author(s):

Tae-Hwan Kim ◽

Hun Do Cho ◽

Yong Won Choi ◽

Hyun Woo Lee ◽

Seok Yun Kang ◽

...

Keyword(s):

Gastric Cancer ◽

Real World ◽

Group Performance ◽

Eastern Cooperative Oncology Group ◽

Conversion Surgery ◽

Single Center ◽

Her2 Positive ◽

Real World Data ◽

World Data ◽

The Real

Abstract Background Since the results of the ToGA trial were published, trastuzumab-based chemotherapy has been used as the standard first-line treatment for HER2-positive recurrent or primary metastatic gastric cancer (RPMGC). However, the real-world data has been rarely reported. Therefore, we investigated the outcomes of trastuzumab-based chemotherapy in a single center. Methods This study analyzed the real-world data of 47 patients with HER2-positive RPMGC treated with trastuzumab-based chemotherapy in a single institution. Results With the median follow-up duration of 18.8 months in survivors, the median overall survival (OS) and progression-free survival were 12.8 and 6.9 months, respectively, and the overall response rate was 64%. Eastern Cooperative Oncology Group performance status 2 and massive amount of ascites were independent poor prognostic factors for OS, while surgical resection before or after chemotherapy was associated with favorable OS, in multivariate analysis. In addition, 5 patients who underwent conversion surgery after chemotherapy demonstrated an encouraging median OS of 30.8 months, all with R0 resection. Conclusions Trastuzumab-based chemotherapy in patients with HER2-positive RPMGC in the real world demonstrated outcomes almost comparable to those of the ToGA trial. Moreover, conversion surgery can be actively considered in fit patients with a favorable response after trastuzumab-based chemotherapy.

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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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Gemcitabine plus nab-paclitaxel in older patients with metastatic pancreatic cancer: A post-hoc analysis of the real-world data of a multicenter study (the NAPOLEON study)

Journal of Geriatric Oncology ◽

10.1016/j.jgo.2021.06.011 ◽

2021 ◽

Author(s):

Futa Koga ◽

Yasunori Kawaguchi ◽

Mototsugu Shimokawa ◽

Kenichiro Murayama ◽

Shunya Nakashita ◽

...

Keyword(s):

Pancreatic Cancer ◽

Multicenter Study ◽

Real World ◽

Older Patients ◽

Metastatic Pancreatic Cancer ◽

Real World Data ◽

World Data ◽

The Real ◽

Post Hoc Analysis ◽

Post Hoc

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An algorithm for fuzzy soft set based decision making approach

Yugoslav journal of operations research ◽

10.2298/yjor190715026m ◽

2020 ◽

Vol 30 (1) ◽

pp. 59-70

Author(s):

Shehu Mohammed ◽

Akbar Azam

Keyword(s):

Decision Making ◽

Set Theory ◽

Group Decision Making ◽

Group Decision ◽

Soft Set ◽

Mathematical Tool ◽

Fuzzy Soft Set ◽

Soft Sets ◽

Fuzzy Soft Sets ◽

Priority Table

The notion of soft set theory was initiated as a general mathematical tool for handling ambiguities. Decision making is viewed as a cognitive-based human activity for selecting the best alternative. In the present time, decision making techniques based on fuzzy soft sets have gained enormous attentions. On this development, this paper proposes a new algorithm for decision making in fuzzy soft set environment by hybridizing some existing techniques. The first novelty is the idea of absolute scores. The second concerns the concept of priority table in group decision making problems. The advantages of our approach herein are stronger power of objects discrimination and a well-determined inference.

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A note on soft near-rings and idealistic soft near-rings

Filomat ◽

10.2298/fil1101053s ◽

2011 ◽

Vol 25 (1) ◽

pp. 53-68 ◽

Cited By ~ 21

Author(s):

Aslıhan Sezgin ◽

Osman Atagün ◽

Emin Aygün

Keyword(s):

Set Theory ◽

Theoretical Aspect ◽

Soft Set ◽

Mathematical Tool ◽

Soft Sets ◽

Theoretical Approaches

Molodtsov introduced the theory of soft sets, which can be seen as an effective mathematical tool to deal with uncertainties, since it is free from the difficulties that the usual theoretical approaches have troubled. In this paper, we apply the definitions proposed by Ali et al. [M. I. Ali, F. Feng, X. Liu, W. K. Min and M. Shabir, On some new operations in soft set theory, Comput. Math. Appl. 57 (2009), 1547-1553] to the concept of soft near- rings and substructures of soft near-rings, proposed by Atag?n and Sezgin [A. O. Atag?n and A. Sezgin, Soft Near-rings, submitted] and show them with illustrating examples. Moreover, we investigate the properties of idealistic soft near-rings with respect to the near-ring mappings and we show that the structure is preserved under the near-ring epimorphisms. Main purpose of this paper is to extend the study of soft near-rings from a theoretical aspect.

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