Concept Of Interval-valued Fuzzy Set Research Articles

Interval-Valued Topology on Soft Sets

In this paper, we study the concept of interval-valued fuzzy set on the family SSX,E of all soft sets over X with the set of parameters E and examine its basic properties. Later, we define the concept of interval-valued fuzzy topology (cotopology) τ on SSX,E. We obtain that each interval-valued fuzzy topology is a descending family of soft topologies. In addition, we study some topological structures such as interval-valued fuzzy neighborhood system of a soft point, base and subbase of τ and investigate some relationships among them. Finally, we give some concepts such as direct sum, open mapping and continuous mapping and consider connections between them. A few examples support the presented results.

Decision-making in selecting reverse logistics alternative using interval-valued fuzzy sets combined with VIKOR approach

Reverse logistics has become a strong strategic tool in today’s turbulent marketplace. Recently many companies have been found adapting reverse logistics strategies in order to achieve competitive advantage in global business by solving environmental problems as well as by reducing production costs. The growing need for the proper implication of reverse logistics strategies in the contemporary company has now been well understood. However, the managerial-decision regarding selection of an appropriate reverse manufacturing alternative has always been a key strategic consideration of any product recovery system. Such decision-making problems are basically complicated, multidimensional, and unstructured due to uncertainty in environment and imprecise-vague information regarding time, quantity and quality of returns, etc. Fuzzy decision-modeling offers an alternative framework to deal with such kinds of reverse logistics system complicacies and to determine suitable decision strategies for best alternative selection for reprocessing. In this paper, an expert decision modeling tool which utilises concept of Interval-Valued Fuzzy Sets (IVFS) in combination with VIKOR method has been developed and implemented in a real case study. The proposed model facilitates in designing effective product recovery policy depending on various criteria-attributes.

Interval-valued Fuzzy Ideals and Bi-ideals of a Semigroup

We apply the concept of interval-valued fuzzy sets to theory of semigroups. We give some properties of interval-valued fuzzy ideals and interval-valued fuzzy bi-ideals, and characterize which is left [right] simple, left [right] duo and a semilattice of left [right] simple semigroups or another type of semigroups in terms of interval-valued fuzzy ideals and intervalvalued fuzzy bi-ideals.

A soft computing method of performance evaluation with MCDM based on interval-valued fuzzy numbers

This study presented a new performance evaluation method for tackling fuzzy multicriteria decision-making (MCDM) problems based on combining VIKOR and interval-valued fuzzy sets. The performance evaluation problem often exists in complex administrative processes in which multiple evaluation criteria, subjective/objective assessments and fuzzy conditions have to be taken into consideration simultaneously in management. Here, the subjective, imprecise, inexact and uncertain evaluation processes are modeled as fuzzy numbers by means of linguistic terms, as fuzzy theory can provide an appropriate tool to deal with such uncertainties. However, the presentation of linguistic expressions in the form of ordinary fuzzy sets is not clear enough [15,21]. Interval-valued fuzzy sets can provide more flexibility [4,14] to represent the imprecise/vague information that results, and it can also provide a more accurate modeling. This paper presents the interval-valued fuzzy VIKOR, which aims to solve MCDM problems in which the weights and performances of criteria are unequal by using the concepts of interval-valued fuzzy sets. A case study for evaluating the performances of three major intercity bus companies from an intercity public transport system is conducted to illustrate the effectiveness of the method.

Improving the performance of fuzzy rule-based classification systems with interval-valued fuzzy sets and genetic amplitude tuning

Among the computational intelligence techniques employed to solve classification problems, Fuzzy Rule-Based Classification Systems (FRBCSs) are a popular tool because of their interpretable models based on linguistic variables, which are easier to understand for the experts or end-users. The aim of this paper is to enhance the performance of FRBCSs by extending the Knowledge Base with the application of the concept of Interval-Valued Fuzzy Sets (IVFSs). We consider a post-processing genetic tuning step that adjusts the amplitude of the upper bound of the IVFS to contextualize the fuzzy partitions and to obtain a most accurate solution to the problem. We analyze the goodness of this approach using two basic and well-known fuzzy rule learning algorithms, the Chi et al.’s method and the fuzzy hybrid genetics-based machine learning algorithm. We show the improvement achieved by this model through an extensive empirical study with a large collection of data-sets.

Interval-valued [formula omitted]-fuzzy K-algebras

The notion of interval-valued fuzzy sets was first introduced by Zadeh in 1975 as a generalization of fuzzy sets. Using the concept of interval-valued fuzzy sets, we introduce a new kind of generalized fuzzy subalgebra of a K-algebra called, an interval-valued ( α , β ) -fuzzy subalgebra. We present some interesting properties of an interval-valued ( α , β ) -fuzzy subalgebra of a K-algebra. Some characterization theorems of the interval-valued ( ∈ , ∈ ∨ q ) -fuzzy subalgebra are established. Next we investigate the properties of interval-valued fuzzy subalgebras with thresholds. Finally we present characterization theorems of implication based interval-valued fuzzy subalgebras.