In this paper, the notion of an interval valued intuitionistic fuzzy subsemiring (ideal) of a semiring with respect to t−norm T and s−norm S is given and the characteristic properties are described. The homomorphic image and inverse image are investigated. In particular, by the help of the congruence relations on semirings, new interval valued intuitionistic (S, T )−fuzzy subsemirings (ideals) ...

Abstract— This paper develops a solution procedure of multi-objective intuitionistic fuzzy optimization to solve a non-linear model with inexact co-efficient and resources. Interval approximation method is used here to convert the imprecise co-efficient which is a triangular fuzzy number to an interval number. We transform this interval number to a parametric interval valued functional form and...

We describe the formal equivalence between interval valued and intuitionistic fuzzy subsets. We then discuss the role of fuzzy set methods in multi-criteria decision-making. We note that when an application involves non-standard, interval valued or intuitionistic fuzzy subsets, a problem arises in choosing a best alternative. This problem is a result of the fact that the membership grades of th...

Intuitionistic fuzzy sets in the sense of Atanassov and interval-valued fuzzy sets can be seen as L-fuzzy sets w.r.t. a special lattice L . Deschrijver [2] introduced additive and multiplicative generators on L based on a special kind of addition introduced in [3]. Actually, many other additions can be introduced. In this paper we investigate additive generators on L as far as possible independ...

The objective of this work is to present a triangular interval type-2 (TIT2) intuitionistic fuzzy sets and their corresponding aggregation operators, namely, TIT2 intuitionistic fuzzy weighted averaging, TIT2 intuitionistic fuzzy ordered weighted averaging and TIT2 intuitionistic fuzzy hybrid averaging based on Frank norm operation laws. Furthermore, based on these operators, an approach to mul...

in this paper, we introduce  the notions of   interval-valued and $(in,ivq)$-interval-valued fuzzy ($p$-,$q$- and $a$-) ideals    of   bci algebras   and investigate some of their properties.   we then derive characterization theorems for these generalized interval-valued fuzzy ideals  and discuss their relationship.

Cubic intuitionistic fuzzy (CIF) set is the hybrid set which can contain much more information to express an interval-valued intuitionistic fuzzy set and an intuitionistic fuzzy set simultaneously for handling the uncertainties in the data. Unfortunately, there has been no research on the aggregation operators on CIF sets so far. Since an aggregation operator is an important mathematical tool i...

In this paper, we introduce the concept of interval valued fuzzy weak bi-ideals of $Gamma$-near-rings, which is a generalized concept of fuzzy weak bi-ideals of $Gamma$- near-rings. We also characterize some properties and examples of interval valued fuzzy weak bi-ideals of $Gamma$-near-rings.

Due to the increasing competition of globalization, selection of the most appropriate supplier is one of the key factors for asupply chain management’s success. Due to conflicting evaluations and insufficient information about the criteria, Intuitionisticfuzzy sets (IFSs) considered as animpressive tool and utilized to specify the relative importance of the criteria. The aim of this paper is to...