Mathematical programming methods for consistency and consensus in group decision making with intuitionistic fuzzy preference relations

Considering the deficiency of existing individual decision-making method with intuitionistic fuzzy preference relation (IFPR), in this manuscript, based on multiplicative consistency of IFPRs, we propose a new individual decision- making method for solving the individual decision-making problems with an incomplete IFPR. First, a new multiplicative consistency index of IFPRs is introduced and then an acceptable consistency is defined. Then, an optimization model is constructed by maximizing the consistency level of the obtained complete IFPR to supplement the default values in an incomplete IFPR. Moreover, other two optimization models are constructed for obtaining the completely and acceptably multiplicative consistent IFPRs, respectively. Finally, a new individual decision-marking method with an incomplete IFPR is developed, and the effectiveness of which is to be demonstrated by an example.

Optimization-based group decision making using interval-valued intuitionistic fuzzy preference relations

An enhanced consensus reaching process in group decision making with intuitionistic fuzzy preference relations

Group decision-making (GDM) is crucial in various components of graph theory, management science, and operations research. In particular, in an intuitionistic fuzzy group decision-making problem, the experts communicate their preferences using intuitionistic fuzzy preference relations (IFPRs). This approach is a way that decision-makers rank or select the most desirable alternatives by gathering criteria-based information to estimate the best alternatives using a wider range of knowledge and experience. This article proposes a new statistical measure in a fuzzy environment when the data is ambiguous or unreliable to solve a decision-making problem. This study uses the variation coefficient measure combined with intuitionistic fuzzy graphs (IFG) and Laplacian energy (LE) to solve a GDM problem that utilizes intuitionistic fuzzy preference relations (IFPRs) to select a reliable alliance partner. Initially, the Laplacian energy determines the weight of individual standards, and the obtained weight average further estimates the overall criterion weight vector. We establish the authority criteria weights using the variation coefficient measure and then ultimately rank the alternatives for each criterion using the same measure. We examine four distinct companies Alpha, Beta, Delta, and Zeta to conduct a realistic GDM to choose which alliance partner would be ideal. We successfully implemented the suggested technique, determining that Alpha satisfies company standards and is ranked first among other companies. Moreover, this technique is useful for all kinds of Intuitionistic fuzzy group decision-making problems to select optimal ones.

Szmidt and Kacprzyk (Lecture Notes in Artificial Intelligence 3070:388---393, 2004a) introduced a similarity measure, which takes into account not only a pure distance between intuitionistic fuzzy sets but also examines if the compared values are more similar or more dissimilar to each other. By analyzing this similarity measure, we find it somewhat inconvenient in some cases, and thus we develop a new similarity measure between intuitionistic fuzzy sets. Then we apply the developed similarity measure for consensus analysis in group decision making based on intuitionistic fuzzy preference relations, and finally further extend it to the interval-valued intuitionistic fuzzy set theory.

The frame of intuitionistic fuzzy preference relations (IFPRs) is an effective tool of representing pairwise preference order based group voting information. However, existing intuitionistic fuzzy translations of Tanino’s additive consistency and previous methods of acquiring utility vectors from IFPRs are often unable to achieve a satisfactory solution for hierarchical multi-criteria decision making (HMCDM) with IFPRs. This study analyzes existing notions of additively consistent IFPRs (ACIFPRs) and shows their shortages. A novel intuitionistic fuzzy translation of Tanino’s additive consistency is developed and an index computational formula is provided to measure additive inconsistency of IFPRs. A new approach is offered to generate ACIFPRs from vectors with intuitionistic fuzzy elements and a frame is put forward to normalize intuitionistic fuzzy vectors. Subsequently, a closed-form solution based method is presented to secure normalized intuitionistic fuzzy utility vectors from ACIFPRs and a linear program is built to acquire an optimal and normalized intuitionistic fuzzy utility vector from any IFPR. An approach is proposed to tackle HMCDM problems with pairwise preference order based group voting information. The reasonability and performance of the models developed are validated by an illustrative example and a case study about outstanding teacher recommendation based on large-scale group votes on teaching satisfaction.

The intuitionistic fuzzy preference relation (IFPR), whose elements are intuitionistic fuzzy values (IFVs), is more powerful than the traditional multiplicative preference relation and the fuzzy preference relation in expressing comprehensive preference information of a decision maker. The aim of this paper is to investigate a new approach to derive the priority weights from an IFPR. To do so, we give a new definition of multiplicative consistent IFPR, which is based on the membership and nonmembership degrees of the intuitionistic fuzzy judgments. After that, a formula, which involves the underlying intuitionistic fuzzy weights of the IFPR, is proposed to construct such a multiplicative consistent IFPR. Based on the formula, some fractional programming models are built to generate the intuitionistic fuzzy priority weighting vector of the IFPR. Several numerical examples are given to illustrate the validity and applicability of the proposed method.

A graph based group decision making approach with intuitionistic fuzzy preference relations

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

Compatibility measures and consensus models for group decision making with intuitionistic multiplicative preference relations

A group decision making method for sustainable design using intuitionistic fuzzy preference relations in the conceptual design stage

Deriving the priority vectors of the alternatives from preference relations is an interesting research topic for group decision making with preference information. This paper uses an example to show that the ranking or the optimal alternative could not always be derived from the existing additively consistent intuitionistic fuzzy preference relations. Thus, we provide novel additively consistent intuitionistic fuzzy preference relations and characterize them with Tanino’s normalized (T-normalized) intuitionistic fuzzy priority vectors. Then, we propose some methods to check and achieve the T-normalization, acceptably additive consistency and consensus of the intuitionistic fuzzy preference relations in group decision making using the local, individual and optimal collective intuitionistic fuzzy priority vectors, respectively. We also give some examples to show how the proposed models work and make comparisons with the existing methods to demonstrate the advantages of the proposed methods.

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

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.

15 - Modified neutrosophic fuzzy optimization model for optimal closed-loop supply chain management under uncertainty