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.

Intuitionistic Fuzzy Aggregation Operators

Theory of fuzzy integrals and its applications

General Topology-I

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.

A first course in noncommutative rings, by T. Y. Lam. Pp. 385. £37 (pb), £62.50 (hb). 2001. ISBN 0 387 95325 6 (pb), 0 387 95183 0 (hb) (Springer-Verlag).

Intuitionistic preference relations and their application in group decision making

This paper considers a relationship between fuzzy sets and m,n-ary hypermodules We introduce the notion of a fuzzy and anti fuzzy m,n-ary sub-hypermodules A generalization of ideas presented by Davvaz and Corsini [Information Sciences 177 2007 865-875] and Bhakat and Das [Fuzzy Sets and Systems 80 1996 359-368], is presented In fact, we study ∈, ∈ ∨ q-fuzzy m,n-ary sub-hypermodules Also, the concept of a fuzzy m,n-ary sub-hypermodule with thresholds is investigated

Fuzzy m,n-ary sub-hypermodules with thresholds

In the theory of hyperrings, fundamental relations make a connection between hyperrings and ordinary rings. The fundamental relation α on hyperrings is studied by Davvaz and Vougiouklis in Communications in Algebra [8]. Now, in this article, we obtain more results about this relation. In particular, we determine necessary and sufficient conditions such that the relation α is transitive.

Relationship between Rings and Hyperrings by Using the Notion of Fundamental Relations

Fuzzy semigroup theory concentrates on theoretical aspects, but also includes applications in the areas of fuzzy coding theory, fuzzy finite state machines, and fuzzy languages. In this paper, we introduce the concept of an (ߙ,ߚ )-fuzzy filter of an ordered semigroup , where ߙ,ߚ אሼ א,ݍ,אשݍ,ארݍ ሽ with ߙ אר ݍ. Since the concept of (א,אש ݍ )-fuzzy filter is an important and useful generalization of ordinary fuzzy filter, we discuss some fundamental aspects of (א,אש ݍ )-fuzzy filters. An (א,אש ݍ )-fuzzy filter is a generalization of the existing concept of a fuzzy filter. The concept of (א,א שݍ )-fuzzy filters is also introduced and some related properties are investigated. The relationships among ordinary fuzzy filters, (א,אש ݍ )-fuzzy filters and (א,א שݍ )-fuzzy filters are discussed. We discuss the concept of (א,אש ݍ )-fuzzy left (right and bi)-filters and provide some characterization theorems. Finally, we extend the concept of a fuzzy subgroup with thresholds to the concept of a fuzzy left (right and bi)-filter with thresholds of�� .

https://ijsts.shirazu.ac.ir/article_2059_e1d9e85b68cd7d6e286f67c81cfa4dfe.pdf

Generalized fuzzy filters in ordered semigroups

In this paper a new notion of an exact sequence is introduced which is called U-exact sequence. Some interesting results concerning this concept are proved. i M ⎯ ⎯→ ⎯ i f i M ⎯ ⎯→ ⎯ +1 i f 1 + i M L → then ) ( ker ) ( Im 1 + = i i f f or }). 0 ({ ) ( Im 1 1 − + = i i f f Our aim in this paper is to introduce a new notion exact sequence. It is a natural question to ask what does happen if we substitute a submodule 1 + i U of 1 + i M instead of the trivial submodule } 0 { in the above definition. In this paper we introduce the concept of U-exact sequences and answer the above question. We also obtain properties of the U-exact sequences, for example, a generalization of Five Lemma holds, and we obtain a relationship between U-exact sequences and ascending chain condition similar to the ordinary exact sequences. Finally from a U-exact sequence, we get an 1 − S U-exact sequence of module of fractions. Throughout this paper we let R to be a commutative ring and C

/pdf/a-note-on-exact-sequences-ketpqae951.pdf

Bijan Davvaz

Papers

Fuzzy m,n-ary sub-hypermodules with thresholds

Relationship between Rings and Hyperrings by Using the Notion of Fundamental Relations

Generalized fuzzy filters in ordered semigroups

A Note on Exact Sequences

Fuzzy hyperrings (Hv-rings) based on fuzzy universal sets