LeSheng Jin

OWA Generation Function and Some Adjustment Methods for OWA Operators With Application

We propose the concept of ordered weighted averaging (OWA) generation function with some properties, illustrative examples, and usages. A number of new properties of OWA operators and relations between some well-known OWA operators are proposed and proved using OWA Generation Functions. We discuss some orness/andness adjustment methods for a predetermined OWA operator. A practical application about investment prediction problem is given with detailed illustration and analysis, which can show the advantages of the adjustment methods proposed in this paper. In particular, the concept consistent adjustment matrix is proposed and the interests and advantages of it can be shown by its special properties.

Some properties and representation methods for Ordered Weighted Averaging operators

This study demonstrates or proposes some new properties and representation methods for Ordered Weighted Averaging (OWA) operators. The interweaving representation allows some well-known OWA operators to be decomposed into two other well-known OWA operators. A theorem is proposed for determining the relations between OWA operators with respect to their degree of orness/andness. We also provide a complex iteration method for well-known OWA operators, as well as some new generation methods and possible adjustment methods for well-known Centered OWA operators. Furthermore, we investigate some new methods for generating Step OWA and orlike/andlike window OWA operators, where these methods are accurate in terms of their orness/andness degree. We also demonstrate two interesting and useful properties of OWA operators, i.e., Stage OWA and Dew OWA, and one of their applications.

On Obtaining Piled OWA Operators

In this study, we propose the concept of piled ordered weighted averaging (OWA) operators, which generalize the centered OWA operators and also connect the step OWA operators with the Hurwicz OWA operators with given the orness degree. We propose a controllable algorithm to generate the family of piled OWA operators depending on their predefined three parameters: orness degree, step‐like or Hurwicz‐like degree, and the numbers of “supporting” vectors. By these preferences, we can generate infinite more piled OWA operators with miscellaneous forms, and each of them is similar to the well‐known binomial OWA operator, which is very useful but only has one form corresponding to one given orness degree.

Discrete and continuous recursive forms of OWA operators

Abstract We firstly present an evaluation problem for online shop based on gradually increasing number of inputs. Then we propose a model using Recursive OWA operator with constant orness/andness grade involved. Next, we analyze properties of discrete Recursive OWA operators, show their relationship with Pascal Triangle and further generalize this relationship to Γ function. For the continuous case, we propose a concept of self-similar ordered weighting functions (OWF) and analyze some properties of OWF. Using these concepts, we present the recursive aggregation method of continuous arguments under continuous OWF. We show a relationship of OWF with the Regular Increasing (RIM) quantifier. Furthermore, based on an isomorphism relation between discrete and continuous recursive OWA operators, Left Recursive OWA can be seen as the discrete form of continuous OWF.

Vector t-Norms With Applications

Some basic t-norms defined on [0, 1] are well known in many study areas and applications. However, more general extension of them into vector forms can be used in a lot of new decision-making realms. In this study, we first define preference vector on a linearly ordered set, which includes different special vectors that are mathematically equivalent but with different application backgrounds and practical meanings. As a reasoning rule, we provide a merging method for more than two preference vectors to be aggregated into a finally resultant preference vector. The merging method is based on a special vector value function, which can be seen as a reasonable counterpart of product t-norm, f(x, y) = xy (x and y belong to [0, 1]). In addition, we use bilinear frame to define corresponding four types of basic bilinear vector t-norms, which are just counterparts of basic t-norms from many aspects. Mathematically, preference vectors are related to decreasing matrices, and we find the general entry relation for the decreasing matrices, by which we prove that a decreasing matrix is commutative and closed under matrix multiplication. Thus, we finally present the definition of preference multiplication commutative monoid, which is equivalent to product bilinear vector t-norm. We also show illustrative examples and applications of some results.

Aggregation functions and capacities

Abstract Inspired by earlier results of Bayes and Benvenuti et al. [3] , we introduce and study some construction methods and transformations for capacities. First we introduce constructions of capacities based on n-ary aggregation functions and implications from fuzzy set theory, parameterized by vectors x ∈ [ 0 , 1 ] n . Later, implication based transforms of capacities, parameterized by subsets B ⊆ { 1 , 2 , . . . , n } , are given, exemplified and discussed.

Certainty aggregation and the certainty fuzzy measures

Aggregation functions are mostly used in decision‐making situations that require information fusion in a meaningful manner. The main purpose of aggregation is to turn a group of input data into a single and comprehensive one. However, in real decision‐making and system evaluation problems, the decision maker may exhibit only some amount of certainty in her decision inputs. In this study, we show how to aggregate these certainty degrees assigned to a group of inputs in an intuitive and reasonable manner. One of the interesting aspects of the problem is that the value aggregation is independent of their certainty degrees while the certainty aggregation essentially depends on both the input values and the value aggregation function. The construction of the aggregation function gives rise to a fuzzy measure that satisfies some very interesting properties. The technique presented here has wide range of applications.

The Metric Space of Ordered Weighted Average Operators with Distance Based on Accumulated Entries

Ordered weighted average (OWA) operators with their weighting vectors are very important in many applications. We show that directly taking Minkowski distances (including Manhattan distance and Euclidean distance) as the distances for any two OWA operator is not reasonable. In this study, we propose the standard distance measures for any two OWA operators and then propose a standard metric space for the set of all n‐dimension OWA operators. We analyze and discuss some properties of the introduced OWA metric and further propose a metric space of Choquet integrals represented by the underlying fuzzy measures. Some applications in decision making of OWA distances are also presented in this study.

On Some Properties and Comparative Analysis for Different OWA Monoids

We study the properties of OWA multiplication monoid. By introducing and‐accumulation vectors of OWA operators, we consider the set of all n‐dimensional OWA operators as a lattice. Then, we analyze some monotonicity properties of OWA operators based on an ordering induced by and‐accumulation vectors. We also show that the lattice‐theoretical operations are a kind of counterpart of the OWA multiplication monoid (and its dual, additive monoid). An example of using the OWA multiplication monoid and the lattice‐theoretical structure in decision making problem is provided.

Cognitive Integrals With Its Generalized and Adapted Forms

Motivated by some cognition styles, this study first proposes a new type of preaggregation functions called cognitive integrals with its generalized forms. Rather than being affected only by selected capacity, generalized cognitive integrals consider other two parameters, the cognitive strength and the involved semicopula. Our main focus is on cognitive strength, by which the integrals values will be monotonically decreasing with respect to our cognitive strength. After some appropriated adaptations, we later propose the concept of adapted cognitive integrals with two equivalent forms of itself. Not only being a type of the preaggregation functions, we prove that adapted cognitive integrals are indeed one new type of aggregation functions, still equipped with the two new parameters like in cognitive integrals.