On Interval-Valued Intuitionistic Fuzzy Hyper BCK-Ideals of Hyper BCK Algebras

In this paper, we apply the concept of an interval-valued intuitionistic fuzzy set to hyper BCK-ideals in hyper BCK-algebras. The notion of an interval-valued intuitionistic fuzzification of (strong, weak, s-weak) hyper BCK-ideals is introduced, and related properties are investigated. Characterizations of an interval-valued intuitionistic fuzzification of hyper BCK-ideals are established

Interval valued intuitionistic (S,T)(S,T)-fuzzy HvH_v-submodules

On the basis of the concept of the interval valued intuitionistic fuzzy sets introduced by K.Atanassov, the notion of interval valued intuitionistic fuzzy $H_v$-submodules of an $H_v$-module with respect to $t$-norm $T$ and $s$-norm $S$ is given and the characteristic properties are described. The homomorphic image and the inverse image are investigated.In particular, the connections between interval valued intuitionistic $(S,T)$-fuzzy $H_v$-submodules and interval valued intuitionistic $(S,T)$-fuzzy submodules are discussed

A Geometric Interpretation of the Neutrosophic Set - A Generalization of the Intuitionistic Fuzzy Set

In this paper we generalize the intuitionistic fuzzy set (IFS), paraconsistent set, and intuitionistic set to the neutrosophic set (NS). Several examples are presented. Also, a geometric interpretation of the Neutrosophic Set is given using a Neutrosophic Cube. Many distinctions between NS and IFS are underlined.Comment: 9 pages. Presented at the 2003 BISC FLINT-CIBI International Workshop on Soft Computing for Internet and Bioinformatics, University of Berkeley, California, December 15-19, 2003, under the title "Generalization of the Intuitionistic Fuzzy Set to the Neutrosophic Set

Interval Valued intuitionistic Fuzzy Homomorphism of BF-algebras

The notion of interval-valued intuitionistic fuzzy sets was first introduced by Atanassov and Gargov as a generalization of both interval-valued fuzzy sets and intuitionistic fuzzy sets. Satyanarayana et. al., applied the concept of interval-valued intuitionistic fuzzy ideals to BF-algebras. In this paper, we introduce the notion of interval-valued intuitionistic fuzzy homomorphism of BF-algebras and investigate some interesting properties. Keywords: BF-algebras, interval valued intuitionistic fuzzy sets, i-v intuitionistic fuzzy ideals

A New Type of Compositive Information Entropy for IvIFS and Its Applications

We first show the interval-valued intuitionistic fuzzy entropy which reflects intuitionism and fuzziness of interval-valued intuitionistic fuzzy set (IvIFS) based on interval-valued intuitionistic fuzzy cross-entropy. As for intuitionism and fuzziness of IvIFS, we propose interval-valued intuitionistic entropy and interval-valued fuzzy entropy, respectively. Furthermore, we establish the interval-valued span entropy describing the uncertainty of membership degree and nonmembership degree and show some concrete measure formulas. Combining intuitionistic factor, fuzzy factor, and span factor, we ultimately put forward the axiomatic definition of the compositive entropy and give a measure formula of compositive entropy. In addition, the effectiveness of the compositive entropy measure is illuminated by comparison with other entropy measures. Furthermore, the compositive entropy is applied to multiple attributes’ decision-making by using the weighted correlation coefficient between IvIFSs and pattern recognition by a similarity measure transformed from the compositive entropy

ASSESSMENT OF SUSTAINABLE WASTEWATER TREATMENT TECHNOLOGIES USING INTERVAL-VALUED INTUITIONISTIC FUZZY DISTANCE MEASURE-BASED MAIRCA METHOD

Effective wastewater treatment has significant effects on saving water and preventing unnecessary water scarcity. An appropriate wastewater treatment technology (WWTT) brings economic benefits through reuse in different sectors and benefits the society and environment. This study aims to develop a decision-making framework for evaluating the sustainable WWTTs under interval-valued intuitionistic fuzzy set (IVIFS) environment. The proposed MCDM framework is divided into two stages. First, a new Hellinger distance measure is developed to determine the degree of difference between IVIFSs and also discussed its desirable characteristics. Second, an interval-valued intuitionistic fuzzy extension of multi-attribute ideal-real comparative analysis (MAIRCA) model is developed using the proposed Hellinger distance measure-based weighting tool. Further, the proposed model is implemented on an empirical study of sustainable WWTTs evaluation problem. Sensitivity and comparative studies are made. The results indicate that odor impacts, sludge production, maintenance and operation are the most effective sustainable factors and Microbial fuel cell (MFC) technology is the best WWTT followed by natural treatment methods