Soft set theory and uni–int decision making

Molodtsov introduced the concept of soft sets, which can be seen as a new mathematical tool for dealing with uncertainty. In this paper, we initiate the study of soft semirings by using the soft set theory. The notions of soft semirings, soft subsemirings, soft ideals, idealistic soft semirings and soft semiring homomorphisms are introduced, and several related properties are investigated.

Soft semirings

In this work, we define soft matrices and their operations which are more functional to make theoretical studies in the soft set theory We then define products of soft matrices and their properties We finally construct a soft max-min decision making method which can be successfully applied to the problems that contain uncertainties

Soft matrix theory and its decision making

Molodtsov [D. Molodtsov, Soft set theory - First results, Comput. Math. Appl. 37 (1999) 19-31] introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. In this paper we apply the notion of soft sets by Molodtsov to the theory of BCK/BCI-algebras. The notion of soft BCK/BCI-algebras and soft subalgebras are introduced, and their basic properties are derived.

Soft BCK/BCI-algebras

Applications of soft sets in ideal theory of BCK/BCI-algebras

On fuzzy h -ideals in hemirings

Molodtsov [8] introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. In this paper we apply the notion of soft sets by Molodtsov to the theory of subtraction algebras. The notion of soft WS-algebras, soft subalgebras and soft deductive systems are introduced, and their basic properties are derived.

Soft ws-algebras

. In this paper, as a generalization of derivation on a lattice,the notion of f -derivation for a lattice is introduced and some relatedproperties are investigated. 1. Introduction and preliminariesLattices play an important role in many ﬁelds such as information theory,information retrieval, information access controls and cryptanalysis [2, 6, 13, 8].Recently the properties of lattices were widely researched [1, 2, 5, 7, 8, 9, 13, 14].In the theory of rings and near rings, the properties of derivations are animportant topic to study [3, 4, 11, 12]. Y. B. Jun and X. L. Xin [10] appliedthe notion of derivation in ring and near ring theory to BCI-algebras. In[15], J. Zhan and Y. L. Liu introduced the notion of left-right (or right-left) f -derivation of a BCI algebra and investigated some properties. In [14], X. L. Xin,T. Y. Li, and J. H. Lu introduced the notion of derivation on a lattice anddiscussed some related properties.In this paper, as a generalization of derivation on a lattice, the notion of

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On f-derivations of lattices

Intuitionistic nil radicals of intuitionistic fuzzy ideals and Euclidean intuitionistic fuzzy ideals in rings

Our aim in this paper is to introduce and study the fuzzy soft ring and \(\left( \in,\in\vee q\right) \)-fuzzy soft subring that is generalization of fuzzy soft ring. We also study some of their basic properties and give several examples.

Mehmet Ali Öztürk

Papers

On fuzzy h -ideals in hemirings

Soft ws-algebras

On f-derivations of lattices

Intuitionistic nil radicals of intuitionistic fuzzy ideals and Euclidean intuitionistic fuzzy ideals in rings

Fuzzy soft rings and fuzzy soft ideals