Interval-Valued$m$-Polar Fuzzy Positive Implicative Ideals in$BCK$-Algebras

Abstract

In this paper, the notion of interval-valued m -polar fuzzy positive implicative ideals in BCK-algebras is presented. Then, the relationships between interval-valued m -polar fuzzy positive implicative ideals and interval-valued m -polar fuzzy ideals are investigated. After that, the concepts of interval-valued m -polar ∈ , ∈ ∨ q κ ˜ -fuzzy positive implicative ideals and interval-valued m -polar ∈ , ∈ ∨ q κ ˜ -fuzzy ideals are defined and some equivalent conditions are provided. Furthermore, we show that interval-valued m -polar ∈ , ∈ ∨ q κ ˜ -fuzzy positive implicative ideals are interval-valued m -polar ∈ , ∈ ∨ q κ ˜ -fuzzy ideals, but the converse need not be true in general and an example is given in this aim.

Approach to Multiattribute Decision-Making Problems Based on Neutrality Aggregation Operators of Picture Fuzzy Information

“…Zeng [16] made decisionmaking more effective by utilizing uncertain intelligence. Muhiuddin et al [17,18] recorded their extension in the field of interval valued m polar fuzzy structure. Pan and Deng [19] established a new similarity measure to discuss the clustering problems under IFS.…”

Retracted: Interval‐Valued m‐Polar Fuzzy Positive Implicative Ideals in BCK‐Algebras

“…This article has been retracted by Hindawi following an investigation undertaken by the publisher [1]. This investigation has uncovered evidence of one or more of the following indicators of systematic manipulation of the publication process:…”