Theory of fuzzy integrals and its applications

We first look at some nonstandard fuzzy sets, intuitionistic, and interval-valued fuzzy sets. We note both these allow a degree of commitment of less then one in assigning membership. We look at the formulation of the negation for these sets and show its expression in terms of the standard complement with respect to the degree of commitment. We then consider the complement operation. We describe its properties and look at alternative definitions of complement operations. We then focus on the Pythagorean complement. Using this complement, we introduce a class of nonstandard Pythagorean fuzzy subsets whose membership grades are pairs, (a, b) satisfying the requirement a
 2
 + b
 2
 ≤ 1. We introduce a variety of aggregation operations for these Pythagorean fuzzy subsets. We then look at multicriteria decision making in the case where the criteria satisfaction are expressed using Pythagorean membership grades. The issue of having to choose a best alternative in multicriteria decision making leads us to consider the problem of comparing Pythagorean membership grades.

Pythagorean membership grades in multicriteria decision making

Distance and similarity measures for hesitant fuzzy sets

The notion of fuzziness as defined in this paper relates to situations in which the source of imprecision is not a random variable or a stochastic process, but rather a class or classes which do not possess sharply defined boundaries, e.g., the “class of bald men,” or the “class of numbers which are much greater than 10,” or the “class of adaptive systems,” etc. A basic concept which makes it possible to treat fuzziness in a quantitative manner is that of a fuzzy set, that is, a class in which there may be grades of membership intermediate between full membership and non-membership. Thus, a fuzzy set is characterized by a membership function which assigns to each object its grade of membership (a number lying between 0 and 1) in the fuzzy set. After a review of some of the relevant properties of fuzzy sets, the notions of a fuzzy system and a fuzzy class of systems are introduced and briefly analyzed. The paper closes with a section dealing with optimization under fuzzy constraints in which an approach to...

Fuzzy sets and systems

Despite the importance of decision-making (DM) techniques for construction of effective decision models for supplier selection, there is a lack of a systematic literature review for it. This paper provides a systematic literature review on articles published from 2008 to 2012 on the application of DM techniques for supplier selection. By using a methodological decision analysis in four aspects including decision problems, decision makers, decision environments, and decision approaches, we finally selected and reviewed 123 journal articles. To examine the research trend on uncertain supplier selection, these articles are roughly classified into seven categories according to different uncertainties. Under such classification framework, 26 DM techniques are identified from three perspectives: (1) Multicriteria decision making (MCDM) techniques, (2) Mathematical programming (MP) techniques, and (3) Artificial intelligence (AI) techniques. We reviewed each of the 26 techniques and analyzed the means of integrating these techniques for supplier selection. Our survey provides the recommendation for future research and facilitates knowledge accumulation and creation concerning the application of DM techniques in supplier selection.

Application of decision-making techniques in supplier selection: A systematic review of literature

An approach to manipulate interactive attribute weights strategically with its application in university rankings

Group decision making using bilateral agreement matrix

A restaurant recommendation approach with the contextual information

Data envelopment analysis (DEA) is a non-parametric method for measuring the efficiencies of decision-making units (DMUs) by using a set of inputs and a set of outputs. However, traditional DEA models always assume that the inputs or outputs are independent of each other, which is unrealistic in practical problems. To reflect the interactions between inputs or outputs, the Choquet integral is employed in DEA models. The traditional DEA models are usually used to find some specific input and output weights of DMUs to optimize the efficiency score of DMUs, but the corresponding input and output weights for the optimal efficiency score of a DMU may not be distributed symmetrically, that is to say, the space of weights may be different for different DMUs. Instead of finding the self-efficiency score and the cross-efficiency score of a DMU in traditional DEA models based on some specific input and output weights, stochastic multicriteria acceptability analysis is used to explore the input or output evaluation space and weight space to calculate the Choquet-integral-based acceptability indices of DMUs. The proposed method considers the interactions between inputs or outputs, which can make more DMUs efficient and can also measure the acceptability of a DMU to become an efficient one by exploring the supporting information space. Examples are given to illustrate the proposed method.

https://www.mdpi.com/2073-8994/14/4/642/pdf?version=1648031698

Choquet-Integral-Based Data Envelopment Analysis with Stochastic Multicriteria Acceptability Analysis

Preference relations are powerful techniques to ex- press the preferences over alternatives (or criteria) and mainly fall into two categories: fuzzy preference relations (also called recip- rocal preference relations) and multiplicative preference relations. For a pair of alternatives, a fuzzy preference relation only gives the degree that an alternative is prior to another; thus, the intuitionistic fuzzy preference relation is introduced by adding the degree that an alternative is not prior to another, which can describe the pref- erences over two alternatives more comprehensively. However, the intuitionistic fuzzy preference uses the symmetrical scale to express the decision makers' preference relations, which are inconsistent with our intuition in some situations. If we use the unsymmetrical scale to express the preferences about two alternatives instead of the symmetrical scale in intuitionistic fuzzy preference relation, then a new concept is introduced, which we call the intuitionis- tic multiplicative preference relation reflecting our intuition more objectively. In this paper, we study the aggregation of intuition- istic multiplicative preference information, propose some aggre- gation techniques, investigate their properties, and apply them to decision making based on intuitionistic multiplicative preference relations.

Meimei Xia

Papers

An approach to manipulate interactive attribute weights strategically with its application in university rankings

Group decision making using bilateral agreement matrix

A restaurant recommendation approach with the contextual information

Choquet-Integral-Based Data Envelopment Analysis with Stochastic Multicriteria Acceptability Analysis

Preference Relations Based on Intuitionistic