Author
Bijan Davvaz
Other affiliations: Tarbiat Modares University, Khon Kaen University, University of the Punjab ...read more
Bio: Bijan Davvaz is an academic researcher from Yazd University. The author has contributed to research in topics: Fuzzy logic & Fuzzy set. The author has an hindex of 41, co-authored 568 publications receiving 7317 citations. Previous affiliations of Bijan Davvaz include Tarbiat Modares University & Khon Kaen University.
Papers published on a yearly basis
Papers
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01 Jul 2010
TL;DR: A possible fusion of fuzzy sets and rough sets is proposed to obtain a hybrid model called rough soft sets, based on a Pawlak approximation space, and a concept called soft–rough fuzzy sets is initiated, which extends Dubois and Prade's rough fuzzy sets.
Abstract: Theories of fuzzy sets and rough sets are powerful mathematical tools for modelling various types of uncertainty. Dubois and Prade investigated the problem of combining fuzzy sets with rough sets. Soft set theory was proposed by Molodtsov as a general framework for reasoning about vague concepts. The present paper is devoted to a possible fusion of these distinct but closely related soft computing approaches. Based on a Pawlak approximation space, the approximation of a soft set is proposed to obtain a hybrid model called rough soft sets. Alternatively, a soft set instead of an equivalence relation can be used to granulate the universe. This leads to a deviation of Pawlak approximation space called a soft approximation space, in which soft rough approximations and soft rough sets can be introduced accordingly. Furthermore, we also consider approximation of a fuzzy set in a soft approximation space, and initiate a concept called soft---rough fuzzy sets, which extends Dubois and Prade's rough fuzzy sets. Further research will be needed to establish whether the notions put forth in this paper may lead to a fruitful theory.
607 citations
TL;DR: The notion of strong intuitionistic fuzzy graphs is introduced and some of their properties are investigated and some propositions of self complementary and self weak complementary strong intuitionists fuzzy graphs are discussed.
Abstract: We introduce the notion of strong intuitionistic fuzzy graphs and investigate some of their properties. We discuss some propositions of self complementary and self weak complementary strong intuitionistic fuzzy graphs. We introduce the concept of intuitionistic fuzzy line graphs.
200 citations
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TL;DR: The notion of rough subring with respect to an ideal of a ring which is an extended notion of a subring (resp. ideal) in a ring and some properties of the lower and the upper approximations in a rings are given.
188 citations
01 Feb 2006
TL;DR: The aim in this paper is to introduce and study the new sort of fuzzy subnear-ring of a near-ring called (∈, ∈ ∨q)-fuzzy sub Near-ring (ideal and prime ideal) which is characterized by their level ideals.
Abstract: Our aim in this paper is to introduce and study the new sort of fuzzy subnear-ring (ideal and prime ideal) of a near-ring called (?, ? ?q)-fuzzy subnear-ring (ideal and prime ideal). These fuzzy subnear-rings (ideals) are characterized by their level ideals. Finally, we give a generalization of (?, ? ?q)-fuzzy subnear-rings (ideals).
176 citations
TL;DR: The notion of a partial n-hypergroupoid, associated with a binary relation, induced by relations, is introduced and the transitivity of the relation @b in n-semihypergroups is studied.
Abstract: In this paper, we introduce and study the notion of a partial n-hypergroupoid, associated with a binary relation. Some important results concerning Rosenberg partial hypergroupoids, induced by relations, are generalized to the case of n-hypergroupoids. Then, n-hypergroups associated with union, intersection, products of relations and also mutually associative n-hypergroupoids are analyzed. Finally, n-hypergroupoids associated with relations are used in order to study the transitivity of the relation @b in n-semihypergroups.
144 citations
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TL;DR: Based on score function and accuracy function, a method is introduced for the comparison between two intuitionistic fuzzy values and some aggregation operators are developed, such as the intuitionism fuzzy weighted averaging operator, intuitionists fuzzy ordered weighted averaging operators, and intuitionistic fuzziness hybrid aggregation operator, for aggregating intuitionist fuzzy values.
Abstract: An intuitionistic fuzzy set, characterized by a membership function and a non-membership function, is a generalization of fuzzy set. In this paper, based on score function and accuracy function, we introduce a method for the comparison between two intuitionistic fuzzy values and then develop some aggregation operators, such as the intuitionistic fuzzy weighted averaging operator, intuitionistic fuzzy ordered weighted averaging operator, and intuitionistic fuzzy hybrid aggregation operator, for aggregating intuitionistic fuzzy values and establish various properties of these operators.
2,131 citations
TL;DR: In this paper, a text on rings, fields and algebras is intended for graduate students in mathematics, aiming the level of writing at the novice rather than at the expert, and by stressing the role of examples and motivation.
Abstract: This text, drawn from the author's lectures at the University of California at Berkeley, is intended as a textbook for a one-term course in basic ring theory. The material covered includes the Wedderburn-Artin theory of semi-simple rings, Jacobson's theory of the radical representation theory of groups and algebras, prime and semi-prime rings, primitive and semi-primitive rings, division rings, ordered rings, local and semi-local rings, and perfect and semi-perfect rings. By aiming the level of writing at the novice rather than at the expert, and by stressing the role of examples and motivation, the author has produced a text which is suitable not only for use in a graduate course, but also for self-study by other interested graduate students. Numerous exercises are also included. This graduate textbook on rings, fields and algebras is intended for graduate students in mathematics.
1,479 citations
TL;DR: This paper develops an approach to group decision making based on intuitionistic preference relations and an approach based on incomplete intuitionism preference relations respectively, in which the intuitionistic fuzzy arithmetic averaging operator and intuitionism fuzzy weighted arithmetic averagingoperator are used to aggregate intuitionistic preferences.
781 citations