NEW CLASS OF SOFT LINEAR ALGEBRAIC CODES AND THEIR PROPERTIES USING SOFT SETS

Algebraic codes play a signiÖcant role in the minimization of data corruption which caused by defects such as inference, noise channel, crosstalk, and packet lost. In this paper, we introduced soft codes (soft linear codes) through the application of soft sets which is an approximated collection of codes. We also discussed several types of soft codes such as type-1 soft codes, complete soft codes etc. The innovative idea of soft codes is advantageous, for it can simultaneously transmit n-distinct messages to n-set of receivers. Further this new technique makes use of bi-matrices or to be more general uses the concept of n-matrices. Certainly this notion will save both time and economy. Moreover, we develop two techniques for the decoding of soft codes. At the end, we present a soft communication process and develop a model for this soft communication process. The distinctions and comparison of soft linear codes and linear codes are also presented

Notas sobre Soft Sets - Preliminaries

[ES]Muchos problemas de la vida real requieren el uso de datos imprecisos o inciertos. Su análisis debe implicar la aplicación de principios matemáticos capaces de captar estas características. La teoría de los conjuntos difusos supuso un cambio paradigmático en las Matemáticas al permitir la pertenencia parcial. Para una definición y argumentos acerca de su aplicabilidad a varios campos, nos interesa especialmente una generalización de los conjuntos difusos: la aplicación de la teoría de los soft sets y sus extensiones a los problemas de toma de decisiones

Intertemporal Choice of Fuzzy Soft Sets

This paper first merges two noteworthy aspects of choice. On the one hand, soft sets and fuzzy soft sets are popular models that have been largely applied to decision making problems, such as real estate valuation, medical diagnosis (glaucoma, prostate cancer, etc.), data mining, or international trade. They provide crisp or fuzzy parameterized descriptions of the universe of alternatives. On the other hand, in many decisions, costs and benefits occur at different points in time. This brings about intertemporal choices, which may involve an indefinitely large number of periods. However, the literature does not provide a model, let alone a solution, to the intertemporal problem when the alternatives are described by (fuzzy) parameterizations. In this paper, we propose a novel soft set inspired model that applies to the intertemporal framework, hence it fills an important gap in the development of fuzzy soft set theory. An algorithm allows the selection of the optimal option in intertemporal choice problems with an infinite time horizon. We illustrate its application with a numerical example involving alternative portfolios of projects that a public administration may undertake. This allows us to establish a pioneering intertemporal model of choice in the framework of extended fuzzy set theorie

Softarisons: theory and practice

[EN] This paper introduces the concept of softarison. Softarisons merge soft set theory with the theory of binary relations. Their purpose is the comparison of alternatives in a parameterized environment. We develop the basic theory and interpretations of softarisons. Then, the normative idea of ‘optimal’ alternatives is discussed in this context. We argue that the meaning of ‘optimality’ can be adjusted to fit in with the structure of each problem. A sufficient condition for the existence of an optimal alternative for unrestricted sets of alternatives is proven. This result means a counterpart of Weierstrass extreme value theorem for softarisons; thus, it links soft topology with the act of choice. We also provide a decision-making procedure—the minimax algorithm—when the alternatives are compared through a softarison. A case-study in the context of group interviews illustrates both the application of softarisons as an evaluation tool, and the computation of minimax solutions.Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature.Publicación en abierto financiada por el Consorcio de Bibliotecas Universitarias de Castilla y León (BUCLE), con cargo al Programa Operativo 2014ES16RFOP009 FEDER 2014-2020 DE CASTILLA Y LEÓN, Actuación:20007-CL - Apoyo Consorcio BUCL

Algorithms for neutrosophic soft decision making based on EDAS and new similarity measure

This paper presents two novel single-valued neutrosophic soft set (SVNSS) methods.First, we initiate a new axiomatic definition of single-valued neutrosophic simlarity measure, which is expressed by single-valued neutrosophic number (SVNN) that will reduce the information loss and remain more original information

Pengambilan Keputusan Incomplete N-Soft Sets Pada Data Untuk Mengukur Indikator Sustainable Development Goals

Data dapat dibedakan berdasarkan kejelasan tipe data yaitu data pasti dan data tidak pasti. Data pasti merupakan data yang secara makna tidak ambigu. Contohnya, data pribadi mahasiswa seperti nama, usia, latar belakang pendidikan, dan alamat. Sebaliknya, data yang tidak pasti merupakan data yang secara pemaknaan dapat lebih dari satu interpretasi. Contohnya, perempuan cantik, lelaki tinggi, sementara penilaian cantik dan tinggi relatif untuk setiap individu. Contoh lain dalam pengambilan keputusan bisnis antara lain mitra terpercaya, rekan kerja penuh tanggung jawab, konsumen potensial. Meskipun data dapat bersifat tidak tentu dalam hal nilai namun teknik dan model penyelesaian masalahnya harus tetap runut dan dapat dipertanggungjawabkan secara ilmiah. Diantaranya, probabilitas, interval matematika, fuzzy sets, rough sets, vague sets, dan soft sets serta perluasan dan kombinasi dari berbagai cabang ilmu lainnya

Notas sobre N-soft sets – Definiciones

[ES]Muchos problemas en los campos de la economía, la informática, la medicina, el medio ambiente y otras ciencias conllevan incertidumbre, imprecisión o subjetividad. Introducida por Molodtsov, la teoría de los soft sets ha demostrado su aplicabilidad a diversos campos. Fatimah et al. proponen el modelo de soft sets ampliado que denominan N-soft sets. Debido a la importancia de las calificaciones en situaciones del mundo real, los N-soft sets introducen descripciones parametrizadas del universo de opciones que dependen de un nu ́mero finito de calificaciones

Mining Temporal Association Rules with Temporal Soft Sets

This work was partially supported by the National Natural Science Foundation of China (grant no. 11301415), the Shaanxi Provincial Key Research and Development Program (grant no. 2021SF-480), and the Natural Science Basic Research Plan in Shaanxi Province of China (grant no. 2018JM1054).Traditional association rule extraction may run into some difficulties due to ignoring the temporal aspect of the collected data. Particularly, it happens in many cases that some item sets are frequent during specific time periods, although they are not frequent in the whole data set. In this study, we make an effort to enhance conventional rule mining by introducing temporal soft sets. We define temporal granulation mappings to induce granular structures for temporal transaction data. Using this notion, we define temporal soft sets and their Q-clip soft sets to establish a novel framework for mining temporal association rules. A number of useful characterizations and results are obtained, including a necessary and sufficient condition for fast identification of strong temporal association rules. By combining temporal soft sets with NegNodeset-based frequent item set mining techniques, we develop the negFIN-based soft temporal association rule mining (negFIN-STARM) method to extract strong temporal association rules. Numerical experiments are conducted on commonly used data sets to show the feasibility of our approach. Moreover, comparative analysis demonstrates that the newly proposed method achieves higher execution efficiency than three well-known approaches in the literature.National Natural Science Foundation of China (NSFC) 11301415Shaanxi Provincial Key Research and Development Program 2021SF-480Natural Science Basic Research Plan in Shaanxi Province of China 2018JM105

New Soft Set Based Class of Linear Algebraic Codes

In this paper, we design and develop a new class of linear algebraic codes defined as soft linear algebraic codes using soft sets. The advantage of using these codes is that they have the ability to transmit m-distinct messages to m-set of receivers simultaneously. The methods of generating and decoding these new classes of soft linear algebraic codes have been developed. The notion of soft canonical generator matrix, soft canonical parity check matrix, and soft syndrome are defined to aid in construction and decoding of these codes. Error detection and correction of these codes are developed and illustrated by an example