Iranian journal of fuzzy systems
Volume:20 Issue: 4, Jul-Aug 2023

In this work, we examine several widely-used interval-valued fuzzy logical connectives with respect to admissible orders. We are concerned with interval-valued fuzzy negations, automorphisms, fuzzy implications and aggregation functions with respect to $K_{\alpha,\beta}$ orders and arbitrary intervals on $L([0, 1])$. We also make a discussion of width-preserving interval-valued fuzzy equivalence functions and fuzzy dissimilarity functions with respect to arbitrary admissible orders and the intervals with the same width on $L([0, 1])$. Then we bring some approaches to constructing the proposed interval-valued fuzzy logical connectives with respect to admissible orders.

Fuzzy soft set is a general mathematical tool to deal with uncertain and fuzziness information. But inadequacy lies in which cannot express various uncertainty in a more natural and accurate manner, due to the reason of adopting the fuzzy membership which restricts to [0, 1]. As a result, it merely concerns non-negative fuzzy belongingness of elements, so as to be incapable of capturing the conflict information that supporting, neutral and opposing scenarios regarding belongingness of elements in a set to taken into account. To overcome the limitation, this paper extends fuzzy soft set to bilateral fuzzy soft set (BFSS), which considers both non-negative and negative sides for fuzzy membership and normalizes the range to [−1, 1]. Then defines some basic operations on BFSS, as well as a detail study of relevant properties. In order to eliminate redundant parameters and draw the essential part of BFSS, the parameters reduction on BFSS is also investigated, and the significance of parameters is introduced accordingly. On this basis, an assessment approach for multi-criteria multi-person decision making under conflict information, together with the algorithm for implementation is presented. Finally, a typical numerical example regarding voting demonstrates the validity and feasibility of the proposed method.

The primary aim of the notion of consistency fuzzy set (CFS) is to model the uncertain information given in a fuzzy multi environment and so to obtain meaningful data from the fuzzy multi-sets and to present this data in a compact form via some statistical tools. The data collected by fuzzy multi-sets are processed via CFSs and a sort of data science is done in the fuzzy environment. In this paper, we present a cross entropy measure and a sine entropy measure between CFSs to contribute to processing and modeling of data obtained by statistical methods. Also, we construct a new VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method by using CFSs that is called CF-VIKOR to carry out decision process in multi-criteria decision making. We apply the proposed method to a multi-criteria decision making problem from the literature and give a comparison analysis between the obtained results and the existing results in literature. Finally, by using the Spearman's and Kendall's rank correlation coefficient measures and Wang and Triantaphyllou validity test we show the efficiency and rationality of the proposed CF-VIKOR method.

This paper investigates a novel distributed fuzzy adaptive iterative learning control protocol of exact consensus for second-order unknown nonlinear strict-feedback multi-agent systems with partially unknown time-varying control directions. Fuzzy logic system estimates the unknown nonlinear dynamics of each agent. Based on Nussbaum function, the control protocols of all follower agents with partially unknown virtual and actual control directions are designed by the backstepping method. The proposed protocol guarantees that the output of every follower agent could exactly track the desired output trajectory on a finite time interval. As an extension, the formation control results can also be solved. Finally, two simulation examples prove that the proposed control scheme is effective and rigorous.

The ordinal sum construction is an important way to generate new triangular norms (t-norms for short) on real unit interval from existing ones. Saminger extended the ordinal sum construction of t-norms to bounded lattices in a direct way and proved that, except for very special cases the ordinal sum of t-norms on bounded lattices may be not a t-norm. To ensure the ordinal sum of t-norms is always a t-norm, several modified ordinal sum of t-norms have been developed. This note reviews several such constructions. As a byproduct, we point out that some recent results concerning ordinal sum of t-norms by A\c{s}ici can be seen as corollaries of these construction.

Binary option is an exotic option which is popular in Over the Counter market for hedging and speculation. According to their different payoff, there are two types of binary options, that is, cash-or-nothing and asset-or-nothing option. This paper investigates the fuzzy financial market based on the exponential Ornstein-Uhlenbeck model and derives binary option pricing formulas. In order to better understand the mathematical properties of these formulas, we give a few numerical examples and some figures to illustrate the changes of binary option price with different parameters when others are fixed.

In this work, we supplement two methods to construct a 2-uninorm on a bounded lattice using two uninorms, and illustrate that the method proposed by Ertugrul is a special case of the new ones. Furthermore, the relationships between 2-uninorms on bounded lattices obtained by all existing methods are showed at the end of this work.

Intuitionistic fuzzy set (IFS) is a reliable device for resolving uncertainty and haziness encountered in decision-making process. In most cases, the significance of IFSs are explored based on correlation measures in myriad of areas like in engineering, image segmentation, pattern recognition, diagnosticanalysis, etc. Some methods for computing intuitionistic fuzzy correlation coefficient (IFCC) have been investigated, however with some inadequacies. In this present work, a new method of IFCC is developed to correct the drawbacks in some existing techniques in terms of mathematical presentation and the exclusion of the hesitation parameter to enhance reasonable output. A comparative analysis is presented to ascertain the edge of the new technique over some similarapproaches. In addition, the new correlation coefficient technique is applied to discuss some pattern recognition problems. This new IFCC method could be investigated based on spherical fuzzy data, q-rung orthopair fuzzy data, and picture fuzzy data.

Modularity equation plays an important role in the eld of information fusion, which helps to selectaggregation functions and reduce the failure rate in the process of aggregation. Based on this, we focus on the study of modularity equation between overlap (grouping) functions and semi-t-operators. We give the solutions of this equation between overlap (grouping) functions and semi-t-operators with continuous pseudo-t-norm or continuous pseudo-t-conorm in the corresponding cases.

This paper characterizes a uninorm distributive over a noncontinuous t-(co)norm, where the uninorm is locally internal on the boundary. Firstly, when the uninorm is disjunctive, the necessary conditions (resp. the sufficient conditions) for a uninorm distributive over a noncontinuous t-norm are analyzed under the certain condition. Secondly, the distributivity of a conjunctive uninorm over a noncontinuous t-conorm is characterized by duality. In particular, this paper is related to the open question recalled by Klement in the Linz2000 closing session, which provides the noncontinuous solutions of that question.

The concept of a fuzzy number is expanded to the case of a finite carrier set of partially ordered elements; the set is a lattice, and the membership function of such an expansion also takes values in a lattice. Zadeh's extension principle for determining the degree of membership of a function of fuzzy numbers is changed for this expansion. An analogue of the concept of a mean value is also suggested. The use of partially ordered values in cognitive maps with multiple expert assessments is considered.

In this study, we focus on bivariate transformations of trivariate quasi-copulas. We characterize necessary and sufficient conditions of transformations that can be written in the form of compositions between two quasi-copulas and a quadratic polynomial function. The conditions only depend on the coefficients of the quadratic polynomial. The set of these coefficients is convex with linear-section boundary and it lies on the seven-dimensional Euclidean space. All extreme points of this set have been characterized via CAS and can be used to construct quasi-copulas. Construction examples are also given.