Prioritized multi-criteria decision making based on preference relations

A fuzzy multi-criteria decision-making model by associating technique for order preference by similarity to ideal solution with relative preference relation

A famous multi-criteria decision-making(MCDM) method called technique for order preference by similarity to ideal solution(TOPSIS) was often fuzzy generalized into fuzzy multi-criteria decision-making(fuzzy MCDM). In generalizing TOPSIS, fuzzy preference relation on interval-valued fuzzy numbers(IVFNs) is to find the ideal solution and anti-ideal solution for reserving lots of information. Usually, the work is complicated on computation. Practically, IVFNs is more difficult than others. In order to resolve the above tie for the decision-making problem about airport performance evaluation, we utilize TOPSIS and relative preference relation(RPR) in fuzzy MCDM. By combining RPR with TOPSIS, the performance evaluating problem of airports could be easily solved.

The breaking of additively reciprocal property of fuzzy preference relations and its implication to decision making under uncertainty

On the basis of geometric consistency (GCI) of multiplicative preference relations and the transformation relation between multiplicative preference relations and fuzzy preference relation, inconsistency measure of fuzzy preference relation and the thresholds associated with it are studied. A new satisfactory consistency concept of fuzzy preference relation is defined. For a fuzzy preference relation, which does not possess satisfactory consistency, an improving consistency approach is provided. Then, programming models for estimating interval priority weights from fuzzy preference relations is established. Finally, an example is given to illustrate the validity and practicality of the proposed methods.

This is a first approach to the study of the connection between fuzzy preference relations and fuzzy choice functions. In particular we depart from a fuzzy preference relation and we study the conditions it must satisfy in order to get a fuzzy choice function from it. We are particulary interested in one function: G-rationalization. We discuss the relevance of the completeness condition on the departing preference relation. We prove that not every non-complete fuzzy preference relation leads to a choice function.Keywordsfuzzy preference relation G-rational choice functioncomplete fuzzy relation

Some issues on consistency of fuzzy preference relations

Study on Assessment Level of Experts based on Difference Preference Information

Although medical waste usually accounts for a small fraction of urban municipal waste, its proper disposal has been a challenging issue as it often contains infectious, radioactive, or hazardous waste. This article proposes a two-level hierarchical multicriteria decision model to address medical waste disposal method selection (MWDMS), where disposal methods are assessed against different criteria as intuitionistic fuzzy preference relations and criteria weights are furnished as real values. This paper first introduces new operations for a special class of intuitionistic fuzzy values, whose membership and non-membership information is cross ratio based ]0, 1[-values. New score and accuracy functions are defined in order to develop a comparison approach for ]0, 1[-valued intuitionistic fuzzy numbers. A weighted geometric operator is then put forward to aggregate a collection of ]0, 1[-valued intuitionistic fuzzy values. Similar to Saaty’s 1–9 scale, this paper proposes a cross-ratio-based bipolar 0.1–0.9 scale to characterize pairwise comparison results. Subsequently, a two-level hierarchical structure is formulated to handle multicriteria decision problems with intuitionistic preference relations. Finally, the proposed decision framework is applied to MWDMS to illustrate its feasibility and effectiveness.

Multi criteria decision making (MCDM) and group decision making (GDM) are two well practiced approaches to solve decision making problems. Group decision making combines opinions from Decision makers (DMs) into a coherent group decision. The aim of this paper is to develop a new fuzzy group decision making algorithm and apply it to a real-world groundwater development problem to select the most preferred alternative. Five decision makers (DMs) are selected to express their judgments about relative importance of 3 criteria (water pumped, cost, and risk) and have given their preferences as ordinal preferences, utility values, fuzzy preference relations and multiplicative preference relations. Decision makers' opinions are aggregated based on a fuzzy group decision making. Ordered weighted averaging (OWA) operator has been used to aggregate decision makers' opinions. Consensus measure is also defined to evaluate convergence between group and individual opinions. The outcomes of the proposed algorithm show that proposed fuzzy group decision making process is a relevant approach to aggregate the individual expert's opinion and is a desirable tool to reach consensus among DMs.

The ordinal consistency of a fuzzy preference relation

In fuzzy decision problems, the ordering of fuzzy numbers is the basic problem. The fuzzy preference relation is the reasonable representation of preference relations by a fuzzy membership function. This paper studies Nakamura’s and Kołodziejczyk’s preference relations. Eight cases, each representing different levels of overlap between two triangular fuzzy numbers are considered. We analyze the ranking behaviors of all possible combinations of the decomposition and intersection of two fuzzy numbers through eight extensive test cases. The results indicate that decomposition and intersection can affect the fuzzy preference relations, and thereby the final ranking of fuzzy numbers.

Additive consistent interval-valued Atanassov intuitionistic fuzzy preference relation and likelihood comparison algorithm based group decision making

This paper reflects the results of research analyzing models of multi-attribute decision-making based on fuzzy preference relations. Questions of constructing the corresponding multi-attribute models to deal with quantitative information concomitantly with qualitative information based on experts’ knowledge are considered. Human preferences may be represented within the fuzzy preference relations and by applying diverse other preference formats. Considering this, so-called transformation functions reduce any preference format to fuzzy preference relations. This paper’s results can be applied independently or as part of a general approach to solving a wide class of problems with fuzzy coefficients, as well as within the framework of a general scheme of multi-criteria decision-making under conditions of uncertainty. The considered techniques for fuzzy preference modeling are directed at assessing, comparing, choosing, prioritizing, and/or ordering alternatives. These techniques have served to develop a computing system for multi-attribute decision-making. It has been implemented in the C# programming language, utilizing the “.NET” framework. The computing system allows one to represent decision-makers’ preferences in one of five preference formats. These formats and quantitative estimates are reduced to nonreciprocal fuzzy preference relations, providing homogeneous preference information for decision procedures. This paper’s results have a general character and were applied to analyze power engineering problems.

Measuring the success possibility of implementing advanced manufacturing technology by utilizing the consistent fuzzy preference relations

Normalizing rank aggregation method for priority of a fuzzy preference relation and its effectiveness